Question

There is a two-digit number x. 47 divided by x gives a remainder of 5, 91

divided by x gives a remainder of 7 and 132 divided by x gives a remainder of 6.
Find x.​

Answer 1

• x = 21 or x = 42

Explanation:

Given

• 47 = mx + 5 ⇒ mx = 42
• 91 = nx + 7 ⇒ nx = 84
• 132 = kx + 6 ⇒ kx = 126

As we see, the number x is factor of 42, 84 and 126. The two-digit factors are:

• 42 = 1*42 = 2*21
• 84 = 2*42 = 4*21
• 126 = 3*42 = 6*21

We have two possible solutions:

• 21 and 42

Proof:

• 47/21 = 2 rem 5, 47/42 = 1 rem 5
• 91/21 = 4 rem 7, 91/42 = 2 rem 7
• 132/21 = 6 rem 6, 132/42 = 3 rem 6