When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3.

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When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?

A. 9
B. 10
C. 11
D. 12
E. 13


OA E

Source: Veritas Prep

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BTGmoderatorDC wrote:
Sun Dec 04, 2022 9:48 pm
When positive integer y is divided by 7, the remainder is 2. When y is divided by 11, the remainder is 3. What is the sum of the digits of the smallest possible value that meets the definition for y?

A. 9
B. 10
C. 11
D. 12
E. 13


OA E

Source: Veritas Prep
Solution:

We are given that when positive integer y is divided by 7, the remainder is 2, and that when y is divided by 11, the remainder is 3.

Let’s first determine the values of y that produce a remainder of 2 when divided by 7:

y could be: 2, 9, 16, 23, 30, 37, 44, 51, 58, ...

Next let’s determine the values of y that produce a remainder of 3 when divided by 11:

y could be: 3, 14, 25, 36, 47, 58, ...

Thus, we see that the smallest value is 58 and the sum of the digits of 58 is 13.

Answer: E

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