The four integers a, b, c, and d are such that a

Question

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

chetan2u · Accepted Answer

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

amanvermagmat · Answer

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

Archit3110 · Answer

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

RiyaJain69 · Answer

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.

Bunuel · Answer

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.

RiyaJain69 · Answer

Oh! Thank you for sharing this info. I had not checked the timer details. And thanks for all your amazing questions and explanations!

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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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