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# M03#29

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M03#29 [#permalink]  14 Mar 2009, 18:14
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A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -3

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!
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Re: M03#29 [#permalink]  03 Jan 2011, 03:07
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gmatdelhi wrote:
tingle15 wrote:
I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?

When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, .... For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

But in the original question, stem says consecutive terms of the sequence A (which is given to be arithmetic progression) and not consecutive integers, so the common difference is not necessary to be 1 in this case.

As for the question:

A computer generated a sequence $$A$$ of numbers using the following formula: $$A_n = A_1 + (n-1)d$$. $$d$$ is the common difference between any two consecutive terms of the sequence $$A$$. If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?
A. 3
B. 2
C. 1
D. -1
E. -3

Given:
$$a_2+a_5=(a_1+d)+(a_1+4d)=2a_1+5d=8$$;
$$a_3+a_7=(a_1+2d)+(a_1+6d)=2a_1+8d=14$$;

Subtract 1 from 2: $$3d=6$$ --> $$d=2$$ --> as $$2a_1+5d=8$$ then $$2a_1+5*2=8$$ -> $$a_1=-1$$.

Hope it helps.
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Re: M03#29 [#permalink]  14 Mar 2009, 20:48
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its AP
A, A+d,A+2d,A+3d,.........,A+(n-1)d
sorry I cant able to write the equation here but its a simple problem
solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:
Quote:

A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(C) 2008 GMAT Club - m03#29

* 3
* 2
* 1
* -1
* -3

$$\left{ \begin{eqnarray*} A_2+A_5 &=& A_1 + d + A_1 + 4d = 2A_1 + 5d = 8\\ A_3+A_7 &=& A_1 + 2d + A_1 + 6d = 2A_1 + 8d = 14\\ \end{eqnarray*}$$
$$\left{ \begin{eqnarray*} d &=& 2\\ A_1 &=& -1\\ \end{eqnarray*}$$

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

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Re: M03#29 [#permalink]  22 May 2010, 07:24
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The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.
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Re: M03#29 [#permalink]  16 Mar 2009, 07:51
nitya34 wrote:
its AP
A, A+d,A+2d,A+3d,.........,A+(n-1)d
sorry I cant able to write the equation here but its a simple problem
solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:
Quote:

A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(C) 2008 GMAT Club - m03#29

* 3
* 2
* 1
* -1
* -3

$$\left{ \begin{eqnarray*} A_2+A_5 &=& A_1 + d + A_1 + 4d = 2A_1 + 5d = 8\\ A_3+A_7 &=& A_1 + 2d + A_1 + 6d = 2A_1 + 8d = 14\\ \end{eqnarray*}$$
$$\left{ \begin{eqnarray*} d &=& 2\\ A_1 &=& -1\\ \end{eqnarray*}$$

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

Response:
---------------------------------------------------------------------------------------------------------------------------------------------------------------

It is an arithmetic progression sequence where you have formula:

$$a_n = a_1 + (n-1)d$$

And now if you put n = 5, n = 2, n =7 you will get these forumuas.
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Re: M03#29 [#permalink]  30 Sep 2010, 08:28
2a+5d=8 and 2a+8d=14 => d=3 and a = -1. Answer D wins.
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Re: M03#29 [#permalink]  30 Sep 2010, 09:04
An=A1-(n-1)d
is the formula for nth term in an arithmetic progression.
hence 7th term A7=A1-(7-1)d
Similarly,2nd term A2=A1-(2-1)d
3rd term A3=A1-(3-1)d
and 5th term A5=A1-(5-1)d

Now According to question,A2+A5=8 i.e 2A1+5d=8
and A3+A7=14 i.e, 2A1+8d=14

Solving these two we will get A1=-1

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Re: M03#29 [#permalink]  30 Sep 2010, 15:12
Arithmetic sequence.
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Re: M03#29 [#permalink]  30 Sep 2010, 16:04
D.

I tried back-substitution and didn't get anywhere. had to solve it the old-fashioned - 2 equations, 2 variables way.
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Re: M03#29 [#permalink]  12 Oct 2010, 12:27
sidhu4u wrote:
The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.

I agree... Can someone please provide a resolution for this...
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Re: M03#29 [#permalink]  03 Jan 2011, 00:16
tingle15 wrote:
sidhu4u wrote:
The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.

I agree... Can someone please provide a resolution for this...

I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?
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Re: M03#29 [#permalink]  04 Oct 2011, 10:02
Easy one. Its an AP with d as common difference and A1 as first term.
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CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
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Re: M03#29 [#permalink]  04 Oct 2011, 16:21
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Re: M03#29 [#permalink]  14 Nov 2011, 22:19
ThinkingHat wrote:
A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -3

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

Its pretty easy when you set it up as equations to solve.

Equation one is =
A + (2-1)d + A + (5-1)d = 8 => 2A + 5d = 8

Equation two is =
A + (3-1)d + A + (7-1)d = 14 => 2A + 8d = 14

Since the only difference between the two equations is 3d = 6 we know that d = 2. Plug that into one of the equations and you get A = -1.
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Re: M03#29 [#permalink]  17 Dec 2011, 03:34
a2+a5=8

a3+a7=14 or a2+d+a6+d=14 a2+24+a5+d=14 8+3d=14 d=2

a1+d+a1+4d=8 2a1+5d=8 2a1=5*2=8 a1=-1
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Re: M03#29 [#permalink]  04 Oct 2012, 11:04
i don't know how long the GMAC will continue to ask such question in the real test because this one is easy yet time consuming.

A2+A5
=> { A1+(2-1)d}+{A1+(5-1)d=8
=> 2A1+5d=8----------------------------------(i)

A3+A7
=> {A1+(3-1)d}+{A1+(7-1)d=14
=> 2A1+8d=14-------------------------------(ii)

solve (i) & (ii)

d=2

putting the value of d in (i) [or (ii)]

A1=-1

D wins
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Re: M03#29   [#permalink] 04 Oct 2012, 11:04
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