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How many integers between 18 and 3399 are multiples of 17?

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by Max@Math Revolution » Wed Feb 13, 2019 12:35 am
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[GMAT math practice question]

How many integers between 18 and 3399 are multiples of 17?

A. 198
B. 199
C. 200
D. 201
E. 202
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by Brent@GMATPrepNow » Wed Feb 13, 2019 6:31 am
Max@Math Revolution wrote:[GMAT math practice question]

How many integers between 18 and 3399 are multiples of 17?

A. 198
B. 199
C. 200
D. 201
E. 202
Let's list the multiples of 17 that are between 18 and 3399 :
34 = 2(17)
51 = 3(17)
68 = 4(17)
85 = 5(17)
.
.
.
3383 = 199(17)

So, the number of multiples of 17 is EQUAL to the number of integers from 2 to 199 inclusive

ASIDE: A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 2 to 199 inclusive = 199 - 2 + 1 = 198

Answer: A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Fri Feb 15, 2019 12:03 am
=>

18 = 17*1 + 1, 34 = 17*2 is the least multiple of 17 greater than 18.
3399 = 17*199 + 16, 3383 = 17*199 is the greatest multiple of 17 less than 3399.
Thus, the multiples of 17 between 18 and 3399 are 34=17*2, … , 3383 = 17*199. There are 198 = (199 – 2) + 1 of these numbers as they are in one-to-one correspondence with the integers between 2 and 199, inclusive.

Therefore, the answer is A.
Answer: A
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