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Home / Aptitude / Do the Magic with Numbers – Waving your Brain

# Do the Magic with Numbers – Waving your Brain

When you are trying to do a definite type of work at a certain level with matched competency, the whole object is defined as very popular and sweet term – “TALENT”, and it’s resultant is called “Aptitude”. The naive nature of aptitude is in contrast to achievement, that is sketched through knowledge and the ability which is developed through extensive learning. Numbers are crucial part of aptitude, which are of different types, could be juggled with logic and thoughts and the resultant is called “Numbers Aptitude” or “Problems on Numbers“. Here are 8 interesting questions are placed with their answer options and proper explanation:

1. If 1/3rd of 1/4th of a number is 15, then what will be the 3/10th of that number:

A. 37
B. 39
C. 51
D. 54

54

### Explanation

Let the number be x.

Then, 1/3 of 1/4 of x = 15.

Therefore, x = 15*12 = 180.

So, required number = ( 3/10 * 180 ) = 54

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2. The product of the digits of two digit number is 8. Upon adding 18 to that number, the digits are completely reversed. Tell the number:

A. 16
B. 24
C. 63
D. 89

24

### Explanation

Let the ten’s and unit digit be x and 8/x respectively.

Then, (10x + 8/x)+ 18 = 10 x 8/x + x

10×2 + 8 + 18x = 80 + x2

9×2 + 18x – 72 = 0

x2 + 2x – 8 = 0

(x + 4)(x – 2) = 0

x = 2.

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3. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?

A. 1
B. 4
C. 7
D. None of these

4

### Explanation

Let the ten’s digit be x and unit’s digit be y.

Then, (10x + y) – (10y + x) = 36

9(x – y) = 36

x – y = 4.

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4. When you consider the first of 3 consecutive odd integers and take 3 times of that, it will be 3 more than twice the third. What is the third integer?

A. 7
B. 9
C. 11
D. 15

15

### Explanation

Let the three integers be x, x + 2 and x + 4.

Then, 3x = 2(x + 4) + 3      x = 11.

Third integer = x + 4 = 15.

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5. The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?

A. 6
B. 8
C. 12
D. None of these

8

### Explanation

Since the number is greater than the number obtained on reversing the digits, so the ten’s digit is greater than the unit’s digit.

Let ten’s and unit’s digits be 2x and x respectively.

Then, (10 x 2x + x) – (10x + 2x) = 36

9x = 36

x = 4.

Required difference = (2x + x) – (2x – x) = 2x = 8.

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6. A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:

A. 9
B. 11
C. 13
D. 17

11

### Explanation

Let the ten’s digit be x and unit’s digit be y.

Then, number = 10x + y.

Number obtained by interchanging the digits = 10y + x. (10x + y) + (10y + x) = 11(x + y), which is divisible by 11.

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7. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

A. 18
B. 20
C. 30
D. None of these

20

### Explanation

Let the numbers be a, b and c.

Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.

(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.

(a + b + c) = Sq. Rt of 400 = 20.

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8. The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?

A. 63
B. 72
C. 86
D. None of these

None of these

### Explanation

Let the ten’s digit be x and unit’s digit be y.

Then, x + y = 15 and xy = 3   or   yx = 3.

Solving x + y = 15   and   xy = 3, we get: x = 9, y = 6.

Solving x + y = 15   and   yx = 3, we get: x = 6, y = 9.

So, the number is either 96 or 69.

Hence, the number is none of these.

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