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Inequality

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by polter » Mon May 09, 2011 3:04 pm
Is x less than 20?
(1) sum of x and y is less than 20
(2) y is less than 20

My Logic:
x + y < 20 .... (1)
y < 20 ..... (2)

Subtracting (2) from (1), x < 0. Hence my answer is C.


OA [spoiler]Correct Answer = E[/spoiler]
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Source: — Data Sufficiency |
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by djiddish98 » Mon May 09, 2011 4:45 pm
I don't think you can treat 2 inequalities like 2 algebraic equations.

There's no constraint on negative numbers here, so Y could be -20 and X could be 39.
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by cyrwr1 » Mon May 09, 2011 7:22 pm
I'll skip why A,B,D are insufficient.

Combining you know y is less than 20 and the sum of x and y < 20.

Both negative? YEs
X Positive Y Negative? Yes
Both positive ? Yes
Y positive and X negative? Yes

All these are possible so E.

Try with #'s.

set y as 1, x=19 okay less
set y as -10000 X can be positive(or positive>20) or negative

Hence, insuff.
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by polter » Tue May 10, 2011 1:32 am
Thanks for your responses cyrwr1 & djiddish98.

2 Learnings for me.
1.> Not to treat Inequalities as equations.
2.> Easier to substitute numbers
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by cyrwr1 » Tue May 10, 2011 7:43 am
Just one thing I would like to add.

WHen testing #'s that involve fractions, powers or roots.

You need to test 4 ranges:
a value <-1
-1<a value<0
0<a value<1
1<a value

P.s. on a problem in which the values are low(here sum 20), it is much easy to test #'s than doing the possibilities in mind.
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by MAAJ » Tue May 10, 2011 8:38 am
You cannot subtract inequalities neither divide them.
You can combine (sum) inequalities when they have the same INEQ sign (<or>)
You can multiply inequalities when they have the same INEQ sign and if all terms are positive
Also you can use GT(x) or LT(x) to refer to less than or greater than respectively

x + y < 20 -> x < 20 - y
y < 20 -> y = LT(20)

x < 20 - LT(20)
x < GT(1)
x is less than a number greater than 1, in sufficient to answer.
polter wrote:Is x less than 20?
(1) sum of x and y is less than 20
(2) y is less than 20

My Logic:
x + y < 20 .... (1)
y < 20 ..... (2)

Subtracting (2) from (1), x < 0. Hence my answer is C.


OA [spoiler]Correct Answer = E[/spoiler]
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
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