A, B, C, D and E are five positive integers such that D is the average

Question

A, B, C, D and E are five positive integers such that D is the average of A and E. Which is the largest of the five integers?

(1) (A − E) is negative, and B is not the smallest of all.

(2) (E − C) is negative, and B is not the largest of all.

logro · Answer

Hey - can you kindly provide the source of this question?

globaldesi · Answer

2d = a+e

(1) (A − E) is negative, and B is not the smallest of all.
e, b, d, a, c or c,e, b, d, a, 
Not sufficient
(E − C) is negative, and B is not the largest of all.
a,d,e, b,c 
or
e , c,d, b,a 
not sufficient
combining both 
a, d, b ,e,c
or

a,b, d,e,c
anyways c is the largest

shameekv1989 · Answer

Given :- D is the avg of A and E -> D is not the largest and D lies between A and E. Statement I -> A - E = -ve -> A A < D < E ---> the largest could be B (as it is not the smallest) or C for which no info can be concluded yet -> Not sufficient Statement II -> E - C = -ve -> E the largest could be either A or C -> E Not sufficient Combining -> A A C is the largest Sufficient Answer - C

gmatophobia · Answer

From the main question stem we know -

D is the average of A and E. So if we imagine a number line, D lies in between A and E.

Note, A and E can be on either side of D (as we do not know which out of the two is greater, A or E). So there can be two possible arrangements as shown below -]

Option 1 ) -------A-------D-------E-------
Option 2 ) -------E-------D-------A-------

Statement 1

1) A - E < 0
 A < E

2) B is not the smallest

As A is less than E, it lies to the right of the number line. Hence out of the two options presented above, only Option 1 is in consideration.

From the second point we know that B is not the smallest, therefore B lies to the right of A at any position.

With this constraint in mind out of many possible arrangements, two possibilities are -

-------A-------D-------E-------B

-------A-------D-------E-------C

Hence we see that either B or C can be the largest.

Hence the statement in itself is   not sufficient  .

Statement 2

1) E - C is negative
 E - C < 0 
 E < C

2) B is not the largest

From the first statement we can conclude that E lies to the left of C in a number line.

Also its given that B is not the largest, which means it is not the right most element.

Again, if we look at the possibilities, E and A can be at the right most position.

-------A-------D-------E-------C-------
-------E-------C-------D-------A-------

The other information given is B is not the largest. However, out of the above two possibilities presented, both are valid.

Hence the statement in itself is   not sufficient  .

Combining

From statement 1 - 
Only Option 1 can be considered
A lies to the left of E

From statement 2-
B is not the largest.
E should lie to the left of C

From the largest number perspective, the arrangement is as follows -

-------A-------D-------E-------C-------

Note : B can lie anywhere between A and C; however, the position is immaterial to what's asked in the question.

We can say for sure that C is the largest.

Hence combining the statements we have a definite answer.

Hence C

A, B, C, D and E are five positive integers such that D is the average

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GMAT Data Sufficiency (DS) Questions

A, B, C, D and E are five positive integers such that D is the average

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