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If y is a positive integer with 3 digits and the ......

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If y is a positive integer with 3 digits and the ......

by Vincen » Wed Jan 24, 2018 8:21 am
If y is a positive integer with 3 digits and the sum of its digits is 11, what is the value of y?

(1) The units digit is 2.
(2) The product of the digits is 0.

The OA is the option C.

How can use both statements together to solve this DS question? Experts, can you give me some help here?
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Source: — Data Sufficiency |

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by [email protected] » Thu Jan 25, 2018 12:09 pm
Hi Vincen,

We're told that Y is a positive 3-digit integer and the sum of its digits is 11. We're asked for the value of Y. This question can be solved by TESTing VALUES.

1) The units digit of Y is 2.

Based on the information in Fact 1, Y could be:
902, 812, 722, 632, 542, 452, 362, 272 or 182
Fact 1 is INSUFFICIENT.

(2) The product of the digits is 0.

Fact 2 tell us that one of the digits MUST be 0, so Y could be:
902, 920, 803, 830, 704, 740, etc.
Fact 2 is INSUFFICIENT.

Combined, we know...
The units digit of Y is 2.
One of the digits of Y is 0
The sum of the digits of Y is 11.

A 3-digit positive integer cannot start with a 0, so the tens digit MUST be the 0. Since the sum of the digits is 11, that means the hundreds digit MUST be 9. Thus, Y = 902.
Combined, SUFFICIENT

Final Answer: C

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