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
