Data Sufficiency

stevecultt wrote:D represents a single digit number from 1 to 9. What is the value of D?

(1) D"¢D + DD = D"¢D x DD
(2) D is not a prime number.

The dot ("¢) represents a decimal.

OA A

Statement 1: D.D + DD = D.D x DD

=> D.D (1 + 10) = D.D x DD

=> 11 = DD; D.D cancels

Thus, D = 1. Sufficient.

Statement 2: D is not a prime number.

Clearly, not sufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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Hi stevecultt,

This question can be solved with a little math and a bit of 'brute force.'

We're told that D is a positive DIGIT (meaning 1-9, inclusive). We're asked for the value of D.

1) D.D + DD = (D.D)(DD)

While this might look complex, if you substitute in a value for D, you'll find that math to be rather straight-forward....

IF.... D = 1, we have...
1.1 + 11 = (1.1)(11)

Does that equation 'balance out?'
1.1 + 11 = 12.1
(1.1)(11) = 12.1
So YES, D could equal 1.

What about D = 2? Does....
2.2 + 22 = (2.2)(22)

You should be able to answer that question WITHOUT actually doing the math. On the left side, you're ADDING 10% of 22 to 22 and on the right side you're MULTIPLYING those values. The right side will clearly be a lot bigger than the left side. This means that D CANNOT equal 2.

Now how about D=3? D=4? Etc. You should see that you run into the same issue that you did when we worked through D=2: the right side is much bigger than the left side, so there's really no need to check all of those values. This means that D=1 is the ONLY possible solution.
Fact 1 is SUFFICIENT.

2) D is not a prime number

This tells us that D cannot be 2, 3, 5 or 7.... but that still leaves us with 5 other possibilities (1, 4, 6, 8 and 9)
Fact 2 is INSUFFICIENT.

Final Answer:A

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Rich