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

Question

How many integers between  18  and  3399  are multiples of  17 ?
 
 A. 198  
 B. 199  
 C. 200  
 D. 201  
 E. 202

Chethan92 · Answer

First integer,a = 34, difference, d = 17.

3400 is divisible by 17, as 17*200
Then last multiple = 3400-17 = 3383.
3383 = 34+(n-1)17
n-1 = (3383-34)/17 = 197. n = 198

A is the answer

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GMATMBA5 · Answer

Range = 3399-18+1=3381
Number of multiples of 17 in the range = 3381/17=198.88 = 198 multiples

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BrentGMATPrepNow · Answer

Another approach:

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

Cheers,
Brent

GMATGuruNY · Answer

17*200 = 3400 = multiple of 17.
3399 is one less than a multiple of 17 and thus cannot itself be a multiple of 17.
Since neither endpoint is a multiple of 17, we can simply divide 17 into the difference between the two endpoints:
 \frac{3399-18}{17} = \frac{3381}{17} = 198\frac{15}{17} .
Since 17 divides into the difference 198 times, there are 198 multiples of 17 between the two endpoints.

A

MathRevolution · Answer

=>

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

ScottTargetTestPrep · Answer

Notice that 17 is a multiple of 17. However, since 17 < 18, we need to go to the next one, 34, as the first multiple of 17 that is within the range of 18 to 3399. Similarly, notice that 3400 is a multiple of 17. However, since 3400 > 3399, we need to go to the previous one, 3383, as the final multiple of 17 that is within the range of 18 to 3399. Therefore, the number of multiples of 17 within the given range is:

(3383 - 34)/17 + 1 = 197 + 1 = 198

Answer: A

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

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

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