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Multiple of 14, 7

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by rijul007 » Mon Dec 26, 2011 4:11 am
A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

20
19
18
17
16
Between every two consecutive multiples of 14, there will be one multiple of 7

example: 14,15,16,17,....,21,22,23,..28

Between two multiples of 14 (14 and 28) lies one multiple of 7 ( 21)

So if there are 9 multiples of 14 in Q, the number of mltiples of 7 would be = 9 + 8 = 17

Option D
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by karthikpandian19 » Tue Dec 27, 2011 9:46 pm
OA is 17
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by kakz » Tue Dec 27, 2011 11:22 pm
@rijul
if we consider A=14 and B =154
We will have 9 multiples of 14 between them i.e. 28 42 56 70 84 98 112 126 140 = 9
And between each of them there will be 8 multiple of 8 so total = 8

But, if is set Q is containing consecutive numbers between 14 to 154, there will be also 21( between 14 and 28) and 147 ( between 140 and 154) so total count equals 2

So shouldn't answer be 19? Plz clarify
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by rijul007 » Wed Dec 28, 2011 3:10 am
kakz wrote:@rijul
if we consider A=14 and B =154
We will have 9 multiples of 14 between them i.e. 28 42 56 70 84 98 112 126 140 = 9
And between each of them there will be 8 multiple of 8 so total = 8

But, if is set Q is containing consecutive numbers between 14 to 154, there will be also 21( between 14 and 28) and 147 ( between 140 and 154) so total count equals 2

So shouldn't answer be 19? Plz clarify
A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, INCLUSIVE. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

Hey kakz,
Have a look at the highlighted part.
Do you see where you are going wrong?
Notify me if you still have a doubt :-)
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by Jeff@TargetTestPrep » Mon Jan 08, 2018 11:13 am
karthikpandian19 wrote:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

20
19
18
17
16
Since Q is the set of consecutive integers between A and B, inclusive, we can let A = 1 x 14 = 14 and B = 9 x 14 = 126. Thus, the number of multiples of 7 in Q is:

(126 - 14)/7 + 1 = 112/7 + 1 = 17

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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