If today were Test Day, how would you do?

Try this sample GRE question and find out.

If v is the greatest prime factor of 102 and w is the smallest prime factor of 105,what is the value of v - w ?

A. 14
B. 17
C. 20
D. 23
E. 48


And the answer is...

A. 14

Let's find the prime factorizations of 102 and 105.
102 = 2 × 51 = 2 × 3 × 17

The prime factorization of 102 is 2 × 3 × 17.
105 = 3 × 35 = 3 × 5 × 7

The prime factorization of 105 is 3 × 5 × 7.

The greatest prime factor of 102 is 17. Thus, v = 17.

The smallest prime factor of 105 is 3. Thus, w = 3.

We now know that v = 17 and w = 3.

Then v - w = 17 - 3 = 14.

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