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 give

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.​

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5 months 2021-08-26T01:07:45+00:00 2 Answers 1 views 0

• x = 21 or x = 42

Step-by-step 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

We can express any no. in the form of

Dividend = divisor × quotient + remainder.

So according to question,

• 47 = px + 5, px = 42.
• 91 = qx + 7, qx = 84.
• 132 = rx + 6, rx = 126.

So the two digits factors of 42, 84 & 126.

42 = 42 × 1 = 21 × 2.

84 = 42 × 2 = 21 × 4.

126 = 42 × 3 = 21 × 6.

So, there is two possible solution of x that is 21 & 42.