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# Is x less than 20?

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Is x less than 20? [#permalink]  20 Mar 2012, 08:07
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81% (01:21) correct 19% (16:13) wrong based on 287 sessions
Is x less than 20?

(1) The sum of x and y is less than 20.
(2) y is less than 20.
[Reveal] Spoiler: OA

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Re: Is x less than 20? [#permalink]  20 Mar 2012, 08:17
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enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?

Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

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Joined: 23 Jun 2008
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Is x less than 20? [#permalink]  04 Feb 2014, 20:56
nfa1rhp wrote:
Is x less than 20?

1) The sum of x and y is less than 20

2) y is less than 20

I thought working together they would be sufficient but they are not.
[/quote]

Ans E

1 & 2 not sufficient : as difference of two numbers does not implicate their magnitude in any way
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Re: Is x less than 20? [#permalink]  01 Mar 2014, 13:16
but if we solve it like this:
subtract
x+y < 20
y < 20

x+y-y<0
x<0

then x will be certainly less than 20...

Why is this approach flawed ?

Bunuel wrote:
enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?

Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 29679
Followers: 4890

Kudos [?]: 53128 [0], given: 8043

Re: Is x less than 20? [#permalink]  02 Mar 2014, 03:20
Expert's post
mariofelix wrote:
but if we solve it like this:
subtract
x+y < 20
y < 20

x+y-y<0
x<0

then x will be certainly less than 20...

Why is this approach flawed ?

Bunuel wrote:
enigma123 wrote:
Is x < 20?

1. Sum of x and y is less than 20

2. y is less than 20

How come the answer is E and not A?

Consider two cases:
x=30 and y=-15;
x=15 and y=-15;

Both examples satisfy the statements and give different answers to the question whether x<20. Not sufficient.

That's wrong because you cannot subtract inequalities with signs in the same direction.

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 $$5>1$$ --> $$3-5<4-1$$.

Hope it helps.
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Question about DS - Is x less than 20? [#permalink]  21 Jul 2014, 15:55
Hi All,

I have a question regarding a data sufficiency problem.

Is x less than 20?

1) x + y < 20
2) y is less than 20

My question refers to 1.). In this case, since it says x + y, can we plug in a negative number in for y even with a + sign in front of it?

ex. if x=25, y=-8,
25 + (-8) = 17
we do not know if x<20, therefore INSUFFICIENT

I am sure this question is pretty basic to most, but it is these small details that seem to throw me off while solving DS problems. Any advice would be very helpful.

BTW - This question is from the CAT on GMATPrep software.

Thanks,
Mike
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Posts: 29679
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Kudos [?]: 53128 [0], given: 8043

Re: Is x less than 20? [#permalink]  22 Jul 2014, 02:24
Expert's post
MikeA2606 wrote:
Hi All,

I have a question regarding a data sufficiency problem.

Is x less than 20?

1) x + y < 20
2) y is less than 20

My question refers to 1.). In this case, since it says x + y, can we plug in a negative number in for y even with a + sign in front of it?

ex. if x=25, y=-8,
25 + (-8) = 17
we do not know if x<20, therefore INSUFFICIENT

I am sure this question is pretty basic to most, but it is these small details that seem to throw me off while solving DS problems. Any advice would be very helpful.

BTW - This question is from the CAT on GMATPrep software.

Thanks,
Mike

Merging similar topics. Please refer to the discussion above.

As for your question: y is some number, it could be negative, positive or 0. So, you can plug any number you want there.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, and 7. Thank you.

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Re: Is x less than 20?   [#permalink] 22 Jul 2014, 02:24
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