If the average height of three people with different heights is 68 inc

Question

If the average height of three people with different heights is 68 inches, is the shortest person more than 60 inches tall?

(1) The height of the tallest person is 72 inches.

(2) One of the persons is 70 inches tall.

amanvermagmat · Answer

Let the heights of three be denoted by a, b, c respectively such that a <= b <= c Given: a+b+c = 3*68 = 204. We have to determine whether a > 60 or not. Now if a=60, then b+c = 204-60 = 144. This means if (b+c) < 144, then definitely a > 60 otherwise not. (1) Given c=72, this means (a+b) = 204-72 = 132. We could have b=72, then a=60. We could also have b=71 ,then a=61. (b could be 72 but not more than 72, since tallest person is 72 inches only) So 'a' may or may not be greater than 60. Not sufficient . (2) One person is 70. Sum of heights of other two = 204-70 = 134. Its possible that out of that 134, one of them is 60 and other is 74. But its also possible that one of them is 61 and other is 73. So 'a' may or may not be greater than 60. Not sufficient . Combining the two statements, one of them (tallest) is 72, other is 70. Their sum = 72+70 = 142. this is < 144, so definitely a will be > 60. (actually a = 204-142 = 62) So sufficient . Hence C answer

GMATinsight · Answer

Let Heights of three people are A, B and C such that A < B < C i.e. A+B+C = 68*3 = 204 Question : Is A > 60? Statement 1 : C = 72 i.e. A+B = 204-72 = 132 But now maximum value of B must be less than 72 as Tallest has height 72 60+72 = 132 therefore if B < 72 then A > 60, Hence SUFFICIENT Statement 2 : One of the persons is 70 inches tall. Case 1: C = 70, B = 69, A = 65 i.e. A > 60 Case 2: C = 80, B = 70, A = 54 i.e. A < 60 NOT SUFFICIENT Answer: Option A

DavidTutorexamPAL · Answer

Since we're asked about the height of the shortest person, we'll look at the extremes of the range.
This is a Logical approach.

(1) If the tallest is 72, we'll try making the second tallest as tall as possible (so that the shortest will be as short as possible).
Then the second tallest is 71.
Since the tallest is 72-68=4 more than average and the second tallest is 71-68=3 more than average,
the shortest needs to balance them out by being 4+3=7 less than average, which is 68 - 7 = 61.
Then our answer is YES.
Sufficient.

(2) Again let's try looking at the extremes. First, say the heights are very different from each other.
Say our tallest is 90 or even 100. Then clearly the shortest must be much less than 60 (we won't bother calculating this!)
Now, let's look at the other extreme - where the heights are very close to each other.
If the tallest is 70, the middle is exactly average, then the shortest needs to be 'opposite' to 70, that is, at 66.
Insufficient.

(A) is our answer.

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.

If the average height of three people with different heights is 68 inc

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

If the average height of three people with different heights is 68 inc

Prep Toolkit

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