The number of multiples of only one of 5 or 7 between 200 and 500, inc

Question

The number of multiples of only one of 5 or 7 between 200 and 500, inclusive, is

my answer came out to be 95, after calculating ( no. of multiples of 5 + no. of multiples of 7 - no. of multiples of 35)

but the actual answer is 104.

please explain.

EMPOWERgmatRichC · Answer

Hi Sujan Sareen,

You would like get more of a response if you posted this question in the Quant Forum here:

gmat-quantitative-section-7/

I can help you to answer this question, but first I'd like to know more about the work that you did:

How many multiples of 5 and 7 did you determine are in this range? And how many multiples of 35 did you find?

GMAT assassins aren't born, they're made,
Rich

gmat1123 · Answer

Hi,
No of multiples of 5 is 61.
No of multiples of 7 is 43. 
No of multiples of 35 is 9.

so my answer= 61+43-9 = 95.

I need urgent help. As my exam is approaching.

EMPOWERgmatRichC · Answer

Hi Sujan Sareen,

Your individual calculations ARE correct (there are 61 multiples of 5, 43 multiples of 7, and 9 multiples of 35 in that range). However, 104 is NOT the correct answer to this question (and neither is 95). Here's why:

If we're looking for multiples of 5 OR 7, but NOT both, then we have to remove all of the multiples of 35 that occur in BOTH the 'multiples of 5' group AND the 'multiples of 7' group (since those multiples of 35 showed up in both groups).

(61 - 9) + (43-9) = 52 + 34 = 86.

What is the source of this question? And why did it not come with the 5 answer choices?

GMAT assassins aren't born, they're made,
Rich

Mo2men · Answer

Hi Rich,
How did 61 come from? 500-200=300 so 300/5=60. Also 300/7=42.7. Is any general rule or formula? It is hard to count number withing range.

EMPOWERgmatRichC · Answer

HI Mo2men,

You have to remember to include the number 200 (which IS a multiple of 5). By calculating (500-200)/5 you actually REMOVED the 200 from consideration.

Here's a simple example of this concept. If you read pages 2 through 5 (inclusive) in a book, then how many pages have you actually read?

It's NOT 3 pages. You have read pages 2, 3, 4 and 5... that's a total of 4 pages.

This is often referred to as a 'fence-post' problem/calculation (since you have to be sure to count the first 'post' and last 'post'). The general 'formula' for these types of calculations is:

(Bigger Number) - (Smaller Number) + 1 = Total

GMAT assassins aren't born, they're made,
Rich

The number of multiples of only one of 5 or 7 between 200 and 500, inc

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