# Problems on Numbers - Aptitude Questions and Answers

## Problems on Numbers Questions and Answers

Learn and practice the chapter "Problems on Numbers" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

## Use of Problems on Numbers

The questions and examples given in this section will be useful to all the freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE, Bank exams - IBPS, SBI, RBI, RRB, SSB, SSC, UPSC etc.

Practice with this online test to crack your placements and entrance tests!
1. Suppose X and Y are two numbers such that, X + Y = 36 and X * Y = 248.
 Find the sum of 1 + 1 x Y
 a. 9 62
 b. 65 248
 c. 248 36
d. 212

Explanation:

 ∴ 1 + 1 = Y+X = 36 = 9 X Y XY 248 62

2. Five consecutive numbers add up to 335. What will be the sum of largest and smallest number?

a. 134
b. 150
c. 174
d. 226

Explanation:

Let 5 consecutive numbers be N, N+1, N+2, N+3, N+4
Sum = N+(N+1)+(N+2)+(N+3)+(N+4) = 5N + 10 = 335
∴ N (Smallest Number) = 65; Largest Number = 65 + 4 = 69
∴ 65 + 69 = 134 = Sum of largest and smallest number

3. We reverse a number and form a new one. The old number is 45 less than new number. The sum of the digits of the old number is 9. What is the new number?

a. 36
b. 54
c. 72
d. 81
e. None of the above

Explanation:

Method 1: Solving Equations

Let the two digits be X and Y.
Let the older number be A and newer one be B.
A = 10X + Y
∴ B = 10 Y + X
From given, B = 45 + A = 45 + 10X + Y
10Y + X = 45 + 10X + Y
So, 9Y - 9X = 45;
Y - X = 5 ----------------- (1)
X + Y = 9 ---------------- (2)
Solving (1) and (2), Y = 7; X = 2
So, A = 27; B = 72

Method 2: Trial and error

A and B have same digits so both have sum of digits = 9
Check 1: Is the sum of digits in all options = 9? Yes.
Check 2:
Option 1 → Reverse 36. We get 63
36+45 ≠ 63
Option 2 → Reverse 81. We get 18
18+45 ≠ 81
Option 3 → Reverse 54. We get 45
45+45 ≠ 54
Option 4 → Reverse 72. We get 27
27+45 = 72. So, this is the right answer.

4. A farm rears geese and dogs. The headcount in the farm is 84 and the leg count is 282. How many geese are there?

a. 27
b. 30
c. 54
d. 57

Explanation:

Let geese be denoted by 'G' and Dogs by 'D'
Geese have 2 legs; Dogs have 4 legs.
Total Heads = G + D = 84 ------------------------- (1)
Total Legs = 2G + 4D = 282 --------------------- (2)
Divide equation 2 by 2, we get,
G + 2D = 141 -------------------------------------- (3)
Equation 3 - Equation 2
G + 2D - G - D = 141 - 84
∴  D = 57
So, Geese = 84 - 57 = 27

Note: To directly find the number of geese, you can eliminate D from equations instead of G. But then you have to multiply equation 1 by 4 which will make numbers bigger and time needed to solve them will be more.

5. Rather than multiplying a number by 3/4, Mitali divided it by 3/4. This lead to a difference of 14 in the final outcome. What is the number?

a. 10
b. 12
c. 24
d. 30

 A - A x 3 = 14 3/4 4