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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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Bunuel
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The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   23 Nov 2017, 06:57
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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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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   23 Nov 2017, 07:29
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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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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   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.

Hence A answer
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   15 Jul 2021, 01:52
given
a < b < c < d, d = 7a, and b - a = c - b = d - c
from b - a = c - b = d - c we can say that they are equally spaced
target a+b+c+d /4

#1
c = 25
so b= 15 and a= 5 , d= 35
sufficient
#2
c/a = 5
c=5a
so for any value of a c is 5 times its value , but without any specific value of a we cannot find avg of abcd
insufficient
option A

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
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   17 Jul 2021, 11:13
Hello! What's the difficulty level of this question? Does this come into 600-650 range, or 650-700 or 700+? This bunch of statistics questions is the first time I am attempting GMAT DS questions, not getting any answer right, so want to know the difficulty level of DS questions that are throwing me off. Thanks in advance.
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   17 Jul 2021, 11:20
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RiyaJain69 wrote:
Hello! What's the difficulty level of this question? Does this come into 600-650 range, or 650-700 or 700+? This bunch of statistics questions is the first time I am attempting GMAT DS questions, not getting any answer right, so want to know the difficulty level of DS questions that are throwing me off. Thanks in advance.


You can check difficulty level of a question along with the stats on it in the first post. For this question Difficulty = 700 Level. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   17 Jul 2021, 11:57
Oh! Thank you for sharing this info. I had not checked the timer details. And thanks for all your amazing questions and explanations!

Bunuel wrote:
RiyaJain69 wrote:
Hello! What's the difficulty level of this question? Does this come into 600-650 range, or 650-700 or 700+? This bunch of statistics questions is the first time I am attempting GMAT DS questions, not getting any answer right, so want to know the difficulty level of DS questions that are throwing me off. Thanks in advance.


You can check difficulty level of a question along with the stats on it in the first post. For this question Difficulty = 700 Level. The difficulty level of a question is calculated automatically based on the timer stats from the users which attempted the question.
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink] New post   29 Nov 2022, 03:38
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Re: The four integers a, b, c, and d are such that a < b < c < d, d = 7a [#permalink]
29 Nov 2022, 03:38
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