Problems on Numbers MCQs



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PROBLEMS ON NUMBERS QUIZZES

Q.1 : If (17)3 is subtracted from the square of a number and obtained 416. Then find the number ?

  • A - 83
  • B - 63
  • C - 73
  • D - 53

Correct Answer is option - C
Explanation :

Let the number be X.

Then according to the question, X2 - (17)3 = 416

or, X2 = 416 + 4913 = 5329

or, X = √5329 = 73

Q.2 : Three-fourth of a number is 60 more than its one-third . Find the number ?

  • A - 144
  • B - 120
  • C - 169
  • D - 121

Correct Answer is option - A
Explanation : 

Let the number be, X.

Then three-fourth of X = 3X/4 and one-third of X = X/3

According to the question, 3X/4 - X/3 = 60

or, (9X - 4X)/12 = 60

or, X = (60 × 12)/5

or, X = 144

Q.3 : A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find the number ?

  • A - 12
  • B - 28
  • C - 20
  • D - 24

Correct Answer is option - D
Explanation :

Let the ten's digit be, X and unit's digit be, 8/X .

So, the number = 10X + 8/X

Then, (10X + 8/X) + 18X = 10(8/X) + X

or, 10X2 + 8 + 18X = 80 + X2

or, 10X2 - X2 + 18X = 80 - 8

or, 9X2 + 18X = 72

or, 9X2 + 18X - 72 = 0

or, X2 + 2X - 8 = 0

or, X2 + 4X - 2X - 8 = 0

or, X(X + 4) -2(X + 4) = 0

or, (X + 4)(X - 2) = 0

or, X = 2

So, the number = 10 × 2 + 8/2 = 20 + 4 = 24

Q.4 : The sum of the squares of three numbers is 370, while the sum of their products taken two at a time is 265. Find the sum of three numbers ?

  • A - 20
  • B - 30
  • C - 35
  • D - 40

Correct Answer is option - B
Explanation :

Let the numbers be a, b and c.

We have (a2 + b2 + c2) = 370 and (ab + bc + ca) = 265.

We know the formula that, (a + b + c)2 = (a2 + b2 + c2) + 2 (ab + bc + ca)

or, (a + b + c)2 = 370 + 2 × 265 = 370 + 530 = 900

or, (a + b + c) = √900 = 30

Q.5 : The sum of the digits of a two-digit number is 13 and the difference between the digits is 1. What is the two-digit number ?

  • A - 76
  • B - 67
  • C - Can't be determined
  • D - Either A or B

Correct Answer is option - D
Explanation :

Let the digits are X and Y.

Then, (X + Y) = 13 ------------(i)

and (X - Y) = 1 ------------(ii)

By adding the both equations we have, (X + Y + X - Y) = 13 + 1 = 14

or, 2X = 14 or, X = 7

Now we place the value in the equation (i)

Then, (X + Y) = 13 or, 7 + Y = 13 or, Y = 13 - 7 = 6

So, the number is either 76 or 67.

Q.6 : Two numbers are such that the ratio between them is  4 : 7. If each is increased by 4, the ratio becomes 3 : 5. Find the smaller number ?

  • A - 56
  • B - 32
  • C - 21
  • D - 28

Correct Answer is option - B
Explanation :

Let the numbers be, 4X and 7X.

Then (4X + 4) : (7X + 4) = 3 : 5

or, 5(4X + 4) = 3(7X + 4)

or, 20X + 20 = 21X + 12

or, 21X - 20X = 20 - 12

or, X = 8

.·. The smaller number = 4 × 8 = 32

Q.7 : A two digit number has 4 for its unit's digit, and the sum of digits is 1/7 of the number. Find the number ?

  • A - 74
  • B - 94
  • C - 84
  • D - 64

Correct Answer is option - C
Explanation :

Let the unit's digit be X. Then the number = 10X + 4

According to the question, (X + 4) = 1/7 (10X + 4)

or, 7X + 28 = 10X + 4

or, 10X - 7X = 28 - 4

or, 3X = 24

or, X = 8

.·. The number = 84

Q.8 : The sum of two number is 29 and their difference is 13. Find the product of the numbers ?

  • A - 168
  • B - 672
  • C - 268
  • D - 618

Correct Answer is option - A
Explanation :

Let the numbers be, X and Y.

Then, (X + Y) = 29 and (X - Y) = 13

We know that, 4XY = (X + Y)2 - (X - Y)2 

or, 4XY = 292 - 132 = 841 - 169 = 672

or, XY = 672/4 = 168

Q.9 : If the sum of two numbers is 48 and their difference is 6. Then find the ratio of the numbers ?

  • A - 7 : 9
  • B - 11 : 9
  • C - 9 : 7
  • D - 9 : 11

Correct Answer is option - C
Explanation :

Let the numbers be, X and Y.

Then (X + Y) = 48 and (X - Y) = 6

(X + Y) : (X - Y) = 48 : 6 = 8 : 1

or, 8(X - Y) = 1(X + Y)

or, 8X - 8Y = X + Y

or, 7X = 9Y

or, X : Y = 9 : 7

Q.10 : The sum of three consecutive odd numbers is 20 more than the first of these numbers. Then find the middle number ?

  • A - 7
  • B - 11
  • C - 5
  • D - 9

Correct Answer is option - D
Explanation :

Let the numbers be X, X + 2 and X + 4

Then, X + X + 2 + X + 4 = X + 20

or, 3X + 6 = X + 20

or, 3X - X = 20 - 6

or, 2X = 14

or, X = 7

.·. The middle number = 7 + 2 = 9

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