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!

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions