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# Is x less than 20?

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General Discussion
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Is x less than 20? [#permalink]
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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]
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.

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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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Re: Is x less than 20? [#permalink]
For people like me who like equations (especially under time pressure of the GMAT)

For C=>

Just add 1 + 2 (same sign) to get:
x + 2y < 40
x < 40 - 2y

Its then clear x can be any number - depending on y - and less/more than 20... So E.

Further (not needed but why not), the range of x would be:
x > 2y -40
x > 2(20) -40 ( y < 20, so max y ~ 20)
x > 0
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rahsin wrote:
Is x less than 20 ?

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

2. y is less than 20.

Statement 1

x+y<20

say x=5, y=14, sum is 19. so x+y < 20. Also x is less than 20.

Now take x=25, y=-16, sum is 9. so x+y < 20. BUT x is more than 20.

So not sufficient

Statement 2
This statement does not say anything about x. Clearly Not sufficient.

Combining Statements 1 and 2

Our above examples will suit the purpose, as in both cases y is less than 20.

say x=5, y=14, sum is 19. so x+y < 20. Also y is less than 20. Here x is less than 20
Now take x=25, y=-16, sum is 9. so x+y < 20. Also y < 20. BUT x is more than 20.

So even after combining Not sufficient.

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Is x less than 20 ?
(1) The sum of x and y is less than 20.
(2) y is less than 20.

Solution:

Answer should be E. Here it is how:

1: x+y < 20 ---> tells us nothing about y or x. say x=24, y= -10 then x < 20 No. Say x = 17 y =1 then x <20 Yes. --- > Insufficient.
2: y <20 , nothing is told about x. ----> clearly insufficient.

Combined.
x+y < 20 and y <20. Again, use the example given in statement 1. If x=24, y= -10 then x < 20 No. If x = 17, y =1 then x <20 Yes.

Please give kudos if this helps!
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Re: Is x less than 20? [#permalink]
rraghun wrote:
Is x less than 20 ?
(1) The sum of x and y is less than 20.
(2) y is less than 20.

Required: Is x < 20?
Statement 1: x + y < 20
Case 1: x = 1, y = 18
Case 2: x = 21, y = -29
Nothing can be said about x
INSUFFICIENT

Statement 2: y < 20
This does not give us anything about x
INSUFFICIENT

Combining both statements: x + y < 20 and y < 20
Case 1: x = 21, y = -2
Case 2: x = 18, y = 1
Still nothing can be said about x
INSUFFICIENT

Correct Option: E

Does this help?
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Re: Is x less than 20? [#permalink]
enigma123 wrote:
Is x less than 20?

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

(1) The sum of x and y is less than 20.
x+y<20 ; infinite possible values of x ; NOT SUFFICIENT

(2) y is less than 20
Doesn't even talk about x; NOT SUFFICIENT

MERGING
x+less than 20<20
Case 1 ) Y is negative
x+(-30)<20 ==> x<50 {{{ Is x less than 20? = NO}}}

Case 1 ) Y is Positive
x+14<20 ==> x<6 {{{Is x less than 20? =YES}}}

NOT SUFFICIENT

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Re: Is x less than 20? [#permalink]
Statement 1: (x + y) < 20
Possible combinations,
1. x = 50, y = -10
2. x = 10, y = 5
so, value of x can be more than 20 or less than 20 we don't know about that.

Not sufficient

Statement 2: No information regarding x.

Not sufficient

1 & 2 Together: Same examples as in statement 1.

Not sufficient

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Re: Is x less than 20? [#permalink]
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enigma123 wrote:
Is x less than 20?

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

Target question: Is x less than 20?

When I scan the two statements, I can quickly see that neither statement alone is sufficient.
So let's jump straight to....
.
.
.

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 5 and y = 5. In this case, the answer to the target question is YES, x is less than 20
Case b: x = 30 and y = -30. In this case, the answer to the target question is NO, x is not less than 20
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Is x less than 20? [#permalink]
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enigma123 wrote:
Is x less than 20?

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

Nowhere is mentioned that y is positive. so any value can be x have.
not enough information to arrive at solution.

IMO E
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Re: Is x less than 20? [#permalink]
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Re: Is x less than 20? [#permalink]
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