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# Integer x equals the number of terms of an arithmetic progression and

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Joined: 07 Dec 2014
Posts: 1218
Integer x equals the number of terms of an arithmetic progression and  [#permalink]

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02 Mar 2019, 21:51
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Difficulty:

45% (medium)

Question Stats:

63% (01:42) correct 37% (01:50) wrong based on 35 sessions

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Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11
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Joined: 02 Aug 2009
Posts: 8281
Re: Integer x equals the number of terms of an arithmetic progression and  [#permalink]

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02 Mar 2019, 22:57
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11

Let the common difference be d, and the first element be a.
so $$d=x$$, and last term = $$a+(x-1)d$$..

Now RANGE = last term-first term = $$(a+(x-1)d)-1=(x-1)d=6x$$
Substitute d=x, so $$(x-1)x=6x.....x-1=6$$ or $$x=7$$
We cancelled out x from both sides as x cannot be 0.

C
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Re: Integer x equals the number of terms of an arithmetic progression and  [#permalink]

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03 Mar 2019, 00:49
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11

Hi,

Given:
n=d=x,
Range = nth term - 1st term = 6x
a+(n-1)d-a = 6x
(x-1)x = 6x
x-1 = 6
x = 7

Option C

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Re: Integer x equals the number of terms of an arithmetic progression and  [#permalink]

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03 Mar 2019, 07:47
chetan2u wrote:
gracie wrote:
Integer x equals the number of terms of an arithmetic progression and it's common difference. If the range of the progression is 6x, what is the value of x?

A. 3
B. 5
C. 7
D. 9
E. 11

Let the common difference be d, and the first element be a.
so $$d=x$$, and last term = $$a+(x-1)d$$..

Now RANGE = last term-first term = $$(a+(x-1)d)-1=(x-1)d=6x$$
Substitute d=x, so $$(x-1)x=6x.....x-1=6$$ or $$x=7$$
We cancelled out x from both sides as x cannot be 0.

C

Hello Chetan Sir,

Just a query..

X equals Y and Z means mean X=Y ,X=Z

I initially assumed this wrong int this question .
x= NUMBER OF terms of AP + Common diffrerence..

I guess this was wrong .
Re: Integer x equals the number of terms of an arithmetic progression and   [#permalink] 03 Mar 2019, 07:47
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