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Question (11)

QN0029523

Choose the correct statement for any two-digit number with distinct digits.

(A) The difference of the number and its reverse is always divisible by 7.
(B) The difference is always divisible by 9.
(C) The sum is always divisible by 9.
(D) The product is always divisible by 11.

Correct Answer: B

Explanation:

If the number is ab, then the difference is (10a + b) – (10b + a) = 9(a – b), which is always divisible by 9.

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Question (12)

QN0029524

If the number 83 is reversed and subtracted, the quotient obtained after dividing the difference by 9 is

(A) 3
(B) 5
(C) 6
(D) 7

Correct Answer: B

Explanation:

83 – 38 = 45 and 45 ÷ 9 = 5.

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Question (13)

QN0029525

The sum of a two-digit number and its reverse is always divisible by

(A) 5
(B) 7
(C) 9
(D) 11

Correct Answer: D

Explanation:

For number ab, (10a + b) + (10b + a) = 11(a + b), which is always divisible by 11.

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Question (14)

QN0029526

For any three-digit number abc, the sum abc + bca + cab is always divisible by

(A) 27 only
(B) 37 only
(C) 37 and 3
(D) 11 only

Correct Answer: C

Explanation:

abc + bca + cab = 111(a + b + c) = 3 × 37 × (a + b + c). Hence, it is divisible by both 3 and 37.

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Question (15)

QN0029527

A six-digit number is formed as 428428. After dividing successively by 7, 11 and 13, the final quotient is

(A) 42
(B) 428
(C) 84
(D) 4284

Correct Answer: B

Explanation:

428428 = 428 × 1001 and 1001 = 7 × 11 × 13. Therefore, the final quotient is 428.

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Question (16)

QN0029528

A farm has 40 animals consisting of horses and hens. If there are 112 legs altogether, the number of horses is

(A) 12
(B) 16
(C) 20
(D) 24

Correct Answer: B

Explanation:

If all 40 animals were hens, there would be 80 legs. The extra 32 legs come from horses. Since each horse contributes 2 extra legs, there are 16 horses.

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Question (17)

QN0029529

A mother is four times as old as her son. After 10 years, she will be twice his age. The son's present age is

(A) 8 years
(B) 10 years
(C) 12 years
(D) 14 years

Correct Answer: B

Explanation:

Let the son's age be x years. Then, 4x + 10 = 2(x + 10). Solving gives x = 10 years.

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Question (18)

QN0029530

Two friends have cows. One says, “You have three times as many cows as I do.” If 6 cows are transferred from the richer friend to the poorer friend, both have equal cows. The poorer friend originally had

(A) 6
(B) 8
(C) 12
(D) 18

Correct Answer: A

Explanation:

Let the poorer friend have x cows. Then the richer friend has 3x cows. After transfer, x + 6 = 3x – 6, giving x = 6.

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Question (19)

QN0029531

A dosa seller spends ₹5000 as fixed cost per day and ₹15 per dosa. If 200 dosas are sold at ₹50 each, the profit is

(A) ₹1000
(B) ₹1500
(C) ₹2000
(D) ₹2500

Correct Answer: C

Explanation:

Revenue = 200 × 50 = ₹10000. Total cost = ₹5000 + 200 × ₹15 = ₹8000. Profit = ₹2000.

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Question (20)

QN0029532

The fraction (1 + 3 + 5 + 7)/(9 + 11 + 13 + 15 + 17) is equal to

(A) 4/9
(B) 8/13
(C) 16/65
(D) 1/2

Correct Answer: C

Explanation:

The numerator is 1 + 3 + 5 + 7 = 16 and the denominator is 9 + 11 + 13 + 15 + 17 = 65. Hence, the fraction equals 16/65.

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Question (11)

Choose the correct statement for any two-digit number with distinct digits.

Explanation:

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Question (12)

If the number 83 is reversed and subtracted, the quotient obtained after dividing the difference by 9 is

Explanation:

Link:

Question (13)

The sum of a two-digit number and its reverse is always divisible by

Explanation:

Link:

Question (14)

For any three-digit number abc, the sum abc + bca + cab is always divisible by

Explanation:

Link:

Question (15)

A six-digit number is formed as 428428. After dividing successively by 7, 11 and 13, the final quotient is

Explanation:

Link:

Question (16)

A farm has 40 animals consisting of horses and hens. If there are 112 legs altogether, the number of horses is

Explanation:

Link:

Question (17)

A mother is four times as old as her son. After 10 years, she will be twice his age. The son's present age is

Explanation:

Link:

Question (18)

Two friends have cows. One says, “You have three times as many cows as I do.” If 6 cows are transferred from the richer friend to the poorer friend, both have equal cows. The poorer friend originally had

Explanation:

Link:

Question (19)

A dosa seller spends ₹5000 as fixed cost per day and ₹15 per dosa. If 200 dosas are sold at ₹50 each, the profit is

Explanation:

Link:

Question (20)

The fraction (1 + 3 + 5 + 7)/(9 + 11 + 13 + 15 + 17) is equal to

Explanation:

Link:

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