in case
set X={1,4,5,6}
set Y={-1,4,5,6}
(1) no -> sufficient from set X
(2) no(from set X), yes(from set Y) -> insufficinet
therefore A
Is it right?
Interesting Set problem - Gmat800
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
Stuart@KaplanGMAT
- GMAT Instructor
- Posts: 3225
- Joined: Tue Jan 08, 2008 2:40 pm
- Location: Toronto
- Thanked: 1710 times
- Followed by:614 members
- GMAT Score:800
Just a quick note:
(1) is not sufficient alone.
The range of {1, 4, 14} is 13. Adding 13 to the set doesn't increase the range.
The range of {50, 51, 63} is 13. Adding 13 to the set does increase the range.
We can get both a yes and a no, insufficient.
(1) is not sufficient alone.
The range of {1, 4, 14} is 13. Adding 13 to the set doesn't increase the range.
The range of {50, 51, 63} is 13. Adding 13 to the set does increase the range.
We can get both a yes and a no, insufficient.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
-
netigen
- Legendary Member
- Posts: 631
- Joined: Mon Feb 18, 2008 11:57 pm
- Thanked: 29 times
- Followed by:3 members
This is the solution I found for this Q
1. A is insufficient for the reason noted by Stuart above
2. Lets look at option 2
Avg of set A(n) = Total of Set A(n) / n (assuming n=numbers in set A)
Avg of set A(n+1) = Total of Set A(n) + R/ (n+1) < R
Total of Set A(n) + R < R (n+1)
Total of Set A(n) + R < Rn + R
or Total of Set A(n) / n < R
which means that Avg of set A(n) < R
This means that there are number less than and greater than R in the A hence the range will not increase by addition of R hence the ans C
1. A is insufficient for the reason noted by Stuart above
2. Lets look at option 2
Avg of set A(n) = Total of Set A(n) / n (assuming n=numbers in set A)
Avg of set A(n+1) = Total of Set A(n) + R/ (n+1) < R
Total of Set A(n) + R < R (n+1)
Total of Set A(n) + R < Rn + R
or Total of Set A(n) / n < R
which means that Avg of set A(n) < R
This means that there are number less than and greater than R in the A hence the range will not increase by addition of R hence the ans C
-
ricaototti
- Junior | Next Rank: 30 Posts
- Posts: 29
- Joined: Wed Feb 27, 2008 4:56 am
- Thanked: 2 times
I am sorry but I really dont get it why it should be C.
I think it should be E.
I understand why 1 and 2 are wrong... but not why C is correct. Please, can someone explain it better.
Thanks
I think it should be E.
I understand why 1 and 2 are wrong... but not why C is correct. Please, can someone explain it better.
Thanks
-
parallel_chase
- Legendary Member
- Posts: 1153
- Joined: Wed Jun 20, 2007 6:21 am
- Thanked: 146 times
- Followed by:2 members
Clearly statement I and II alone are insufficient for the same reasons mentioned by Stuart.netigen wrote:This is an interesting Range problem. I am trying to figure out the best approach to solve it
Combining I & II
New number added = R
all the number in the set are positive
NEW MEAN of the set with NEW NUMBER added is less than R.
4,4,4
range = 0
mean = 4
new number= 0
0,4,4,4
mean=3
range=4
Range increased from 0 to 4
2,4,8
range=6
new number=6
2,4,6,8
mean=5
range=6
range remains the same.
Hence E.
I dont know how OA can be C, or am i missing something.
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
The range of a set A is R. A number having a value of R is added to set A. Will the range of set A increase?
1) All numbers in set A are positive.
2) The mean of the new set is smaller than R.
I think the above posts confirm that the answer is either C or E, so I won't bother looking at the statements individually. Let's look at both statements together.
When we add R to set A, the range will only increase if R is either the largest element in the new set, or the smallest element in the new set. We want to know if R could be the largest or the smallest element in the new set.
Let's assume A contains at least two elements, and call the largest g, and the smallest s. So set A is {s, other stuff, g}. Then R = g - s. From this, because g and s are positive, R must be less than g. So R can't be the largest element in the new set.
The only question is whether R might be the smallest; that is, we want to know if it's possible that R < s. This would make R smaller than everything else in the set, since s was the smallest element of the old set. But if R is the smallest element of the new set, there's no way statement 2 could be true; the mean of a set cannot be smaller than its smallest element. So R can neither be the smallest nor the largest element in the set, and the range of the new set must be equal to the range of the old set. Sufficient. C.
1) All numbers in set A are positive.
2) The mean of the new set is smaller than R.
I think the above posts confirm that the answer is either C or E, so I won't bother looking at the statements individually. Let's look at both statements together.
When we add R to set A, the range will only increase if R is either the largest element in the new set, or the smallest element in the new set. We want to know if R could be the largest or the smallest element in the new set.
Let's assume A contains at least two elements, and call the largest g, and the smallest s. So set A is {s, other stuff, g}. Then R = g - s. From this, because g and s are positive, R must be less than g. So R can't be the largest element in the new set.
The only question is whether R might be the smallest; that is, we want to know if it's possible that R < s. This would make R smaller than everything else in the set, since s was the smallest element of the old set. But if R is the smallest element of the new set, there's no way statement 2 could be true; the mean of a set cannot be smaller than its smallest element. So R can neither be the smallest nor the largest element in the set, and the range of the new set must be equal to the range of the old set. Sufficient. C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
GMAT/MBA Expert
-
Ian Stewart
- GMAT Instructor
- Posts: 2623
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
You can't use this example; the mean of the new set is not less than R, the range of the first set, which is zero. This set thus doesn't conform with the information in Statement 2.parallel_chase wrote:
New number added = R
all the number in the set are positive
NEW MEAN of the set with NEW NUMBER added is less than R.
4,4,4
range = 0
mean = 4
new number= 0
0,4,4,4
mean=3
range=4
