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Number System -Test 1

Number System

Online exam in Number System For Quantitative Aptitude for Competitive exams like IBPS BANK PO/Clerical,SBI,RRB,SSC,LIC,UPSC-CSAT,SCRA.MAT,CMAT,MBA,SNAP,CAT,NTSE,CLAT

Number System -Test 1

Subject :- Quantitative Aptitude

Chapter :- Number System-Test 1

Questions :- 25

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Question 1 of 25

1. Question
Let d be a two digit number. If half of d exceeds one third of d by the sum of the digits in d, then the sum of the digits in d is
- 6
- 8
- 9
- 15
- None of these
Correct

Here, let d be 10x + y

According to the question,
$\frac{10 x + y}{2} - \frac{10 x + y}{3} = x + y o r 3 (10 x + y) - 2 (10 x + y) = 6 (x + y) \Rightarrow 30 x + 3 y - 20 x - 2 y = 6 (x + y) 10 x + y = 6 (x + y)$ $\Rightarrow 4 x = 5 y \Rightarrow \frac{x}{y} = \frac{5}{4}$
Then, sum of digits can be 9 as (x+y) is in the multiple of (5+4=9)

Incorrect

Here, let d be 10x + y

According to the question,
$\frac{10 x + y}{2} - \frac{10 x + y}{3} = x + y o r 3 (10 x + y) - 2 (10 x + y) = 6 (x + y) \Rightarrow 30 x + 3 y - 20 x - 2 y = 6 (x + y) 10 x + y = 6 (x + y)$ $\Rightarrow 4 x = 5 y \Rightarrow \frac{x}{y} = \frac{5}{4}$
Then, sum of digits can be 9 as (x+y) is in the multiple of (5+4=9)
Question 2 of 25

2. Question
If a number of two digits is k times the sum of its digits, then the number formed by interchanging the digits is the sum of the digits multiplied by
- 9+k
- 10+k
- 11-k
- k-1
- None of these
Correct

Here, let the number be 10x + y

Then, 10x + y = k(x+y)

Now, by interchanging the digits,

We get the number 10y +x

Now, 10y + x = 11y + 11x – 10x – y

= 11(x+y) – k(x+y)

= (11-k)(x+y)

Hence, correct option is (11-k).

Incorrect

Here, let the number be 10x + y

Then, 10x + y = k(x+y)

Now, by interchanging the digits,

We get the number 10y +x

Now, 10y + x = 11y + 11x – 10x – y

= 11(x+y) – k(x+y)

= (11-k)(x+y)

Hence, correct option is (11-k).
Question 3 of 25

3. Question
The difference between a two digit number and the number obtained by interchanging the two digits of the number is 9. What is the difference between the two digits of the number ?
- 3
- 2
- 1
- Cannot be determined
- None of these
Correct

Let the number be 10x + y

The number by interchanging the position of the digit = 10y + x

Now, (10x + y) – (10y + x) = 9

9x – 9y = 9
$\Rightarrow 9 (x - y) = 9 \Rightarrow (x - y) = 1$

Incorrect

Let the number be 10x + y

The number by interchanging the position of the digit = 10y + x

Now, (10x + y) – (10y + x) = 9

9x – 9y = 9
$\Rightarrow 9 (x - y) = 9 \Rightarrow (x - y) = 1$
Question 4 of 25

4. Question
If the positions of the digits of a two digit number are interchanged, the number obtained is smaller tan the original number by 27. If the digits of the number are in the ratio of 1:2, what is the original number ?
- 36
- 63
- 48
- Cannot be determined
- None of the above
Correct

Let the original number be 10x + y

Now, by interchanging the position of the digits of the number, we get 10y + x.

Now, (10x + y) – (10y + x) = 27
$\Rightarrow 9 x - 9 y = 27 \Rightarrow x - y = 3 \Rightarrow \frac{y}{x} = \frac{1}{2} \Rightarrow x = 2 y I f y = 3 x = 6$
Then number = 10 * 6 + 3 = 63

Incorrect

Let the original number be 10x + y

Now, by interchanging the position of the digits of the number, we get 10y + x.

Now, (10x + y) – (10y + x) = 27
$\Rightarrow 9 x - 9 y = 27 \Rightarrow x - y = 3 \Rightarrow \frac{y}{x} = \frac{1}{2} \Rightarrow x = 2 y I f y = 3 x = 6$
Then number = 10 * 6 + 3 = 63
Question 5 of 25

5. Question
The sum of the digits of a two-digit numbers is 15 and the difference between the two digits of the two digit numbers is 3. What is the product of the two digits of the two digit number ?
- 56
- 63
- 42
- Cannot be determined
- None of these
Correct

Here, let the two digits of the number be x and y.

x + y = 15

x – y = 3

On solving the above equations, we get

2x = 18
$\Rightarrow x = 9$
and y = 6

Hence, x * y = 9*6 = 54

HIT AND TRIAL METHOD :

By going through options, sum of the digits is not 15. Hence, no option is correct.

Incorrect

Here, let the two digits of the number be x and y.

x + y = 15

x – y = 3

On solving the above equations, we get

2x = 18
$\Rightarrow x = 9$
and y = 6

Hence, x * y = 9*6 = 54

HIT AND TRIAL METHOD :

By going through options, sum of the digits is not 15. Hence, no option is correct.
Question 6 of 25

6. Question
The difference between a two digit number and the number obtained by interchanging the two digits of the number is 9. If the sum of the two digits of the number is 15, then what is the original number ?
- 89
- 67
- 87
- Cannot be determined
- None of these
Correct

Here, difference = 9x – 9y

Now, 9(x – y) = 9; x – y = 1

and x + y = 15

Now, x + y = 15
$\frac{x - y = 1}{2 x = 16}$
x = 8

y = 7

Hence Number = 87

Hit and Trial method :

By options, we see that, sum of the digits is not 15 of any option except 87.

And difference between the number and number got by interchanging the position of the digits is 9. Hence, 87 is right option.

Incorrect

Here, difference = 9x – 9y

Now, 9(x – y) = 9; x – y = 1

and x + y = 15

Now, x + y = 15
$\frac{x - y = 1}{2 x = 16}$
x = 8

y = 7

Hence Number = 87

Hit and Trial method :

By options, we see that, sum of the digits is not 15 of any option except 87.

And difference between the number and number got by interchanging the position of the digits is 9. Hence, 87 is right option.
Question 7 of 25

7. Question
In a two digit positive number, the digit at the units place is equal to the square of the digit in ten’s place and the difference between the number and the number obtained by interchanging the digits is 54. What is 40% of the original number ?
- 15.6
- 39
- 37.2
- 24
- None of these
Correct

Let the number be 10x + y
$A n d y = x^{2}$
Now, 10x + y – (10y +x) = 54
$\Rightarrow 9 x - 9 y = 54 \Rightarrow x - y = 6 \Rightarrow x - x^{2} = 6 \Rightarrow x^{2} - x - 6 = 0 \Rightarrow x^{2} - 3 x - 2 x - 6 = 0 \Rightarrow x (x - 3) - 2 (x - 3) = 0 \Rightarrow (x - 2) (x - 3) = 0 \Rightarrow x = 2 o r x = 3 \Rightarrow y = x^{2}$
or y = 4.9

Number is either 24 or 39.

Here, 24 is not possible, so 39 is the number.
$N o w, 30 * \frac{40}{100} = 3.9 * 4 = 15.6$

Incorrect

Let the number be 10x + y
$A n d y = x^{2}$
Now, 10x + y – (10y +x) = 54
$\Rightarrow 9 x - 9 y = 54 \Rightarrow x - y = 6 \Rightarrow x - x^{2} = 6 \Rightarrow x^{2} - x - 6 = 0 \Rightarrow x^{2} - 3 x - 2 x - 6 = 0 \Rightarrow x (x - 3) - 2 (x - 3) = 0 \Rightarrow (x - 2) (x - 3) = 0 \Rightarrow x = 2 o r x = 3 \Rightarrow y = x^{2}$
or y = 4.9

Number is either 24 or 39.

Here, 24 is not possible, so 39 is the number.
$N o w, 30 * \frac{40}{100} = 3.9 * 4 = 15.6$
Question 8 of 25

8. Question
The number obtained by interchanging the digits of a two digit number is less than the original number by 63. If the sum of the digits of the number is 11, what is the original number ?
- 29
- 92
- 74
- Cannot be determined
- None of the above
Correct

Let the number be 10x + y

and difference = 63

9(x – y) = 63
$\Rightarrow x - y = 7$
Now, x + y = 11

x – y = 7
$\Rightarrow 2 x = 18$
x = 9

y = 2

Original number is 92.

Hit and Trial Method :

We can also use elimination method to find out the answer.

Sum of digits of all the given options is 11 but difference between original and the number obtained after interchanging the positions of digits is not 63 except 92.

Hence, correct option is 92.

Incorrect

Let the number be 10x + y

and difference = 63

9(x – y) = 63
$\Rightarrow x - y = 7$
Now, x + y = 11

x – y = 7
$\Rightarrow 2 x = 18$
x = 9

y = 2

Original number is 92.

Hit and Trial Method :

We can also use elimination method to find out the answer.

Sum of digits of all the given options is 11 but difference between original and the number obtained after interchanging the positions of digits is not 63 except 92.

Hence, correct option is 92.
Question 9 of 25

9. Question
In a three digit number, the digit in the unit’s place is twice the digit in the ten’s place and 1.5 times the digit in the hundred’s place. If the sum of all the three digits of the number is 13, what is the number ?
- 364
- 436
- 238
- 634
- None of these
Correct

Let the three digit number be

100a + 10b + c

And c = 2b

Now, c = 15 * a

a + b + c = 13
$H e n c e \frac{c}{1.5} + \frac{c}{2} + c = 13 \Rightarrow 2 c + 15 c + 3 c = 39 \Rightarrow 6.5 c = 39 \Rightarrow c = \frac{39}{6.5}$
Now, c = 6, b = 3, a = 4

So, number is 100 * 4 + 10 * 3 + 6

= 400 + 30 + 6 = 436

Incorrect

Let the three digit number be

100a + 10b + c

And c = 2b

Now, c = 15 * a

a + b + c = 13
$H e n c e \frac{c}{1.5} + \frac{c}{2} + c = 13 \Rightarrow 2 c + 15 c + 3 c = 39 \Rightarrow 6.5 c = 39 \Rightarrow c = \frac{39}{6.5}$
Now, c = 6, b = 3, a = 4

So, number is 100 * 4 + 10 * 3 + 6

= 400 + 30 + 6 = 436
Question 10 of 25

10. Question
The sum of the two digits of a two digit number is 12 and the difference between the two digits of the two digit number is 6. What is the two digit number ?
- 39
- 84
- 93
- Cannot be determined
- None of the above
Correct

Let the two digit number be 10x + y

And x + y = 12

x – y = 6

2x = 18

x = 9

y = 3

Hence, number = 10 * 9 + 3 = 93

Incorrect

Let the two digit number be 10x + y

And x + y = 12

x – y = 6

2x = 18

x = 9

y = 3

Hence, number = 10 * 9 + 3 = 93
Question 11 of 25

11. Question
A certain number of two digits is three times the sum of its digits. If 45 is added to it, the digits are reversed. The number is
- 72
- 32
- 27
- 23
- None of these
Correct

Let the number be 10x + y

Then, 10x + y = 3(x + y)
$\Rightarrow 10 x - 3 x + y - 3 y = 0 \Rightarrow 7 x - 2 y = 0 a n d 10 x + y + 45 = 10 y + x \Rightarrow 9 x - 9 y = - 45 \Rightarrow 9 y - 9 x = 45 \Rightarrow y - x = 5 N o w, 7 x - 2 y = 0 - x + y = 5 (m u l t i p l y b y 2) 7 x - 2 y = 0 - 2 x + 2 y = 5 * 2 5 x = 10 x = 2 y = 7 H e n c e, N u m b e r i s 10 * 2 + 7 = 27$

Incorrect

Let the number be 10x + y

Then, 10x + y = 3(x + y)
$\Rightarrow 10 x - 3 x + y - 3 y = 0 \Rightarrow 7 x - 2 y = 0 a n d 10 x + y + 45 = 10 y + x \Rightarrow 9 x - 9 y = - 45 \Rightarrow 9 y - 9 x = 45 \Rightarrow y - x = 5 N o w, 7 x - 2 y = 0 - x + y = 5 (m u l t i p l y b y 2) 7 x - 2 y = 0 - 2 x + 2 y = 5 * 2 5 x = 10 x = 2 y = 7 H e n c e, N u m b e r i s 10 * 2 + 7 = 27$
Question 12 of 25

12. Question
In a two digit number, the digit in the unit’s place is twice the digit in the ten’s place and the number obtained by interchanging the digits is more than the original number by 27. what is 50% of the original number ?
- 36
- 63
- 48
- 18
- None of these
Correct

Let the original number be

10x + y and y = 2x

The number obtained by interchanging the position of the digits = 10y + x

10x + y + 27 = 10y + x
$\Rightarrow 9 x - 9 y = - 27 \Rightarrow y - x = 3 o r 2 x - x = 3 \Rightarrow x = 3 \Rightarrow y = 3 * 2 = 6 H e n c e n u m b e r s = 36 s o, 50 % o f t h i s n u m b e r i s 18 .$

Incorrect

Let the original number be

10x + y and y = 2x

The number obtained by interchanging the position of the digits = 10y + x

10x + y + 27 = 10y + x
$\Rightarrow 9 x - 9 y = - 27 \Rightarrow y - x = 3 o r 2 x - x = 3 \Rightarrow x = 3 \Rightarrow y = 3 * 2 = 6 H e n c e n u m b e r s = 36 s o, 50 % o f t h i s n u m b e r i s 18 .$
Question 13 of 25

13. Question
The number obtained by interchanging the two digits of a two digit number is less than the original number by 27. If the difference between the two digits of the number is 3, then what is the original number ?
- 74
- 63
- 85
- Cannot be determined
- None of these
Correct

Let the original number be 10x + y

The number obtained by interchanging the position of the digits = 10y + x

Again,difference = 9x – 9y

Now, 9x – 9y = 27
$\Rightarrow x - y = 3$
But, here all the given options fulfill this condition, Hence, we cannot determine an exact answer.

Incorrect

Let the original number be 10x + y

The number obtained by interchanging the position of the digits = 10y + x

Again,difference = 9x – 9y

Now, 9x – 9y = 27
$\Rightarrow x - y = 3$
But, here all the given options fulfill this condition, Hence, we cannot determine an exact answer.
Question 14 of 25

14. Question
In a two digit number, the digit in ten’s place is four times the digit in unit place and sum of the digits is equal to ten. What is the number ?
- 14
- 41
- 82
- Data inadequate
- None of the above
Correct

Here, by going through the options, we see that 2 is the correct option.

Incorrect

Here, by going through the options, we see that 2 is the correct option.
Question 15 of 25

15. Question
The difference between a two digit number and the number obtained by interchanging the positions of the digits is 36.

What is the difference between the two digits of that number ?
- 4
- 9
- 3
- Cannot be determined
- None of these
Correct

Here, let the two digit number be 10x + y and the number by interchanging the position of the digits = 10y + x

Now,

10x + y – (10y + x) = 36
$\Rightarrow 9 x - 9 y = 36 \Rightarrow x - y = 4$

Incorrect

Here, let the two digit number be 10x + y and the number by interchanging the position of the digits = 10y + x

Now,

10x + y – (10y + x) = 36
$\Rightarrow 9 x - 9 y = 36 \Rightarrow x - y = 4$
Question 16 of 25

16. Question
Twice the square of a number is six times the other number. What is the ratio of the first number to the second ?
- 1 : 4
- 2 : 5
- 1 : 3
- Cannot be determined
- None of the above
Correct

Here, let the first number be x and second number by y.

Then,
$2 (x)^{2} = 6 y \Rightarrow x^{2} = 3 y$
Hence, we cannot determine the ratio between these two numbers.

Incorrect

Here, let the first number be x and second number by y.

Then,
$2 (x)^{2} = 6 y \Rightarrow x^{2} = 3 y$
Hence, we cannot determine the ratio between these two numbers.
Question 17 of 25

17. Question
The sum of twice of a number and thrice of 42 is 238. What will be the sum of thrice of that number and twice of 42 ?
- 245
- 250
- 264
- 252
- None of these
Correct

Here, let the number be x.

Then, 2 * x + 3 *42 = 238

or 2x = 238 – 126
$\Rightarrow 2 x = 112 \Rightarrow x = 56$
Now, 3 * 56 + 2 * 42 = 168 + 84 = 252

Incorrect

Here, let the number be x.

Then, 2 * x + 3 *42 = 238

or 2x = 238 – 126
$\Rightarrow 2 x = 112 \Rightarrow x = 56$
Now, 3 * 56 + 2 * 42 = 168 + 84 = 252
Question 18 of 25

18. Question
Three – fourth of one number is equal to five – sixth of another number. What is the respective ratio of the first number to the second number ?
- 12 : 11
- 11 " 9
- 9 : 10
- Cannot be determined
- None of these
Correct

Here, let the two numbers be x and y.
$T h e n \frac{3}{4} * x = \frac{5}{6} * y \Rightarrow \frac{x}{y} = \frac{5}{6} * \frac{4}{3} = \frac{20}{18} = 10 : 9$

Incorrect

Here, let the two numbers be x and y.
$T h e n \frac{3}{4} * x = \frac{5}{6} * y \Rightarrow \frac{x}{y} = \frac{5}{6} * \frac{4}{3} = \frac{20}{18} = 10 : 9$
Question 19 of 25

19. Question
There are two numbers such that the sum of twice the first number and thrice the second number is 100 and the sum of thrice the sum first and twice the second number is 120. Which is the larger number ?
- 32
- 12
- 14
- 35
- None of these
Correct

Here, let the two numbers be x and y.

And 2 * x + 3 * y = 100

Again, 3 * x + 2 * y = 120

2x + 3y = 100 ……… * 2 …….(i)

3x + 2y = 120 ……… * 3 …….(ii)

And subtracting Eq (ii) from Eq (i) we get

4x + 6y = 200

9x + 6y = 360

____________

-5x = -160

x = 32

y = 12

Hence, larger number is 32.

Incorrect

Here, let the two numbers be x and y.

And 2 * x + 3 * y = 100

Again, 3 * x + 2 * y = 120

2x + 3y = 100 ……… * 2 …….(i)

3x + 2y = 120 ……… * 3 …….(ii)

And subtracting Eq (ii) from Eq (i) we get

4x + 6y = 200

9x + 6y = 360

____________

-5x = -160

x = 32

y = 12

Hence, larger number is 32.
Question 20 of 25

20. Question
The sum of five numbers is 290. The average of the first two numbers is 48.5 and the average of last two numbers is 53.5. What is the third number ?
- 72
- 84
- 96
- 108
- None of these
Correct

Here, let the five numbers be a, b, c, d and e.

And a + b + c + d + e = 290

Again, a + b = 2 * 48.5 = 97

And d + e = 2 * 53.5 = 107

So, a + b + d + e = 97 + 107 = 204

Hence, Third number = 290 – 204 = 86

Incorrect

Here, let the five numbers be a, b, c, d and e.

And a + b + c + d + e = 290

Again, a + b = 2 * 48.5 = 97

And d + e = 2 * 53.5 = 107

So, a + b + d + e = 97 + 107 = 204

Hence, Third number = 290 – 204 = 86
Question 21 of 25

21. Question
The difference between the 3/4th of 4/5th of a number and 1/6th of 2/5th of the same number is 648. What is the number ?
- 1110
- 1215
- 1325
- 1440
- None of these
Correct

Here, let the number be x.
$H e n c e \frac{3}{4} * \frac{4}{5} * x - \frac{1}{6} * \frac{2}{5} * x = 648 \Rightarrow \frac{3 x}{5} - \frac{x}{15} = 648 \Rightarrow \frac{9 x - x}{15} = 648 \Rightarrow 8 x = 648 * 15 \Rightarrow x = \frac{648 * 15}{8}$
= 81 * 15 = 1215

Incorrect

Here, let the number be x.
$H e n c e \frac{3}{4} * \frac{4}{5} * x - \frac{1}{6} * \frac{2}{5} * x = 648 \Rightarrow \frac{3 x}{5} - \frac{x}{15} = 648 \Rightarrow \frac{9 x - x}{15} = 648 \Rightarrow 8 x = 648 * 15 \Rightarrow x = \frac{648 * 15}{8}$
= 81 * 15 = 1215
Question 22 of 25

22. Question
A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle. What is the number ?
- 224
- 210
- 140
- 350
- 187
Correct

Here, let the number be x.
$T h e n, x - \frac{x}{7} = 180 [S u m o f a l l t h e a n g l e s o f t r i a n g l e i s 180] \Rightarrow \frac{6 x}{7} = 180 \Rightarrow x = 210$

Incorrect

Here, let the number be x.
$T h e n, x - \frac{x}{7} = 180 [S u m o f a l l t h e a n g l e s o f t r i a n g l e i s 180] \Rightarrow \frac{6 x}{7} = 180 \Rightarrow x = 210$
Question 23 of 25

23. Question
The sum of two even numbers is 6 more than twice of the smaller number. If the difference between these two numbers is 6, which is definitely the smaller number ?
- 18
- 20
- Data provided are not adequate to answer the question
- 12
- 24
Correct

Here, let the first even number be x. Then, second even number is x + 6

Now, x + x + 6 = 2x + 6

or 2x + 6 = 2x + 6

Hence, data provided is not sufficient.

Incorrect

Here, let the first even number be x. Then, second even number is x + 6

Now, x + x + 6 = 2x + 6

or 2x + 6 = 2x + 6

Hence, data provided is not sufficient.
Question 24 of 25

24. Question
The product of two consecutive even numbers is 3248. Which is the larger number ?
- 58
- 62
- 56
- 60
- None of the above
Correct

Here, let the one even number be x.

Then, another even number is (x+2)

Now, x(x + 2) = 3248
$o r x^{2} + 2 x - 3248 = 0 \Rightarrow x^{2} + 58 x - 56 x - 3248 = 0 (b y s p l i t t i n g t h e m i d d l e t e r m) \Rightarrow x (x - 56) + 58 (x - 56) = 0 \Rightarrow (x + 58) (x - 56) = 0 \Rightarrow x = 56$
Hence, Larger number is x + 2 or 56 + 2 = 58

Incorrect

Here, let the one even number be x.

Then, another even number is (x+2)

Now, x(x + 2) = 3248
$o r x^{2} + 2 x - 3248 = 0 \Rightarrow x^{2} + 58 x - 56 x - 3248 = 0 (b y s p l i t t i n g t h e m i d d l e t e r m) \Rightarrow x (x - 56) + 58 (x - 56) = 0 \Rightarrow (x + 58) (x - 56) = 0 \Rightarrow x = 56$
Hence, Larger number is x + 2 or 56 + 2 = 58
Question 25 of 25

25. Question
The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number ?
- 54
- 52
- 48
- 56
- None of these
Correct

Here,

Let the first even number be x.

Then, second number is x + 2
$A g a i n x^{2} + (x + 2)^{2} = 6500 O r x^{2} + x^{2} + 4 + 4 x = 6500 \Rightarrow 2 x^{2} + 4 x + 4 = 6500 \Rightarrow x^{2} + 2 x + 2 = 3250 \Rightarrow x^{2} + 2 x - 3248 = 0 \Rightarrow x^{2} + 58 x - 56 x - 3248 = 0$
(By splitting the middle term)
$\Rightarrow x (x - 56) + 58 (x - 56) = 0 \Rightarrow x = 56 H e n c e, s m a l l e r n u m b e r i s 56$

Incorrect

Here,

Let the first even number be x.

Then, second number is x + 2
$A g a i n x^{2} + (x + 2)^{2} = 6500 O r x^{2} + x^{2} + 4 + 4 x = 6500 \Rightarrow 2 x^{2} + 4 x + 4 = 6500 \Rightarrow x^{2} + 2 x + 2 = 3250 \Rightarrow x^{2} + 2 x - 3248 = 0 \Rightarrow x^{2} + 58 x - 56 x - 3248 = 0$
(By splitting the middle term)
$\Rightarrow x (x - 56) + 58 (x - 56) = 0 \Rightarrow x = 56 H e n c e, s m a l l e r n u m b e r i s 56$

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Number System

Number System -Test 1

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