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# A and B are two multiples of 14, and Q is the set of consecutive integ

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A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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25 Jun 2015, 10:54
2
15
00:00

Difficulty:

85% (hard)

Question Stats:

49% (02:12) correct 51% (02:08) wrong based on 250 sessions

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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?

A. 20
B. 19
C. 18
D. 17
E. 16

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A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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01 Sep 2015, 09:31
6
2
Lets Q's first number be 14
As per question, Q contains 9 multiples of 14 , so let Q's last number be 126. $$(14 * 9)$$
We have,
$$a_n$$ = $$a + (n-1)d$$

Then

126 = 14 + (n-1)7

Solving for n , we get n = 17
##### General Discussion
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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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26 Jun 2015, 05:03
1
I am getting the answer 17.

Let A=14 and B= 154.

Q= {15,16, 17...................153}

The nine multiples of Q are {28......140}.

The number of multiples of 7 between {28......................140} N=17. option d.

reto 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?

A. 20
B. 19
C. 18
D. 17
E. 16

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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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22 Nov 2015, 06:26
Hey

As per your approach you are missing 2 numbers here i.e. 21 and 147, both will be in the set and divisible by 7, hence the answer should be 19.

Thank you

shriramvelamuri wrote:
I am getting the answer 17.

Let A=14 and B= 154.

Q= {15,16, 17...................153}

The nine multiples of Q are {28......140}.

The number of multiples of 7 between {28......................140} N=17. option d.

reto 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?

A. 20
B. 19
C. 18
D. 17
E. 16
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Joined: 02 Aug 2009
Posts: 7334
Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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22 Nov 2015, 07:20
2
rsaahil90 wrote:
Hey

As per your approach you are missing 2 numbers here i.e. 21 and 147, both will be in the set and divisible by 7, hence the answer should be 19.

Thank you

shriramvelamuri wrote:
I am getting the answer 17.

Let A=14 and B= 154.

Q= {15,16, 17...................153}

The nine multiples of Q are {28......140}.

The number of multiples of 7 between {28......................140} N=17. option d.

reto 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?

A. 20
B. 19
C. 18
D. 17
E. 16

Hi,

the Q has a straight logic..

7 is an odd number so its consecutives multiples will be even, odd, even,odd and so on..
and even multiple of 7 will mean multiple of 14..

now we have two ends of the set which are multiples of 14 or in other words even multiple of 7...
and between each set of consecutive even multiple of 7, there will be 1 odd multiple of 7..
so even multiple=9
odd multiple=9-1=8..
total 17 ans
D
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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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01 Jul 2016, 23:01
2
reto 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?

A. 20
B. 19
C. 18
D. 17
E. 16

Visualization question...

Let's try 2 small values..two multiples and three multiples..I will write multiples of 14(which are also multiples of 7) in boldface..

14---21---28 number of multiples of 7? 2 + 1 = 3

Three multiples

14---21---28---35---42 number of multiples of 7? 3 + 2 = 5

So imagine all multiples of 14 written with blanks in between them..multiples of 7 will be

(number of mutiples of 14) + (number of blanks between them)

Thus, 9 + 8 = 17 (D).
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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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02 Jul 2016, 00:48
First multiple of Q : 14 x 1 = 14
Last multiple of Q : 14 x 9 = 126

So, 126 - 14 = 122, and 122/7 = 16
We add + 1 since elements are inclusive

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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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17 Oct 2016, 08:06
reto 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?

A. 20
B. 19
C. 18
D. 17
E. 16

When we include both endpoints, we add one (1 for every 14 + the other end)
So, if we have nine we have (8 + the other end)
7 is 14/2 so we have 2 multiples of 7 for every multiple of 14 + the other end => 2x8 + 1 = 17

Choice D
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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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26 Oct 2017, 14:27
reto 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?

A. 20
B. 19
C. 18
D. 17
E. 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

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Re: A and B are two multiples of 14, and Q is the set of consecutive integ  [#permalink]

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04 Nov 2018, 02:46
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Re: A and B are two multiples of 14, and Q is the set of consecutive integ   [#permalink] 04 Nov 2018, 02:46
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