Proportions and sets

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Carloselopez: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Sep 08, 2013 5:05 pm

by Carloselopez » Sun Sep 08, 2013 5:52 pm

The average height of a group of 5 people is 70 inches. What is the height of the shortest person in the group?

1) If the shortest person left the group, the average height of the group would be 72,5 inches.

2) The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4.

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Source: Beat The GMAT — Data Sufficiency | Sun Sep 08, 2013 5:52 pm

Java_85: Master | Next Rank: 500 Posts; Posts: 234; Joined: Tue Jul 16, 2013 9:00 am; Location: West Virginia; Thanked: 9 times

by Java_85 » Sun Sep 08, 2013 8:37 pm

It's a little tricky question, IMO A is the answer. Here is why.

We've 5 people. the average for 4 of them is 72.5 and for 5 of them 70 ==> ((4*72.5)+(1*Shortest))/5=70 ==> using this equation shortest height can be calculated. ==> (1) is sufficient. ==> A or D

Using (2) we can't calculate the shortest person height because we just have a ratio==> A it is.

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Sun Sep 08, 2013 9:25 pm

Carloselopez wrote:The average height of a group of 5 people is 70 inches. What is the height of the shortest person in the group?

1) If the shortest person left the group, the average height of the group would be 72,5 inches.

2) The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4.

We need to know the total weight of the group before and after a person is removed or that person goes out or another person comes into the group.

Here statement 1 provides exactly the information we need, hence sufficient.

Statement gives a ratio between the tallest and shortest that cannot be used to find who is the shortest, because it relative to only 2 of them.

A

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 09, 2013 7:15 am

Carloselopez wrote:The average height of a group of 5 people is 70 inches. What is the height of the shortest person in the group?

1) If the shortest person left the group, the average height of the group would be 72.5 inches.

2) The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4.

Target question: What is the height of the shortest person in the group?

Given: The average height of a group of 5 people is 70 inches.
So, the sum of all 5 heights = (5)(70) = 350 inches

Statement 1: If the shortest person left the group, the average height of the group would be 72.5 inches
If the average height of 4 people is 72.5 inches, then the sum of the 4 heights = (4)(72.5) = 290 inches
The total height went from 350 inches to 290 inches (a 60-inch difference), so the shortest person in the group must be 60 inches tall
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The ratio of height of the tallest person in the group to the height of the shortest person in the group is 5:4
As vinay1983 and Java_85 noted, this statement is not sufficient. To show this, consider these two conflicting cases:
Case a: the heights are {60, 71, 72, 72, 75} in which case the shortest person in the group is 60 inches tall
Case b: the heights are {64, 68, 68, 70, 80} in which case the shortest person in the group is 64 inches tall
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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s.vishnu: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Mon Jan 02, 2012 6:20 am; Thanked: 2 times

by s.vishnu » Tue Sep 10, 2013 7:07 am

Dear Brent/All,
Sorry if this is a silly question-what if the question statement also mentioned that the heights were in Arithmetic progression or progression .Can statement 2 still not be used sufficiently ?It can be,am i correct?

Regards,[/list][/quote]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Sep 10, 2013 7:31 am

s.vishnu wrote:Dear Brent/All,
Sorry if this is a silly question-what if the question statement also mentioned that the heights were in Arithmetic progression or progression .Can statement 2 still not be used sufficiently ?It can be,am i correct?

Regards,

No, that condition would not change things for statement 2. Consider these two cases:
Case a: the heights are {60, 63.75, 67.5, 71.25, 75} in which case the shortest person in the group is 60 inches tall
Case b: the heights are {64, 68, 72, 76, 80} in which case the shortest person in the group is 64 inches tall

The same would apply to a geometric progression.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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