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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How is it not D?
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Brent@GMATPrepNow
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Target question: Is x + n < 0?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
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
Cheers,
Brent
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j_shreyans
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Brent@GMATPrepNow wrote:Target question: Is x + n < 0?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
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
Hi Brent ,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
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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Brent@GMATPrepNow
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1) When dealing with inequalities, we can ADD or SUBTRACT the same quantity to/from both sides, and the inequality remains valid.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.
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.
Cheers,
Brent
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j_shreyans
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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..
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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Brent@GMATPrepNow
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Those two pairs of values yield the same answer to the target question (YES, x+y IS less than 0}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..
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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Matt@VeritasPrep
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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.
