Problems on Numbers Quiz Set 014

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Question 1

x should be replaced by which minimum number so that 828517x265 is completely divisible by 9?

 A

1.

 B

2.

 C

4.

 D

3.

Soln.
Ans: a

If the above number has to be divisible by 9, the sum of the digits, i.e., 8 + 2 + 8 + 5 + 1 + 7 + x + 2 + 6 + 5, should be divisible by 9. So we can see that $x + 44$ should be divisible by 9. By inspection, x = 1.


Question 2

The sum of two numbers is 39. Their difference is 21. They are in the ratio?

 A

$3{1/3}$.

 B

$6{1/2}$.

 C

$2{1/3}$.

 D

$3{4/5}$.

Soln.
Ans: a

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 39$ ⇒ $b(k + 1) = 39$. Similarly, from the difference we can obtain $b(k - 1) = 21$. Dividing we get ${k + 1}/{k - 1} = 39/21$. By componendo and dividendo, $k = {39 + 21}/{39 - 21}$ = ${10/3}$, which is same as: $3{1/3}$.


Question 3

15 times the middle of three consecutive even numbers is 150 more than 11 times the smallest of the three numbers. What is the middle number?

 A

32.

 B

33.

 C

31.

 D

34.

Soln.
Ans: a

This is the general solution. Let the numbers be 2n - 2, 2n and 2n + 2. We are given 15 × 2n = 150 + 11 × (2n - 2).
⇒ 15 × 2n = 150 + 11 × 2n - 11 × 2.
⇒ 2n × (15 - 11) = 150 - 11 × 2, so 2n = ${150 - 11 × 2}/{15 - 11} = 32$


Question 4

The sum of three consecutive integer numbers is -96. The smallest of the three is?

 A

-33.

 B

-32.

 C

-30.

 D

-31.

Soln.
Ans: a

Let the numbers be n - 1, n and n + 1. The sum is 3n. We are given 3n = -96, ⇒ n = $-96/3$, i.e., n = -32. So the smallest is -33.


Question 5

The sum of two numbers is 25. Their difference is 19. They are in the ratio?

 A

$7{1/3}$.

 B

$12{1/2}$.

 C

$6{1/3}$.

 D

$6{1/5}$.

Soln.
Ans: a

Let the numbers be a and b, and let their ratio be k such that $a/b = k$. We are given $a + b = 25$ ⇒ $b(k + 1) = 25$. Similarly, from the difference we can obtain $b(k - 1) = 19$. Dividing we get ${k + 1}/{k - 1} = 25/19$. By componendo and dividendo, $k = {25 + 19}/{25 - 19}$ = ${22/3}$, which is same as: $7{1/3}$.


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This Blog Post/Article "Problems on Numbers Quiz Set 014" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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