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# M31-06

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Math Expert
Joined: 02 Sep 2009
Posts: 50613

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07 Jun 2015, 08:01
00:00

Difficulty:

25% (medium)

Question Stats:

90% (02:01) correct 10% (01:04) wrong based on 30 sessions

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$$t_1, \ t_2, \ t_3, \ ..., \ t_n, \ ...$$

In the sequence above, each term after the first term is equal to the preceding term plus the constant $$k$$. If $$t_1+ t_3+t_5+t_7=32$$, what is the value of $$t_2+t_4+t_6$$?

A. 8
B. 12
C. 24
D. 32
E. 72

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Math Expert
Joined: 02 Sep 2009
Posts: 50613

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07 Jun 2015, 08:01
Official Solution:

$$t_1, \ t_2, \ t_3, \ ..., \ t_n, \ ...$$

In the sequence above, each term after the first term is equal to the preceding term plus the constant $$k$$. If $$t_1+ t_3+t_5+t_7=32$$, what is the value of $$t_2+t_4+t_6$$?

A. 8
B. 12
C. 24
D. 32
E. 72

According to the stem:

$$t_2=t_1+k$$;

$$t_3=t_2+k=t_1+2k$$;

$$t_4=t_3+k=t_1+3k$$;

...

$$t_n=t_1+(n-1)k$$;

Since $$t_1+t_3+t_5+t_7=32$$, then $$t_1+(t_1+2k)+(t_1+4k)+(t_1+6k)=32$$. So, $$t_1+3k=8$$

We need to find the of $$t_2+t_4+t_6=(t_1+k)+(t_1+3k)+(t_1+5k)=3(t_1+3k)$$. From above we know that $$t_1+3k=8$$, thus $$3(t_1+3k)=3*8=24$$.

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Joined: 24 Oct 2012
Posts: 170

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08 Jun 2015, 04:38
t2 = t1 + k
t3 = t2 + K = t2 = 2K

tn = t1 + (n-1)K

equation1 --- > t1+t3+t5+t7 = 32

Replacing individual component with corresponding t1 , equation 1 becomes
4t1 + 12K = 32
t1 + 3K = 8

Now t2 + t4 + t6 = ?
replacing individual component with corresponding t1 + (n-1)K, above equation becomes

3t1 + 9K = 3( t1 + 3K) = 3 * 8 = 24
option C
Intern
Joined: 14 Oct 2015
Posts: 32
GMAT 1: 640 Q45 V33

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29 Oct 2015, 05:56
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Where is it stated that k is a positive integer? Why can't k be -1/2?
Math Expert
Joined: 02 Sep 2009
Posts: 50613

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29 Oct 2015, 10:40
danjbon wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Where is it stated that k is a positive integer? Why can't k be -1/2?

How does it matter whether k is an integer or not? Where in the solution it's mentioned that k is an integer?
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Joined: 31 Mar 2016
Posts: 386
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

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21 Jul 2016, 05:08
I think this is a high-quality question and I agree with explanation. Nice manipulative question
Intern
Joined: 12 Jan 2018
Posts: 19

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19 Jun 2018, 14:50
Possible alternative method?: plugging in values such that the rules are fulfilled in the original problem.

Set K=2, and t1=2.

Sequence (starting with t1) = 2,4,6,8,10,12,14,16,(...) each term is the previous +2, so given constraint in the problem is fulfilled.

t1+t3+t5+t7=2+6+10+14 = 32 (condition is fulfilled).

Then, t2+t4+t6 = 4+8+12 = 24, therefore (C) is the answer.
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Joined: 18 Sep 2014
Posts: 2
Location: India
GMAT 1: 710 Q50 V37
GMAT 2: 710 Q49 V38
GMAT 3: 760 Q49 V45
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12 Jul 2018, 22:08
Could you help me understand why there's a square box in front of t3, t5 and 32? I assumed this was to indicate that the 'square box' has a certain value but I see that when t3 is converted to t1 + 2k or t5 is converted to t1 + 4k the box is simply removed. What's the point of the box?
Math Expert
Joined: 02 Sep 2009
Posts: 50613

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12 Jul 2018, 22:28
varun72 wrote:
Could you help me understand why there's a square box in front of t3, t5 and 32? I assumed this was to indicate that the 'square box' has a certain value but I see that when t3 is converted to t1 + 2k or t5 is converted to t1 + 4k the box is simply removed. What's the point of the box?

Those boxes are just formatting errors. Edited. Thank you.
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M31-06 &nbs [#permalink] 12 Jul 2018, 22:28
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# M31-06

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