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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.

Answer: E.

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

ADDING/SUBTRACTING INEQUALITIES:

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 \(5>1\) --> \(3-5<4-1\).

Question about DS - Is x less than 20? [#permalink]

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21 Jul 2014, 16:55

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.

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.

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.

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.

(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

ANSWER SHOULD BE E
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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.

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