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LINA recently purchased a new combination lock for her gym

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LINA recently purchased a new combination lock for her gym [#permalink]  02 Jan 2005, 22:41
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LINA recently purchased a new combination lock for her gym locker but canâ€™t remember the combination. What she does remember is that of the four digits, all between 0 and 9, the first is a prime number and the last is an even digit. How many different four-digit number combinations must Lynda try to be certain of opening her lock?

A. 200

B. 1296

C. 1600

D. 1620

E. 2000
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Multiply the Number of Possibilities in each Space [#permalink]  02 Jan 2005, 23:05
In this problem there are four decimal places to consider. We are told that the first place contains a prime. The single digit primes are 2, 3, 5, and 7. That's 4 choices. Since the second and third places have no restriction, thay can be any of the numbers from 0 to 9. So 10 possibilities each. The final place must be occupied by an even digit: 0, 2, 4, 6, or 8. 5 choices.

The numbers chosen for one space do not affect the choices for the other spaces, so just muliply the number of choices for each space together.

4*10*10*5 = 2000.

Answer E.
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Re: PS [#permalink]  03 Jan 2005, 09:43
MA wrote:
LINA recently purchased a new combination lock for her gym locker but canâ€™t remember the combination. What she does remember is that of the four digits, all between 0 and 9, the first is a prime number and the last is an even digit. How many different four-digit number combinations must Lynda try to be certain of opening her lock?

A. 200

B. 1296

C. 1600

D. 1620

E. 2000

Doesn't between on the gmat mean exclusive unless otherwise stated? So on the gmat wouldn't 0 and 9 be excluded values?
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Very Good Point. But then there is no correct answer. [#permalink]  03 Jan 2005, 11:07
Todd,

You raise a very good point. But if we can select only from the digits 1, 2, 3, 4, 5, 6, 7, and 8, then we get a number of possible combinations that is not among the answer choices.

With this restricted set, the first space, which has to be a prime, can only be 2, 3, 5, or 7. That's 4 choices. The second space has all 8 possible digits. The third space has 8 again. The fourth space could be 2, 4, 6, or 8. 4 Choices.

4 * 8 * 8 * 4 = 1024. That number is not offered.

So we have to assume, even if it is contrary to the test's convention, that we are allowed to use 0 and 9.
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Very Good Point. But then there is no correct answer.   [#permalink] 03 Jan 2005, 11:07
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LINA recently purchased a new combination lock for her gym

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