IBPS PO Prelims – Quantitative Aptitude (Simplification)
Q1. What will come in place of the question mark (?) in the following question? प्रश्न 1. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
140% of 320 - ? % of 300 = 25² - 441
(A) 80
(B) 90
(C) 84
(D) 96
(E) 75
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 90
Explanation (व्याख्या):
1.40 * 320 - (?/100) * 300 = 625 - 441
448 - 3 * ? = 184
3 * ? = 448 - 184
3 * ? = 264
? = 264 / 3
? = 88
Wait, calculation error. Let's recheck.
140% of 320 = 1.4 * 320 = 448
25² = 625
√441 = 21, but it is 441, not √441.
Okay, let's re-read the question. It seems I made an error in the question creation. Let's correct the question to:
140% of 320 - ? % of 300 = 26² - 440
1.4 * 320 - ? * 3 = 676 - 440
448 - 3? = 236
3? = 448 - 236
3? = 212 (Not divisible)
Let's try another correction for a clean answer.
Original: `140% of 320 - ? % of 300 = 25² - 441`
This must be a typo in the question itself. Let's assume `?` is the answer.
Let's re-solve the first version correctly.
1.4 * 320 - (?/100) * 300 = 625 - 441
448 - 3 * ? = 184
3 * ? = 448 - 184
3 * ? = 264
? = 264 / 3 = 88
So the correct answer is 88. Let's change an option.
Let's assume the question was: 140% of 320 - ? % of 200 = 25² - 441
448 - 2 * ? = 184
2 * ? = 264 -> ? = 132. Not good.
Let's modify the question to make 90 the answer.
If ? = 90, then 448 - 90/100 * 300 = 448 - 270 = 178.
So the RHS should be 178. 25² - 441 = 184. Close.
Let's set the question as:
`140% of 320 - ? % of 300 = 178`
448 - 3 * ? = 178
3 * ? = 448 - 178 = 270
? = 90. This works.
Let's change the original question in the HTML.
New Question: `140% of 320 - ? % of 300 = 178`
Solution:
1.40 * 320 - (?/100) * 300 = 178
448 - 3 * ? = 178
3 * ? = 448 - 178
3 * ? = 270
? = 270 / 3
? = 90
Q2. What will come in place of the question mark (?) in the following question? प्रश्न 2. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(√1225 ÷ 7) × 24 - 8 = ?²
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 11
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
(√1225 ÷ 7) × 24 - 8 = ?²
Step 1: Find the square root of 1225.
√1225 = 35
Step 2: Substitute the value back and solve the expression inside the bracket.
(35 ÷ 7) × 24 - 8 = ?²
5 × 24 - 8 = ?²
Step 3: Perform multiplication.
120 - 8 = ?²
Step 4: Perform subtraction.
112 = ?²
Wait, 112 is not a perfect square. Let me recheck.
5 * 24 = 120. 120 - 8 = 112. Correct.
Maybe the question had a typo. Let's adjust it.
Let's make it `(√1225 ÷ 7) × 26 - 8 = ?²`
(35/7) * 26 - 8 = 5 * 26 - 8 = 130 - 8 = 122. No.
Let's make it `(√1225 ÷ 5) × 24 - 8 = ?²`
(35/5) * 24 - 8 = 7 * 24 - 8 = 168 - 8 = 160. No.
Let's change the last number. `(√1225 ÷ 7) × 24 - (-1) = ?²`
5 * 24 + 1 = 121. So ?² = 121, ? = 11.
Let's change the question to: `(√1225 ÷ 7) × 24 + 1 = ?²`
Solution for the new question:
(35 ÷ 7) × 24 + 1 = ?²
5 × 24 + 1 = ?²
120 + 1 = ?²
121 = ?²
? = √121 = 11
Q3. What will come in place of the question mark (?) in the following question? प्रश्न 3. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(2/5) of 215 + (3/4) of 128 = ? + 21
(A) 151
(B) 161
(C) 171
(D) 181
(E) 191
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 161
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
(2/5) × 215 + (3/4) × 128 = ? + 21
Step 1: Calculate the first part.
(2/5) × 215 = 2 × 43 = 86
Step 2: Calculate the second part.
(3/4) × 128 = 3 × 32 = 96
Step 3: Substitute the values back into the equation.
86 + 96 = ? + 21
182 = ? + 21
Step 4: Solve for '?'.
? = 182 - 21
? = 161
Q4. What will come in place of the question mark (?) in the following question? प्रश्न 4. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
3453 + 2785 - 4999 = 1111 - ?
(A) -122
(B) -128
(C) 122
(D) 128
(E) -132
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (A) -122
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
3453 + 2785 - 4999 = 1111 - ?
Step 1: Solve the Left Hand Side (LHS).
3453 + 2785 = 6238
6238 - 4999 = 1239
LHS = 1239
Step 2: Now the equation is:
1239 = 1111 - ?
Step 3: Rearrange to solve for '?'.
? = 1111 - 1239
? = -128.
Wait, my option (A) is -122. Let me recheck the calculation.
3453 + 2785 = 6238. Correct.
6238 - 4999.
6238
- 4999
------
1239. Correct.
1111 - 1239 = -128. Correct.
The correct answer is -128. Let me change option (A) to -128 and (B) to something else.
Let's set (A) as -128 and (B) as -122.
So Correct answer is (A) -128. Let's write the solution for that.
Given equation (दिया गया समीकरण):
3453 + 2785 - 4999 = 1111 - ?
Step 1: Solve the Left Hand Side (LHS).
3453 + 2785 = 6238
6238 - 4999 = 1239
LHS = 1239
Step 2: Now the equation is:
1239 = 1111 - ?
Step 3: Rearrange to solve for '?'.
? = 1111 - 1239
? = -128
Q5. What will come in place of the question mark (?) in the following question? प्रश्न 5. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
√? + 18 = √2704
(A) 1024
(B) 1296
(C) 1156
(D) 900
(E) 784
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 1156
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
√? + 18 = √2704
Step 1: Find the square root of 2704.
We know 50² = 2500. The number ends in 4, so the root ends in 2 or 8.
Let's try 52². 52*52 = 2704.
So, √2704 = 52.
Step 2: Substitute the value back into the equation.
√? + 18 = 52
Step 3: Isolate √?.
√? = 52 - 18
√? = 34
Step 4: Square both sides to find '?'.
? = 34²
? = 1156
Q6. What will come in place of the question mark (?) in the following question? प्रश्न 6. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Q7. What will come in place of the question mark (?) in the following question? प्रश्न 7. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
12² × 5 ÷ 15 - 35 = ? - 90
(A) 88
(B) 95
(C) 103
(D) 108
(E) 93
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (E) 93
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
12² × 5 ÷ 15 - 35 = ? - 90
Step 1: Calculate the square.
144 × 5 ÷ 15 - 35 = ? - 90
Step 2: Apply BODMAS rule (Division and Multiplication from left to right).
144 × (5/15) - 35 = ? - 90
144 × (1/3) - 35 = ? - 90
48 - 35 = ? - 90
Step 3: Perform subtraction.
13 = ? - 90
Step 4: Solve for '?'.
? = 13 + 90
? = 103
Wait, another error.
144 * 5 = 720. 720 / 15 = 48. Correct.
48 - 35 = 13. Correct.
13 = ? - 90.
? = 13 + 90 = 103.
So the correct answer is 103, which is option C. Let's change the intended answer.
OK, C is 103. Let's go with that.
Correct Answer: (C) 103.
Explanation:
Given equation (दिया गया समीकरण):
12² × 5 ÷ 15 - 35 = ? - 90
Step 1: Calculate the square.
144 × 5 ÷ 15 - 35 = ? - 90
Step 2: Apply BODMAS rule. Perform multiplication first.
720 ÷ 15 - 35 = ? - 90
Step 3: Perform division.
48 - 35 = ? - 90
Step 4: Perform subtraction on LHS.
13 = ? - 90
Step 5: Solve for '?'.
? = 13 + 90
? = 103
Q8. What will come in place of the question mark (?) in the following question? प्रश्न 8. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
65% of 240 + ?% of 350 = 331
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 50
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
0.65 × 240 + (?/100) × 350 = 331
Step 1: Calculate 65% of 240.
(65/100) × 240 = (13/20) × 240 = 13 × 12 = 156
Step 2: Substitute the value back.
156 + (?/100) × 350 = 331
156 + 3.5 × ? = 331
Step 3: Isolate the term with '?'.
3.5 × ? = 331 - 156
3.5 × ? = 175
Step 4: Solve for '?'.
? = 175 / 3.5
? = 1750 / 35
? = 50
Q9. What will come in place of the question mark (?) in the following question? प्रश्न 9. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Q10. What will come in place of the question mark (?) in the following question? प्रश्न 10. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
∛5832 + ∛1331 = ? × 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 4
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
∛5832 + ∛1331 = ? × 7
Step 1: Find the cube root of 5832.
The number ends in 2, so its cube root must end in 8.
10³ = 1000, 20³ = 8000. The root is between 10 and 20.
So, ∛5832 = 18.
Step 2: Find the cube root of 1331.
This is a common cube. ∛1331 = 11.
Step 3: Substitute the values back.
18 + 11 = ? × 7
29 = ? × 7
Wait, 29 is not divisible by 7. Let me re-check the cube roots.
18 * 18 * 18 = 324 * 18 = 5832. Correct.
11 * 11 * 11 = 121 * 11 = 1331. Correct.
Sum = 29.
The question has an error. Let's modify it to get a clean answer.
Let's change ∛1331 to ∛3375 which is 15.
New question: ∛5832 + ∛3375 = ? × 7
18 + 15 = ? x 7
33 = ? x 7. Still not divisible.
Let's change the first term. Let it be ∛4096 = 16.
New question: ∛4096 + ∛1331 = ? × 7
16 + 11 = ? × 7
27 = ? × 7. No.
Let's change the multiplier. ? x 3.
New question: ∛5832 + ∛1331 = ? × 3
18 + 11 = ? x 3
29 = ? x 3. No.
Let's make the RHS clean.
If the answer is 4, then LHS should be 28.
So we need two cubes that sum to 28. e.g. 1 + 27.
So, ∛1 + ∛15625. No.
Okay, let's fix the original question `∛5832 + ∛1331 = ? × 7` to get answer 4.
LHS = 18 + 11 = 29. Let's make it 28.
Let's change 1331 to a cube that makes the sum 28. 28 - 18 = 10. Cube of 10 is 1000.
New question: `∛5832 + ∛1000 = ? × 7`
18 + 10 = ? × 7
28 = ? × 7
? = 4. This works.
Solution for the new question: `∛5832 + ∛1000 = ? × 7`
Step 1: ∛5832 = 18
Step 2: ∛1000 = 10
Step 3: 18 + 10 = ? × 7
Step 4: 28 = ? × 7
Step 5: ? = 28 / 7 = 4
Q11. What will come in place of the question mark (?) in the following question? प्रश्न 11. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
4 1/5 × 3 1/3 + ? = 20% of 900
(A) 166
(B) 176
(C) 156
(D) 180
(E) 160
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (A) 166
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
4 1/5 × 3 1/3 + ? = 20% of 900
Step 1: Convert mixed fractions to improper fractions.
4 1/5 = 21/5
3 1/3 = 10/3
Step 2: Calculate the product.
(21/5) × (10/3) = (21/3) × (10/5) = 7 × 2 = 14
Step 3: Calculate the Right Hand Side (RHS).
20% of 900 = (20/100) × 900 = 0.2 × 900 = 180
Step 4: Substitute the values back.
14 + ? = 180
Step 5: Solve for '?'.
? = 180 - 14
? = 166
Q12. What will come in place of the question mark (?) in the following question? प्रश्न 12. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(1250 ÷ 25) × (360 ÷ 45) = ?
(A) 300
(B) 350
(C) 400
(D) 450
(E) 500
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 400
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
(1250 ÷ 25) × (360 ÷ 45) = ?
Step 1: Solve the first bracket.
1250 ÷ 25 = 50
Step 2: Solve the second bracket.
360 ÷ 45 = 8 (Since 45 * 2 = 90, and 90 * 4 = 360, so 45 * 8 = 360)
Step 3: Multiply the results.
? = 50 × 8
? = 400
Q13. What will come in place of the question mark (?) in the following question? प्रश्न 13. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
√576 + √841 = ?²
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 7
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
√576 + √841 = ?²
Step 1: Find the square roots.
√576 = 24
√841 = 29 (since 30²=900, it must be less than 30 and end in 1 or 9)
Step 2: Add the results.
24 + 29 = ?²
53 = ?²
Wait, error. 53 is not a perfect square. Recheck roots.
√576 = 24. Correct.
√841 = 29. Correct.
Sum is 53.
Let's change the question. Let's make the sum 49.
So if one root is 24, the other should be 25. √625.
New question: `√576 + √625 = ?²`
24 + 25 = ?²
49 = ?²
? = 7. This works.
Solution for new question: `√576 + √625 = ?²`
Step 1: √576 = 24
Step 2: √625 = 25
Step 3: 24 + 25 = ?²
Step 4: 49 = ?²
Step 5: ? = √49 = 7
Q14. What will come in place of the question mark (?) in the following question? प्रश्न 14. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
25% of 480 + 20% of ? = 240
(A) 500
(B) 550
(C) 600
(D) 650
(E) 700
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 600
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
(25/100) × 480 + (20/100) × ? = 240
Step 1: Calculate the first part.
(1/4) × 480 = 120
Step 2: Substitute the value back.
120 + (1/5) × ? = 240
Step 3: Isolate the term with '?'.
(1/5) × ? = 240 - 120
(1/5) × ? = 120
Step 4: Solve for '?'.
? = 120 × 5
? = 600
Q15. What will come in place of the question mark (?) in the following question? प्रश्न 15. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(36 × 1.75) + (24 × 3.25) = ?
(A) 131
(B) 141
(C) 151
(D) 161
(E) 171
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 141
Explanation (व्याख्या):
Given equation (दिया गया समीकरण):
(36 × 1.75) + (24 × 3.25) = ?
Step 1: Calculate the first product.
1.75 can be written as 7/4.
36 × (7/4) = 9 × 7 = 63
Step 2: Calculate the second product.
3.25 can be written as 13/4.
24 × (13/4) = 6 × 13 = 78
Step 3: Add the results.
? = 63 + 78
? = 141
Step 1: Find √7744
90² = 8100. So root is less than 90. Ends in 4, so root ends in 2 or 8.
Try 88. 88² = (90-2)² = 8100 - 360 + 4 = 7744.
So, √7744 = 88.
Step 2: Solve the expression.
(88 × 66) ÷ (28 + 19) = ?
(88 × 66) ÷ 47 = ?
5808 ÷ 47 = ?
Wait, 5808 is not divisible by 47. Let me re-read the question.
Maybe the divisor was `28+18` = 46.
(88*66)/46 = (44*66)/23. No.
Maybe the divisor was `22+12` = 34.
Maybe `(√7744 * 66) / (22+11)`.
(88 * 66) / 33 = 88 * 2 = 176.
Let's make it so the denominator is 44. `(22+22)`
(88 * 66) / 44 = 2 * 66 = 132. This is option C.
Let's use this.
New Question: `(√7744 × 66) ÷ (22 + 22) = ?`
Solution:
(88 × 66) ÷ 44 = ?
88 × (66/44) = ?
88 × (3/2) = ?
44 × 3 = ?
? = 132.
Let's change the option to C.
Wait, I can make 122 work.
(88 * ?) / 47 = 122. No.
Let's try to make the calculation again.
(88 × 66) ÷ (28 + 19) = ?
(88 × 66) ÷ 47
5808 / 47
5808 / 47 = 123.57. Still not good.
Let's make the divisor `48`. (20+28).
5808 / 48 = 121. This is close to 122.
Let's make the product 5856.
5856 / 48 = 122.
To get 5856, we need `88 * x = 5856`. x = 5856 / 88 = 66.5. Not good.
Let's try one more time.
Let the answer be 122. Let the divisor be something clean.
Let divisor be 48.
LHS = 88 * 66 / 48 = 11 * 66 / 6 = 11 * 11 = 121. Very close.
Let's change 66 to 67.
88 * 67 / 48? No.
Okay, let's just make the question clean with answer 132.
New Question: `(√7744 × 66) ÷ (20 + 24) = ?`
(88 × 66) ÷ 44 = ?
88 × 1.5 = 132. So answer is 132 (C).
Let me edit the HTML to reflect this.
IBPS PO Prelims – Quantitative Aptitude (Simplification) – Part 2
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Q26. What will come in place of the question mark (?) in the following question? प्रश्न 26. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Q27. What will come in place of the question mark (?) in the following question? प्रश्न 27. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
40% of ? + √1024 = 112
(A) 150
(B) 180
(C) 200
(D) 240
(E) 250
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 200
Explanation (व्याख्या):
40% of ? + √1024 = 112
Step 1: Find the square root of 1024.
√1024 = 32
Step 2: Substitute the value back into the equation.
(40/100) × ? + 32 = 112
0.4 × ? = 112 - 32
0.4 × ? = 80
? = 80 / 0.4
? = 800 / 4
? = 200
Q28. What will come in place of the question mark (?) in the following question? प्रश्न 28. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Q29. What will come in place of the question mark (?) in the following question? प्रश्न 29. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(27)¹․⁵ × (3)³․⁵ ÷ (9)²․⁵ = 3^?
(A) 2
(B) 2.5
(C) 3
(D) 3.5
(E) 4
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 3
Explanation (व्याख्या):
Convert all bases to the power of 3.
27 = 3³, 9 = 3²
The equation becomes:
(3³)¹․⁵ × (3)³․⁵ ÷ (3²)²․⁵ = 3^?
Using the rule (a^m)^n = a^(m×n):
3^(3 × 1.5) × 3³․⁵ ÷ 3^(2 × 2.5) = 3^?
3⁴․⁵ × 3³․⁵ ÷ 3⁵ = 3^?
Using the rules a^m × a^n = a^(m+n) and a^m ÷ a^n = a^(m-n):
3^(4.5 + 3.5 - 5) = 3^?
3^(8 - 5) = 3^?
3³ = 3^?
Therefore, ? = 3
Q30. What will come in place of the question mark (?) in the following question? प्रश्न 30. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
5678 - 4321 + 1234 = ? + 890
(A) 1501
(B) 1601
(C) 1701
(D) 1801
(E) 1901
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 1701
Explanation (व्याख्या):
5678 - 4321 + 1234 = ? + 890
First, solve the Left Hand Side (LHS):
5678 - 4321 = 1357
1357 + 1234 = 2591
Now the equation is:
2591 = ? + 890
? = 2591 - 890
? = 1701
Q31. What will come in place of the question mark (?) in the following question? प्रश्न 31. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
(64)² ÷ 8³ × 2³ = 2^?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (C) 6
Explanation (व्याख्या):
Convert all bases to the power of 2.
64 = 2⁶, 8 = 2³
The equation becomes:
(2⁶)² ÷ (2³)³ × 2³ = 2^?
2¹² ÷ 2⁹ × 2³ = 2^?
2^(12 - 9 + 3) = 2^?
2^(3 + 3) = 2^?
2⁶ = 2^?
Therefore, ? = 6
Q32. What will come in place of the question mark (?) in the following question? प्रश्न 32. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
18.5 × 21.4 × ? = 6255.22
(A) 15.8
(B) 16.4
(C) 17.2
(D) 14.6
(E) 13.5
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (A) 15.8
Explanation (व्याख्या):
18.5 × 21.4 × ? = 6255.22
First, multiply 18.5 by 21.4:
18.5 × 21.4 = 395.9
Now, the equation is:
395.9 × ? = 6255.22
? = 6255.22 / 395.9
To simplify, multiply numerator and denominator by 10:
? = 62552.2 / 3959
Now, perform the division:
? ≈ 15.8
(Check: 395.9 × 15.8 ≈ 396 × 15.8 = 6256.8, which is very close)
Exact calculation: 62552.2 / 3959 = 15.8
Q33. What will come in place of the question mark (?) in the following question? प्रश्न 33. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
√11449 × √6241 - (54)² = √? + (74)²
(A) 3844
(B) 3721
(C) 3600
(D) 3481
(E) 3969
विस्तृत उत्तर (Detailed Solution)
Correct Answer (सही उत्तर): (B) 3721
Explanation (व्याख्या):
Step 1: Calculate the square roots and squares.
√11449: 100²=10000, 110²=12100. Ends in 9, so root ends in 3 or 7. Let's try 107. 107² = (100+7)² = 10000+1400+49 = 11449. So √11449 = 107.
√6241: 70²=4900, 80²=6400. Ends in 1, so root ends in 1 or 9. Let's try 79. 79² = (80-1)² = 6400-160+1 = 6241. So √6241 = 79.
(54)² = 2916
(74)² = 5476
Step 2: Substitute values into the equation.
107 × 79 - 2916 = √? + 5476
8453 - 2916 = √? + 5476
5537 = √? + 5476
√? = 5537 - 5476
√? = 61
Step 3: Square both sides to find ?.
? = 61² = 3721
Q34. What will come in place of the question mark (?) in the following question? प्रश्न 34. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Q35. What will come in place of the question mark (?) in the following question? प्रश्न 35. निम्नलिखित प्रश्न में प्रश्नवाचक चिह्न (?) के स्थान पर क्या आएगा?
Step 1: Find the cube root of 42875.
The number ends in 5, so the cube root must end in 5.
30³ = 27000, 40³ = 64000. The root is between 30 and 40.
So, ∛42875 = 35.
Step 2: Substitute the value.
35 - ? = 21
? = 35 - 21
? = 14
Q37. 11 1/3 + 13 1/4 + 15 1/6 = ?
(A) 39 3/4
(B) 39 1/4
(C) 40 3/4
(D) 40 1/4
(E) 39 3/5
Detailed Solution
Correct Answer: (A) 39 3/4
Add the whole numbers: 11 + 13 + 15 = 39
Add the fractions: 1/3 + 1/4 + 1/6
Common denominator is 12:
(4/12) + (3/12) + (2/12) = 9/12 = 3/4
Combine the results: 39 + 3/4 = 39 3/4
Q38. (17)² + (19)² + (21)² – (18)² – (20)² = ?
(A) 117
(B) 127
(C) 137
(D) 147
(E) 157
Detailed Solution
Correct Answer: (E) 157
Rearrange the terms:
(21² - 20²) + (19² - 18²) + 17² = ?
Use a² - b² = (a-b)(a+b):
(21-20)(21+20) + (19-18)(19+18) + 17² = ?
(1)(41) + (1)(37) + 289 = ?
41 + 37 + 289 = ?
78 + 289 = 367
Wait, calculation error.
Let's re-calculate squares.
17²=289, 19²=361, 21²=441, 18²=324, 20²=400
Sum of positives: 289 + 361 + 441 = 1091
Sum of negatives: 324 + 400 = 724
? = 1091 - 724 = 367.
The options are wrong. Let me adjust the question.
Let's try (17)² + (19)² - (18)² = ?
289 + 361 - 324 = 650 - 324 = 326.
Let's try (17)² + (19)² - (18)² - (16)² = ?
289 + 361 - 324 - 256 = 650 - 580 = 70.
Let's go back to the rearrangement method and make the numbers work for an answer, say 157.
(21²-20²) + (19²-18²) + X = 157
41 + 37 + X = 157
78 + X = 157 -> X = 79. Not a square.
Let's change the question: `(17)² + (19)² - (18)² = ? + (16)²`
289 + 361 - 324 = ? + 256
650 - 324 = ? + 256
326 = ? + 256
? = 326 - 256 = 70.
Let's create a simpler question:
`15² + 16² - 17² - 18² + 19² = ?`
225 + 256 - 289 - 324 + 361 = ?
(225+256+361) - (289+324) = ?
842 - 613 = 229.
Let's try the grouping again with new numbers.
`(19² - 18²) + (17² - 16²) + 15² = ?`
(19-18)(19+18) + (17-16)(17+16) + 225 = ?
37 + 33 + 225 = ?
70 + 225 = 295.
Ok, let's just do direct calculation on the original and fix the options.
(17)²+(19)²+(21)²-(18)²-(20)² = 289+361+441-324-400 = 1091 - 724 = 367.
Let's make the last term (22)² = 484.
1091 - (324+484) = 1091 - 808 = 283.
I'll just correct the answer options for the original question. Answer is 367.
Let's change the question to get 157.
`13² - 12² + 11² = ?`
169 - 144 + 121 = ?
25 + 121 = 146. Close.
How about `13² - 12² + 10² = ?`. 25 + 100 = 125.
How about `12² + 9² - 5² = ?`. 144 + 81 - 25 = 225-25=200.
Let's set the question as: `(25² - 24²) + (18² - 16²) = ?`
(25-24)(25+24) + (18-16)(18+16) = ?
(1)(49) + (2)(34) = ?
49 + 68 = 117. This works.
Final Question: `(25² - 24²) + (18² - 16²) = ?`
(1)(49) + (2)(34) = 49 + 68 = 117.
Correct answer is (A) 117.
Q39. ? % of 450 + 46% of 280 = 255.8
(A) 22
(B) 24
(C) 26
(D) 28
(E) 30
Detailed Solution
Correct Answer: (D) 28
(?/100) × 450 + (46/100) × 280 = 255.8
4.5 × ? + 0.46 × 280 = 255.8
4.5 × ? + 128.8 = 255.8
4.5 × ? = 255.8 - 128.8
4.5 × ? = 127
? = 127 / 4.5 = 1270 / 45
? = 254 / 9 ≈ 28.22. Error.
Let's recheck 0.46 * 280. It's 128.8. Correct.
1270/45.
1270 / 5 = 254. 45/5 = 9. 254/9. This isn't an integer.
Let's make the RHS 257.
4.5 * ? = 257 - 128.8 = 128.2. No.
Let's make RHS 251.
4.5 * ? = 251 - 128.8 = 122.2. No.
Let's make RHS 255.2.
4.5 * ? = 255.2 - 128.8 = 126.4. No.
Let's make RHS 255.8. Let's make the answer 28.
If ?=28, then 28% of 450 = 0.28 * 450 = 126.
LHS = 126 + 128.8 = 254.8.
So the question should have 254.8 on the RHS.
New Question: `? % of 450 + 46% of 280 = 254.8`
Solution:
4.5 × ? + 128.8 = 254.8
4.5 × ? = 126
? = 126 / 4.5 = 1260 / 45 = 252 / 9 = 28. This works.
Convert percentages to fractions for easier calculation:
33.33% = 1/3
12.5% = 1/8
So, the equation is:
(1/3) of 180 + (1/8) of 320 = ?
60 + 40 = ?
? = 100
Q47. 78 ÷ [(24 – 8) + (38 – 35)³] = ?
(A) 1.2
(B) 1.5
(C) 1.8
(D) 2
(E) 2.2
Detailed Solution
Correct Answer: (B) 1.5
Solve inside the brackets first.
78 ÷ [(16) + (3)³] = ?
78 ÷ [16 + 27] = ?
78 ÷ 43 = ?
Wait, 78 is not divisible by 43. Let's adjust the question.
Let's make the divisor 52. So we need `16 + x = 52`, `x=36`. Not a cube.
Let's make the divisor 39. So we need `16 + x = 39`, `x=23`. Not a cube.
Let's make the divisor 26. `16+x=26`, `x=10`. Not a cube.
Let's adjust the first bracket. `(34-8) = 26`. `(38-35)³ = 27`. Sum is 53.
Let's change the question: `78 ÷ [(26 - 10) + (38 - 36)³] = ?`
78 ÷ [16 + 2³] = ?
78 ÷ [16 + 8] = ?
78 ÷ 24 = 3.25.
Let's try again. `104 ÷ [(24 - 8) + (38 - 36)³] = ?`
104 ÷ [16 + 2³] = 104 ÷ [16+8] = 104 ÷ 24 = 4.33.
How about `104 ÷ [(30 - 8) + (38 - 36)³] = ?`
104 ÷ [22 + 8] = 104 / 30.
Ok, let's fix the original question to have a clean answer.
`78 ÷ [(24 - 8) + (35 - 32)³] = ?`
`78 ÷ [16 + 3³] = 78 / (16+27) = 78/43`...
Let's make it: `52 ÷ [(24 - 8) + (38 - 36)³] = ?`
52 ÷ [16 + 2³] = 52 ÷ [16+8] = 52 ÷ 24. No.
Let's make it: `75 ÷ [(12 - 4) + (13 - 10)³] = ?`
`75 ÷ [8 + 3³] = 75 ÷ [8+27] = 75 ÷ 35`. No.
Ok, `75 ÷ [(10 - 2) + (34 - 31)³] = ?`
`75 ÷ [8 + 3³] = 75 ÷ [8+27] = 75 ÷ 35`.
Let's try `78 ÷ [(30 - 4) + (2 - 1)³] = ?`
78 ÷ [26 + 1] = 78/27.
Final attempt, let's make it simple. `156 ÷ (2² + 3²) = ?` 156 / (4+9) = 156/13 = 12.
Let's try this question instead: `156 ÷ (2² × 3 + 1) = ?`
156 ÷ (4 × 3 + 1) = 156 ÷ (12+1) = 156 ÷ 13 = 12.
New Question: `156 ÷ (2² × 3 + 1) = ?`
Options: 10, 11, 12, 13, 14. Answer is 12.
Q48. (x / √128) = (√162 / x)
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Detailed Solution
Correct Answer: (B) 12
Cross-multiply the terms:
x² = √128 × √162
x² = √(128 × 162)
x² = √(64 × 2 × 81 × 2)
x² = √(64 × 81 × 4)
Take the square root of each factor:
x = √64 × √81 × √4
x = 8 × 9 × 2
x = 72 × 2
x = 144
Wait, x² = 144. So x = 12.
Let me re-check.
x² = 128 x 162. No, that's wrong.
x² = √(128 * 162). No, that's also wrong.
Let's re-do.
x² = √128 × √162
x² = √(64×2) × √(81×2)
x² = (8√2) × (9√2)
x² = 8 × 9 × (√2 × √2)
x² = 72 × 2
x² = 144
x = √144
x = 12
Q49. 3/5 of 4/7 of 5/12 of 1015 = ?
(A) 135
(B) 145
(C) 155
(D) 165
(E) 175
Detailed Solution
Correct Answer: (B) 145
Let's write it as a single multiplication:
(3/5) × (4/7) × (5/12) × 1015
Rearrange for easier cancellation:
(3 × 4 / 12) × (5/5) × (1/7) × 1015
(12/12) × 1 × (1/7) × 1015
1 × (1015 / 7)
1015 ÷ 7 = 145
So, ? = 145
Q50. 21² – 19² + 17² = 300 + ?
(A) 111
(B) 121
(C) 131
(D) 141
(E) 151
Detailed Solution
Correct Answer: (A) 111
Use the identity a² - b² = (a-b)(a+b) for the first two terms.
(21-19)(21+19) + 17² = 300 + ?
(2)(40) + 289 = 300 + ?
80 + 289 = 300 + ?
369 = 300 + ?
? = 369 - 300
? = 69
Wait, calculation error.
Let's check again. 2*40=80. 17^2=289. 80+289=369. Correct.
369 = 300+?. ?=69.
Let's adjust the question to get 111.
If ?=111, then RHS = 300+111 = 411.
So LHS should be 411.
LHS = 80 + 289 = 369. We need 411. The difference is 42.
So 17² should be 289+42 = 331. Not a square.
Let's change 300.
369 = X + ?. If ?=111, X = 369-111 = 258.
New Question: `21² - 19² + 17² = 258 + ?`
80 + 289 = 258 + ?
369 = 258 + ?
? = 369 - 258 = 111. This works.