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# If w and c are integers is w > 0 ? (1) w + c > 50 (2)

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Manager
Joined: 28 Aug 2010
Posts: 172
If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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16 Dec 2010, 04:28
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25% (medium)

Question Stats:

81% (01:02) correct 19% (01:04) wrong based on 276 sessions

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If w and c are integers is w > 0 ?

(1) w + c > 50
(2) c > 48
Manager
Status: Preparing for GMAT - March 2011
Joined: 21 May 2010
Posts: 116
Location: London
Schools: INSEAD, RSM, HEC, St. Gallen, IF, IESE
WE 1: Finance 6 years
Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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16 Dec 2010, 04:53
ajit257 wrote:
If w and c are integers is w > 0 ?

(1) w + c > 50
(2) c > 48

I have a doubt the ans.

Statement (1) is not SUFFICIENT

w + C > 50
Pick the numbers w=3 & C= 50 where W>0
Now if i pick W=-3 & C=60 , the statement still holds good but in this case W<0
Hence we cannot determine if W<0 or if W>0

Statement (2) is not SUFFICIENT
as it does not reflect anything about the value of W.

Even if we take these two statements together, we cannot determine if W>0 or not.
(i)Pick number since C>48 therefore pick C=49
which mean W+49>50 therefore W has to be greater than or equal to 2

(ii) If C = 52 then W could be W=0, W>0 or W=-1 hence insufficient.

Cheers!!
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Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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16 Dec 2010, 05:12
2
ajit257 wrote:
If w and c are integers is w > 0 ?

(1) w + c > 50
(2) c > 48

I have a doubt the ans.

Obviously each statement alone is not sufficient.

When taken together we can still have both Yes and No answers: if c=100 and w=10 then the answer is Yes but if c=100 and w=-10 then the answer is No.

I feel that it should be w+c<50 for (1). Then as $$c$$ is an integer then the least value of it according to (2) will be 49, so max value of $$w$$ in order $$c+w$$ to be less than 50 is 0 (as $$w$$ is also an integer), which means that the answer to the question is $$w>0$$ is No. So, if it were $$w + c < 50$$ the answer would be C and also the question would be much more interesting.

Hope it's clear.
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Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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17 Dec 2010, 04:32
Bunuel wrote:
ajit257 wrote:
If w and c are integers is w > 0 ?

(1) w + c > 50
(2) c > 48

I have a doubt the ans.

Obviously each statement alone is not sufficient.

When taken together we can still have both Yes and No answers: if c=100 and w=10 then the answer is Yes but if c=100 and w=-10 then the answer is No.

I feel that it should be w+c<50 for (1). Then as $$c$$ is an integer then the least value of it according to (2) will be 49, so max value of $$w$$ in order $$c+w$$ to be less than 50 is 0 (as $$w$$ is also an integer), which means that the answer to the question is $$w>0$$ is No. So if it were $$w + c < 50$$ the answer would be C and also the question would be much more interesting.

Hope it's clear.

Bunuel, taking the qtn as you specified i.e. w+c<50 Please clarify why am i getting w < 2
1) $$w+c<50$$
2) $$c > 48$$

now 2) can be written as $$-c < -48$$
as both the inequalities have the same sign, 1) + 2)
==> $$w < 50-48$$
==> $$w< 2$$
why am i not getting $$w <= 0$$ for the answer to be C

Regards,
Murali.
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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17 Dec 2010, 05:04
1
muralimba wrote:
Bunuel wrote:
ajit257 wrote:
If w and c are integers is w > 0 ?

(1) w + c > 50
(2) c > 48

I have a doubt the ans.

Obviously each statement alone is not sufficient.

When taken together we can still have both Yes and No answers: if c=100 and w=10 then the answer is Yes but if c=100 and w=-10 then the answer is No.

I feel that it should be w+c<50 for (1). Then as $$c$$ is an integer then the least value of it according to (2) will be 49, so max value of $$w$$ in order $$c+w$$ to be less than 50 is 0 (as $$w$$ is also an integer), which means that the answer to the question is $$w>0$$ is No. So if it were $$w + c < 50$$ the answer would be C and also the question would be much more interesting.

Hope it's clear.

Bunuel, taking the qtn as you specified i.e. w+c<50 Please clarify why am i getting w < 2
1) $$w+c<50$$
2) $$c > 48$$

now 2) can be written as $$-c < -48$$
as both the inequalities have the same sign, 1) + 2)
==> $$w < 50-48$$
==> $$w< 2$$
why am i not getting $$w <= 0$$ for the answer to be C

Regards,
Murali.

First of all:
You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

So, you can directly subtract $$c > 48$$ from $$w+c<50$$: $$w+c-c<50-48$$ --> $$w<2$$ (no need to rewrite and then add). But this approach won't work for this question: $$w<2$$ would be correct if we were not told that both $$w$$ and $$c$$ are integers then for example c=48.5>48 and w=1>0 would be valid solutions but since both must be integers then $$c$$ can be 49, 50, 51 ... and $$w$$ can be 0, -1, -2, ... (so c=integer>48 and w=integer<1)

Hope it's clear.
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Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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17 Dec 2010, 05:38
oops. Those are integers. Yes this will not apply in case of integers.
I missed it out.

Thanks Bunuel. Kudos for u...

regards,
Murali.
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Joined: 09 Sep 2013
Posts: 9863
Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)  [#permalink]

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04 Sep 2018, 06:30
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Re: If w and c are integers is w > 0 ? (1) w + c > 50 (2)   [#permalink] 04 Sep 2018, 06:30
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