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Question 1 of 5
1. Question
A person has some books. If he distributes them equally among 9, 12, or 15 students, he is left with 4 books each time. If he distributes them equally among 7 students, none are left. What is the minimum number of books?
Correct
Answer: (b) 364
Explanation:
N − 4 divisible by 9,12,15.
LCM(9,12,15):
9=3², 12=2²×3, 15=3×5 ⇒ LCM=2²×3²×5=4×9×5=180
So N = 180k + 4.Now N divisible by 7:
180k + 4 divisible by 7.Try k=1 ⇒ 184 not divisible by 7
k=2 ⇒ 364 divisible by 7 (7×52) ✓
So minimum N = 364.Incorrect
Answer: (b) 364
Explanation:
N − 4 divisible by 9,12,15.
LCM(9,12,15):
9=3², 12=2²×3, 15=3×5 ⇒ LCM=2²×3²×5=4×9×5=180
So N = 180k + 4.Now N divisible by 7:
180k + 4 divisible by 7.Try k=1 ⇒ 184 not divisible by 7
k=2 ⇒ 364 divisible by 7 (7×52) ✓
So minimum N = 364. -
Question 2 of 5
2. Question
A rectangular floor is 420 cm long and 280 cm wide. It is covered with square tiles of the largest possible size. Minimum number of tiles?
Correct
Answer: (b)
Explanation:
HCF(420,280) = 140 cm
Tiles = (420/140) × (280/140) = 3 × 2 = 6.Q68. Two statements S1 and S2 are given below followed by a question.
S1: x is an odd prime number.
S2: y is a prime number greater than 2.
Question: Is x(y + 1) an even number, where x and y are distinct integers?Which one of the following is correct in respect of the above statements and the question?
(a) S1 alone is sufficient
(b) S2 alone is sufficient
(c) Both S1 and S2 together are sufficient, but neither alone is sufficient
(d) Even together are not sufficientAnswer: (b)
Explanation:
We need to know if x(y+1) is even. Product is even if at least one factor is even.S1: x is an odd prime ⇒ x is odd. But nothing about y+1. Not sufficient.
S2: y is prime > 2 ⇒ y is odd ⇒ y+1 is even. Then product is even regardless of x.
So S2 alone is sufficient actually.Incorrect
Answer: (b)
Explanation:
HCF(420,280) = 140 cm
Tiles = (420/140) × (280/140) = 3 × 2 = 6.Q68. Two statements S1 and S2 are given below followed by a question.
S1: x is an odd prime number.
S2: y is a prime number greater than 2.
Question: Is x(y + 1) an even number, where x and y are distinct integers?Which one of the following is correct in respect of the above statements and the question?
(a) S1 alone is sufficient
(b) S2 alone is sufficient
(c) Both S1 and S2 together are sufficient, but neither alone is sufficient
(d) Even together are not sufficientAnswer: (b)
Explanation:
We need to know if x(y+1) is even. Product is even if at least one factor is even.S1: x is an odd prime ⇒ x is odd. But nothing about y+1. Not sufficient.
S2: y is prime > 2 ⇒ y is odd ⇒ y+1 is even. Then product is even regardless of x.
So S2 alone is sufficient actually. -
Question 3 of 5
3. Question
Three-digit numbers are to be formed using digits from 0–9 without repetition. The first digit cannot be 0.
Statement I: A total of 120 numbers can be formed such that digits are in strictly descending order.
Statement II: The number 951 satisfies the descending order condition.Which of the above statements is/are correct?
Correct
Answer: (c)
Explanation:
Strictly descending means hundreds > tens > units.
Choose any 3 distinct digits from 0–9. For each chosen set, exactly 1 arrangement is strictly descending.If the chosen digits include 0, the descending arrangement will put 0 in units place (never in hundreds), so “first digit cannot be 0” is automatically satisfied.
So count = 10C3 = (10×9×8)/(6) = 120. Statement I is correct.
951 has 9 > 5 > 1, so Statement II is correct.Incorrect
Answer: (c)
Explanation:
Strictly descending means hundreds > tens > units.
Choose any 3 distinct digits from 0–9. For each chosen set, exactly 1 arrangement is strictly descending.If the chosen digits include 0, the descending arrangement will put 0 in units place (never in hundreds), so “first digit cannot be 0” is automatically satisfied.
So count = 10C3 = (10×9×8)/(6) = 120. Statement I is correct.
951 has 9 > 5 > 1, so Statement II is correct. -
Question 4 of 5
4. Question
Three-digit numbers are to be formed using digits from 0–9 without repetition. The first digit cannot be 0.
Statement I: A total of 120 numbers can be formed such that digits are in strictly descending order.
Statement II: The number 951 satisfies the descending order condition.Which of the above statements is/are correct?
Correct
Answer: (c)
Explanation:
Strictly descending means hundreds > tens > units.
Choose any 3 distinct digits from 0–9. For each chosen set, exactly 1 arrangement is strictly descending.If the chosen digits include 0, the descending arrangement will put 0 in units place (never in hundreds), so “first digit cannot be 0” is automatically satisfied.
So count = 10C3 = (10×9×8)/(6) = 120. Statement I is correct.
951 has 9 > 5 > 1, so Statement II is correct.Incorrect
Answer: (c)
Explanation:
Strictly descending means hundreds > tens > units.
Choose any 3 distinct digits from 0–9. For each chosen set, exactly 1 arrangement is strictly descending.If the chosen digits include 0, the descending arrangement will put 0 in units place (never in hundreds), so “first digit cannot be 0” is automatically satisfied.
So count = 10C3 = (10×9×8)/(6) = 120. Statement I is correct.
951 has 9 > 5 > 1, so Statement II is correct. -
Question 5 of 5
5. Question
Consider prime number x and composite number y, where x ≠ 2 and y is even.
S1: x + y is odd.
S2: x² + y is odd.
Which of the statements given above is/are correct?Correct
Answer: (d)
Explanation:
x ≠ 2 and x prime ⇒ x is odd.
y is even (given).S1: odd + even = odd ⇒ always true.
S2: x is odd ⇒ x² is odd, and odd + even = odd ⇒ always true.
So both statements are correct.Incorrect
Answer: (d)
Explanation:
x ≠ 2 and x prime ⇒ x is odd.
y is even (given).S1: odd + even = odd ⇒ always true.
S2: x is odd ⇒ x² is odd, and odd + even = odd ⇒ always true.
So both statements are correct.
