How many two-digit whole numbers yield a remainder of 1 when

BTGmoderatorDC wrote:How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?

A. None
B. One
C. Two
D. Three
E. Four

OA D

Source: Official Guide

...two-digit whole numbers yield a remainder of 1...
Possible values are: 11, 21, 31, 41, 51, 61, 71, 81, and 91

...and also yield a remainder of 1 when divided by 6
Take each value from 11, 21, 31, 41, 51, 61, 71, 81, and 91, and see which ones leave a remainder of 1 when divided by 6
11, 21, 31, 41, 51, 61, 71, 81, and 91

There are 3 such numbers (in green)

Answer: D

Cheers,
Brent

BTGmoderatorDC wrote:How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?

A. None
B. One
C. Two
D. Three
E. Four

OA D

Source: Official Guide

We need to determine how many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6. Let’s list the numbers that have a remainder of 1 when divided by 10.

Remainder of 1 when divided by 10:

11, 21, 31, 41, 51, 61, 71, 81, 91

Of those numbers, only 31, 61 and 91 leave a remainder of 1 when divided by 6..

Alternate Solution:

If we denote the number by n, then the number can be expressed as n = 10p + 1 since it leaves a remainder of 1 when divided by 10 and also as n = 6s + 1 since it leaves a remainder of 1 when divided by 6. Thus, n - 1 = 10p = 6s is a multiple of both 10 and 6. Since the LCM of 10 and 6 is 30, the possible two digit values of n - 1 are 30, 60 and 90. Thus, two digit values of n are 31, 61 and 91. There are three such values.

Answer: D