M24 Q 33

icandy · **Posted:** Thu Mar 12, 2009 1:59 pm

If sets S and T are united into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers

[Reveal] Spoiler: OA

E

Source: GMAT Club Tests - hardest GMAT questions

I will let you guys discuss this. How ever, The two Set opeartions I remember are union and intersection. How are we supposed to interpret merge.

x2suresh · **Posted:** Thu Mar 12, 2009 6:06 pm

icandy wrote:

If sets S and T are merged into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers

(C) 2008 GMAT Club - m24#33

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I will let you guys discuss this. How ever, The two Set opeartions I remember are union and intersection. How are we supposed to interpret merge.

I believe two operations and "union" and "union all" --> if you know ORACLE sql LANGUAGE. :lol:

( I may be wrong.. but thats what I interpret.. as IT .. nerd)

e.g
A ={1,3} B={1,5}

Merge = {1,3,5} ( all distinct elements) avg = 3
Sum = {1,1,3,5} avg= 10/4 = 2.5

another e.g.
A ={1,5} B={3,5}
Merge = {1,3,5} ( all distinct elements) avg = 3
Sum = {1,3,5,5} avg= 14/4 = 3.66

I will go with E.

Economist · **Posted:** Fri Mar 27, 2009 9:47 am

Couldnt get this!!
It is sum of the means of A and B.
e.g
A ={1,3} B={1,5}

Merge = {1,3,5} ( all distinct elements) avg = 3
Sum = {1,1,3,5} avg= 10/4 = 2.5 >> cant understand this.

Sum of means should be 2 + 3 = 6.May be my understanding is wrong. Please explain.

x2suresh wrote:

icandy wrote:

If sets S and T are merged into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers

(C) 2008 GMAT Club - m24#33

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

I will let you guys discuss this. How ever, The two Set opeartions I remember are union and intersection. How are we supposed to interpret merge.

I believe two operations and "union" and "union all" --> if you know ORACLE sql LANGUAGE. :lol:

( I may be wrong.. but thats what I interpret.. as IT .. nerd)

e.g
A ={1,3} B={1,5}

Merge = {1,3,5} ( all distinct elements) avg = 3
Sum = {1,1,3,5} avg= 10/4 = 2.5

another e.g.
A ={1,5} B={3,5}
Merge = {1,3,5} ( all distinct elements) avg = 3
Sum = {1,3,5,5} avg= 14/4 = 3.66

I will go with E.

GMAT TIGER · **Posted:** Sun Mar 29, 2009 7:37 pm

icandy wrote:

If sets S and T are merged into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers

I will let you guys discuss this. How ever, The two Set opeartions I remember are union and intersection. How are we supposed to interpret merge.

For me merged = combined.

1: S and T are one-element sets
If S = T = 2, mean of the merged set (2, 2) = 2 and sum of the means of sets S and T is 4.
If S = 2, and T = -2, mean of the merged set (2, -2) = 0 and sum of the means of sets S and T is 0.
If S = 0, and T = 0, mean of the merged set (2, 2) = 0 and sum of the means of sets S and T is 0. NSF..

2: Neither set S nor set T contains negative numbers
If S = T = 2, mean of the merged set (2, 2) = 2 and sum of the means of sets S and T is 4.
If S = 0, and T = 0, mean of the merged set (2, 2) = 0 and sum of the means of sets S and T is 0. NSF.

Togather alos nsf.
E.

tharunv · **Posted:** Sun Mar 29, 2009 8:39 pm

Answer should be E - not sufficient in any of the cases.
What's the OA?

dzyubam · **Posted:** Mon Mar 30, 2009 3:32 am

The OA is E.

Do you guys think we should replace "merged" with "united" in the question stem?

Economist · **Posted:** Sun Apr 05, 2009 1:59 am

Yes that should be better...United or union of two sets....merged is confusing

dzyubam wrote:

The OA is E.

Do you guys think we should replace "merged" with "united" in the question stem?

topmbaseeker · **Posted:** Thu Mar 11, 2010 6:22 am

Merge of sets means you need to combine.

S= {1}
T= {1,2}

Merge = {1,1,2}

vshrivastava · **Posted:** Thu Mar 11, 2010 7:07 am

Both solution 1 and 2 fail the zero test.

S1: S = {0} and T = {0} => Mean of S = 0 and Mean of T = 0
Set ST = {0, 0} => Mean of ST = 0
Thus, S1 is not sufficient.

S2. Neither S nor T contain negative number.
Take the same sets: S = {0} and T = {0}
S2 is not sufficient.

Answer is E.

bangalorian2000 · **Posted:** Thu Mar 11, 2010 7:35 am

icandy wrote:

If sets S and T are united into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1. S and T are one-element sets
2. Neither set S nor set T contains negative numbers

[Reveal] Spoiler: OA

E

Source: GMAT Club Tests - hardest GMAT questions

s= {1,2,3}
mean1 = 2
t= {2,3,4}
mean2 = 3
sUt= {1,2,3,4}
mean3= 2.5 < mean1 + mean2

s={-1,-2,-3}
mean1 = -2
t={-2,-3,-4}
mean2 = -3
sUt= {-1,-2,-3,-4}
mean3 = -2.5 > mean1 + mean2

s={0}
mean1 = 0
t = {0}
mean2 = 0
sUt = {0}
mean3 = 0 = mean1+mean2

hence none of the two stmts solve this questions. Hence E.

firasath · **Posted:** Thu Mar 11, 2010 3:26 pm

vshrivastava wrote:

Both solution 1 and 2 fail the zero test.

S1: S = {0} and T = {0} => Mean of S = 0 and Mean of T = 0
Set ST = {0, 0} => Mean of ST = 0
Thus, S1 is not sufficient.

S2. Neither S nor T contain negative number.
Take the same sets: S = {0} and T = {0}
S2 is not sufficient.

Answer is E.

You only showed that you can answer the question with a definite NO.
The question being "will the mean of this set be smaller than the sum of means of sets S and T ?"

This sufficiently answers the question as a NO for both cases.

In order for the cases to be insufficient, you need to be able answer the question with both a yes and a no.

hardnstrong · **Posted:** Sun Mar 14, 2010 1:53 am

friends
i understand that both options failed the zero test but why do we need a zero in set

ex- a set of 3 pen, 2 pencil and 0 flower
we can simply say it a set of 3 pen and 2 pencils, why do we consider something like zero in a set

Please explain

sidhu4u · **Posted:** Fri Mar 19, 2010 7:18 am

hardnstrong wrote:

friends
i understand that both options failed the zero test but why do we need a zero in set

ex- a set of 3 pen, 2 pencil and 0 flower
we can simply say it a set of 3 pen and 2 pencils, why do we consider something like zero in a set

Please explain

Zero is considered as an entity here.
like A has 0 sets of readings 2m , 0m, 1m
so zero is the value.

gmatbull · **Posted:** Sat Mar 20, 2010 5:23 am

hardnstrong wrote:

friends
i understand that both options failed the zero test but why do we need a zero in set

ex- a set of 3 pen, 2 pencil and 0 flower
we can simply say it a set of 3 pen and 2 pencils, why do we consider something like zero in a set

Please explain

"zero" in this case does not imply an empty set; rather, it it a set consisting of an element-digit 0.

hardnstrong · **Posted:** Sat Mar 20, 2010 7:48 am

thanks ...........sidhu n gmatbull

mailpravs · **Posted:** Mon Sep 06, 2010 11:36 pm

E.

phuongle · **Posted:** Wed Dec 08, 2010 2:45 am

I think the answer should be C.
(1) and (2) says S = {s} (mean = s) and T = {t} (mean = t), united = {s, t} (mean = (s+t)/2)
s, t = non negative.
Question: s+t < (s+t)/2 ????
If s = t = 0, the answer to the question "will the mean of this set be smaller than the sum of means of sets S and T?" is NO.
If s = 0, t > 0 (and vice versa), the answer to question "will the mean of this set be smaller than the sum of means of sets S and T?" is NO.
If s, t > 0, the answer to the question "will the mean of the set be smaller than the sum of means of sets S and T?" is still NO.
In any case, the answer is still NO. Then (1) and (2) together are sufficient enough.
Why is E the correct answer????

subhashghosh · **Posted:** Tue Mar 15, 2011 5:19 am

The answer is E.

Let A = {2}, B = {3},

So the mean of merge is 2.5, which is < 5

Let A = {1}, B = {1}

So the mean of merge is 1, which is equal to mean of either set.

rongali · **Posted:** Tue Mar 15, 2011 6:38 am

yes it is E...failure case is when they have 0 as an element

rajeshaaidu · **Posted:** Tue Mar 15, 2011 9:48 pm

firasath wrote:

vshrivastava wrote:

Both solution 1 and 2 fail the zero test.

S1: S = {0} and T = {0} => Mean of S = 0 and Mean of T = 0
Set ST = {0, 0} => Mean of ST = 0
Thus, S1 is not sufficient.

S2. Neither S nor T contain negative number.
Take the same sets: S = {0} and T = {0}
S2 is not sufficient.

Answer is E.

You only showed that you can answer the question with a definite NO.
The question being "will the mean of this set be smaller than the sum of means of sets S and T ?"

This sufficiently answers the question as a NO for both cases.

In order for the cases to be insufficient, you need to be able answer the question with both a yes and a no.

I think, vshrivastava has shown that both statement put together also we are getting two answer: one time > and other time =. This much is enough to tell that answer is E.

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M24 Q 33

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