If the digits of a three-digit positive number X are non-zero and distinct...

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e-GMAT

If the digits of a three-digit positive number X are non-zero and distinct, is the sum of its digits equal to 10?

1) The product of the digits of X is equal to 30.
2) Each digit of X is a prime number.

OA C

[Jay@ManhattanReview]

e-GMAT

If the digits of a three-digit positive number X are non-zero and distinct, is the sum of its digits equal to 10?

1) The product of the digits of X is equal to 30.
2) Each digit of X is a prime number.

OA C

Let's take each statement one by one.

Say the three digits are x, y and z. We have to determine whether x + y + z = 10.

1) The product of the digits of X is equal to 30.

Case 1: 30 = 2.3.5; Sum = 2 + 3 + 5 = 10;
Case 2: 30 = 1.5.6; Sum = 1 + 5 + 6 = 12;

No unique answer. Insufficient.

2) Each digit of X is a prime number.

Case 1: Say the digits are 2, 3, and 5; Sum = 2 + 3 + 5 = 10;
Case 2: Say the digits are 2, 3, and 7; Sum = 2 + 3 + 7 = 12;

No unique answer. Insufficient.

(1) and (2) together

Only Case 1 is applicable. Sum = 10. The answer is yes. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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