Simplification- Aptitude Questions and Answers

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The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the square of these two numbers?

A)

1024


B)

1256


C)

1536


D)

1640



Correct Answer :

1536


Explanation :

Let the number are x and 5x
Now, (x )(5x ) = 320
5x2 = 320
x2 = 64
x = 8

Therefore Numbers are 8 and 40.
Hence, difference between their squares= (40)2 - (8)2 = 1600 - 64 = 1536

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If the 8 digit number 5668X25Y is divisible by 48. Find the least value of X + Y ?

A)
10

B)
8

C)
9

D)
7


Correct Answer :

10


Explanation :

if 5668X25Y is divisible by 48 then it should be divisible by co-prime of 48.
There, 3*16 =>3*2*8 =>3*2*2*4=48 where 2, 3, 4, 8 and 16 are co-prime numbers of 48.

5668X25Y divisible by 8 , that means last 3 digit, 25Y should be divisible by 8.
So, Y should be 6

5668X256 to be divisible by 3, that means sum of digits 5+6+6+8+X+2+5+6 should be divisible by 3
So, 38+X is divisible by 3, that means X will be = 1 or 4 or 7

5668X256 divisible by 16,that means last four digits X256 should be divisible by 16
So, suppose X=1, then last four digits 1256 is not divisible by 16.
suppose X=4, then last four digits 4256 is divisible by 16.
suppose X=7, then last four digits 7256 is not divisible by 16.

Hence the correct number is 56684256,which is divisible by 48.
Therefore, least value of X+Y=4+6=10

A two digit number is such that the product of its digits is 12. When 36 is added to the number, its digits are reversed. Find the number ?

A)
62

B)
54

C)
45

D)
26


Correct Answer :

26


Explanation :

Let the digits of number x and y, with x being the tens digit that means the number would be 10x+y.
as per question product of digits x*y = 12 ---------------eq1

When 36 is added to this number the digits inter change their places, so:
10x + y + 36 = 10y + x
9x + 36 = 9y
x + 4 = y ---------------- eq2

Now subsitute eq2 into eq1:
x*y = 12
x*(x + 4) = 12
x2 + 4x - 12 = 0
(x + 6)(x - 2) = 0
x = -6 or 2
ignore the -ve value then x=2 and y=6. Hence number is 26 (there 26+36=62, which is reversed of 26).

While typing, Vipin is four times as fast as Harish and Harish is thrice as fast as Shailendra. Shailendra takes 156 minutes to type an article. How much time Vipin will take?

A)
10 minutes

B)
18 minutes

C)
13 minutes

D)
20 minutes


Correct Answer :

13 minutes


Explanation :

as given, if time taken by Shailendra to do any work is X, then Harish would be do that in X/3 ,and Vipin would be do in X/12

Shailendra takes 156 minutes So X=156 minutes
thus Vipin would take X/12 => 156/12 => 13 minutes

If the digits of a two digit number are interchanged the newly formed number is more than the original number by 18 and sum of the digit is 8 then what was the original number?

A)
53

B)
26

C)
35

D)
42


Correct Answer :

35


Explanation :

Let the digits of number x and y, where x is the tens place, y is the ones place that means Number is: 10x + y

As given the sum of the digits is 8.
x + y = 8 -------------eq1
If the digits are reversed, the new number is 18 greater than the original number.
10y + x = 18 + 10x + y
y - x = 2
y = 2 + x --------------eq2
Substitute value of eq2 in eq1
x + 2 + x = 8
2x = 6
x = 3
So, y = 2 + x = 2 + 3 = 5

Hence number is: 10x + y = 10*3 + 5 = 35

54 is divided into two parts, so that 10 times the first and 22 times the second are together equal to 780. Find the product of the two numbers?

A)
408

B)
562

C)
860

D)
680


Correct Answer :

680


Explanation :

Let 54 is divided into two parts (54 - x) and x.
As given, 10 (54 - x) + 22x = 780
12x = 240
x = 20 and (54 - x) = 34
thus product of the two numbers 20*34=>680

The sum of one half,one third and one fourth of a number exceeds the number by 12. The number is?

A)
144

B)
154

C)
90

D)
174


Correct Answer :

144


Explanation :

let number is x
then according to question
x/3+x/2+x/4 = x+12
(6x+4x+3x) / 12 = x+12
13x = 12(x+12)
13x = 12x+144
13x-12x = 144

hence number is x=144.

What should come in place of the question mark (?) in the following question
(1442 ÷ 48 × 18 ÷ 36) = √?

A)
23328

B)
36

C)
216

D)
46656


Correct Answer :

46656


Explanation :

((144)2 ÷ 48 × 18 ÷ 36)
=> (144*144*18) / (48*36)
=> (144*144*18) / (48*36)
=>216
=>√(216*216)
=>√46656

Divide 935 into three parts in such a way that half of the first part, 1/3 of the second part and 1/6 of the third part are equal. Then the third part is?

A)
170

B)
255

C)
510

D)
1510


Correct Answer :

510


Explanation :

Let equal part be x and three parts are A ,B and C there
A *1/2= B *1/3=C *1/6= x
A = 2x, B = 3x, C =6x
A : B : C = 2 : 3 : 6
Thus,first part = 2x ,second part = 3x and third part = 6x
as sum total of all parts = 935
therefore 2x+3x+6x = 935
11x = 935
x = 935/11 = 85

hence third part = 6x =6*85=510

If (1 + (27/169))1/2=1+(x/13) , then x equal?

A)
3

B)
1

C)
27

D)
13


Correct Answer :

1


Explanation :

(1 + (27/169))1/2=1+(x/13)
=>(1 + (27/169))1/2=1+(x/13)
=>(196/169)1/2=1+(x/13)
=>14/13=1+(x/13)
=>(14/13)-1=x/13
=>1/13=x/13

Hence x=1

If (2x + 3y) : (3x + 5y) = 18 : 29 then x : y is equal to?

A)
2:3

B)
3:4

C)
3:5

D)
1:5


Correct Answer :

3:4


Explanation :

(2x + 3y) : (3x + 5y) = 18 : 29
58x + 87y = 54x + 90y
58x - 54x = 90y - 87y
4x = 3y
Thus, x : y = 3 : 4

If the sum of two numbers is 18 and sum of their square is 164 then the smallest number is?

A)
8

B)
6

C)
12

D)
10


Correct Answer :

8


Explanation :

Let the digits of number x and y, then
x+y = 18 --------------eq1
x2+y2 = 164 ------------eq2
Substitute value of x from eq1 to in eq2
x = (18-y)
(18-y)2 + y2 = 164
324 - 36y + y2 + y2 =164
324 - 36y + 2y2 = 164
2y2 -36y + 160 =0
2(y2 -18y + 80)=0
(y-10)(y-8)=0
y = 8 or 10

from eq1, if y= 8, then x+y = x+8 = 18
x = 10
if y= 10, then x+y = x+10 = 18
x = 8

So the numbers are 8 and 10.and smallest number is 8

(7 + 7 + 7 / 7) / (5 + 5 + 5 / 5) = ?

A)
1

B)
1 / 5

C)
15 / 11

D)
3 / 11


Correct Answer :

15 / 11


Explanation :

(7 + 7 + 7 / 7) / (5 + 5 + 5 / 5)
= (14 + 1) / (10 + 1)
=15 / 11

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