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# The four integers a, b, c, and d are such that a < b < c < d, d = 7a

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Math Expert
Joined: 02 Sep 2009
Posts: 47015
The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink]

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23 Nov 2017, 06:57
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55% (hard)

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35% (01:31) correct 65% (02:17) wrong based on 36 sessions

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The four integers a, b, c, and d are such that a < b < c < d, d = 7a, and b - a = c - b = d - c. What is the average (arithmetic mean) of the four integers?

(1) c = 25

(2) c/a = 5

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Math Expert
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Posts: 6202
Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink]

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23 Nov 2017, 07:29
Bunuel wrote:
The four integers a, b, c, and d are such that a < b < c < d, d = 7a, and b - a = c - b = d - c. What is the average (arithmetic mean) of the four integers?

(1) c = 25

(2) c/a = 5

b - a = c - b MEANS b is average of a and c..
c - b = d - c MEANS c is average of b and d..
this means a, b,c and d are equally spaced..

since d=7a, terms are $$a,3a,5a,7a$$......
if we know any term, we can get all terms..
average = 4a

(1) c = 25
5a = 25....a=5
average = 4*5=20
sufficient

(2) c/a = 5
nothing new we kcow this info from statement itself
c/a = 5a/a = 5
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink]

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23 Nov 2017, 09:19
a < b < c < d, d = 7a, and b - a = c - b = d - c.. This means that the numbers a, b, c, d are in AP.

Let us assume the numbers to be a, a+x, a+2x, a+3x respectively (x is the common difference here). We are given that a+3x = 7a. This gives us x=2a. So the four numbers a, b, c, d become:- a, 3a, 5a and 7a respectively. Average of these four numbers = 16a/4 = 4a.

So, we need the value of a to find the answer.

(1) c=25. OR 5a=25. This will give us the value of a. Sufficient.

(2) c/a = 5. we have c=5a. So c/a will be 5 only, no matter what the value of a. This doesnt give us any value. Insufficient.

Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a   [#permalink] 23 Nov 2017, 09:19
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