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How is it not D?

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How is it not D?

by Rastis » Wed Oct 08, 2014 7:34 am
If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n - 1

(2) -2x > 2n
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by Brent@GMATPrepNow » Wed Oct 08, 2014 8:00 am
Rastis wrote:If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n - 1
(2) -2x > 2n
Target question: Is x + n < 0?

Given: x and n are integers

Statement 1: x + 3 < n - 1
Add 1 to both sides to get: x + 4 < n
In other words, n is GREATER than 4 more than x
There are several values of x and n that satisfy this condition. Here are two:
Case a: x = 1 and n = 6, in which case x + n = 7. In this case, x + n > 0
Case b: x = -10 and n = 0, in which case x + n = -10. In this case, x + n < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -2x > 2n
Add 2x to both sides to get: 0 > 2x + 2n
Divide both sides by 2 to get: 0 > x + n. PERFECT! This is precisely what the target question is asking.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

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by Rastis » Wed Oct 08, 2014 8:42 am
Thanks, Brent. Number properties are always a challenge for me.
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by j_shreyans » Wed Oct 08, 2014 9:57 am
Brent@GMATPrepNow wrote:
Rastis wrote:If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n - 1
(2) -2x > 2n
Target question: Is x + n < 0?

Given: x and n are integers

Statement 1: x + 3 < n - 1
Add 1 to both sides to get: x + 4 < n
In other words, n is GREATER than 4 more than x
There are several values of x and n that satisfy this condition. Here are two:
Case a: x = 1 and n = 6, in which case x + n = 7. In this case, x + n > 0
Case b: x = -10 and n = 0, in which case x + n = -10. In this case, x + n < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: -2x > 2n
Add 2x to both sides to get: 0 > 2x + 2n
Divide both sides by 2 to get: 0 > x + n. PERFECT! This is precisely what the target question is asking.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Hi Brent ,

Few things which i need to ask.

1) How can we add 2x on both side because we don't know whether x is positive or negative.
2) If I solve statement 2: -2x > 2n with out changing and test the values this statement is not sufficient. I am getting the YES or NO if i test the value

Pls suggest me and correct me if i am wrong.
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by Brent@GMATPrepNow » Wed Oct 08, 2014 10:41 am
j_shreyans wrote: Hi Brent ,

Few things which i need to ask.

1) How can we add 2x on both side because we don't know whether x is positive or negative.
2) If I solve statement 2: -2x > 2n with out changing and test the values this statement is not sufficient. I am getting the YES or NO if i test the value

Pls suggest me and correct me if i am wrong.
1) When dealing with inequalities, we can ADD or SUBTRACT the same quantity to/from both sides, and the inequality remains valid.
If we DIVIDE or MULTIPLY both sides by a NEGATIVE value, the inequality gets REVERSED.
If we DIVIDE or MULTIPLY both sides by a POSITIVE value, the inequality remains the same.
So, for example, if we have the inequality 2x < x, we cannot divide both sides by x (to get x < 1) because we don't know whether x is positive or negative. However, we can subtract x from both sides to get x < 0.

2) You are getting YES and NO answers to the target question when you plug in values for x and n that satisfy the condition that -2x > 2n?
Please tell me what values you're plugging in, and we'll go from there.

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Brent
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by j_shreyans » Thu Oct 09, 2014 3:38 am
Hi Brent ,

Thanks for your help , it really helps.

Regarding the statement 2- I re checked the values and i got the answer thanks.

statement 2: -2x > 2n

if x= -10 then max n will be 9

Target = -10+9 will be -1 which is less than 0 ......sufficient

If x=10 then n max will be -11

target = 10+(-11) will be -1 which is less than 0 ........sufficient

Pls check and correct me if i am wrong..
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by Brent@GMATPrepNow » Thu Oct 09, 2014 6:38 am
j_shreyans wrote:Hi Brent ,

Thanks for your help , it really helps.

Regarding the statement 2- I re checked the values and i got the answer thanks.

statement 2: -2x > 2n

if x= -10 then max n will be 9

Target = -10+9 will be -1 which is less than 0 ......sufficient

If x=10 then n max will be -11

target = 10+(-11) will be -1 which is less than 0 ........sufficient

Pls check and correct me if i am wrong..
Those two pairs of values yield the same answer to the target question (YES, x+y IS less than 0}
Of course, if you're going to plug/test values, two cases that yield the same answer to the target question might not provide the CONCLUSIVE evidence some people require to conclude that the answer to the target question will ALWAYS be "yes."

An algebraic solution (as I have provided) is 100% conclusive.

Cheers,
Brent
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by Matt@VeritasPrep » Sun Oct 12, 2014 9:59 pm
Just to piggyback on this: if a question (or statement) gives you x - y but wants x + y, you are rarely able to do this without significant additional information. I've torn out so much hair over the years trying to work with problems that ask you to go from (x - y) to (x + y): it seems so close, but it's so far away! So beware of a DS question that gives, say, x - n when it wants x + n; such a statement (like S1 here) is typically NOT sufficient.
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