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.
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Ans E

1 & 2 not sufficient : as difference of two numbers does not implicate their magnitude in any way

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 ?

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

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html


Hope it helps.
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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

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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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

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.

(E) is the answer.

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.

Hence answer should be E.

Please give kudos if this helps!

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?

(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.

Not sufficient

Statement 2: No information regarding x.

Not sufficient

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

Not sufficient

The correct answer is E.
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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

Answer: E

Cheers,
Brent
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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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