Is x

Question

Is x < y?

(1) z < y
(2) z < x

Bunuel · Answer

SOLUTION

Is x < y?

(1) z < y
(2) z < x

Even when we combine the statements we just have that x and y are greater than some number z, we clearly cannot say whether x<y.

Answer: E.

beatthegmat05 · Answer

As per my understanding best way will be to eliminate choices.
Since both (1) and (2) does not talk about the relation between x and y so we can eliminate option a,b,d.
We are left with option c and option e .

Now we take following two cases satisfying both given condition z<x and z<y -
x=2, y=3, z=1 -> x<y

x= 10, y=5, z =1 -> x>y

we can see that we can not guarantee the statement x>y by using both condition so answer is (E)-Statements (1) and (2) TOGETHER are NOT sufficient to answer the question

reetskaur · Answer

i) No information about 'x'
ii) No information about 'y'
Combining (i) and (ii), we know that z is less than, both x and why, but we do not know which one of the two (x or y) is greater than the other.
Hence (E)

arunspanda · Answer

Is x < y?

(1) z < y
(2) z < x

Statement 1

Given that  z < y , the relationship between  z  and  x  can not be determined, hence it is not possible to evaluate the inequality  x < y  .........Not Sufficient.

Statement 2

Given that  z < x , the relationship between  z  and  y  can not be determined, hence it is not possible to evaluate the inequality  x < y  .........Not Sufficient.

Combining statements (1) and (2), we have  z  less than both  y  and  x  and this statement is not sufficient to evaluate  x < y .
As an example, the sets (x=3, y=4, z=2) and (x=4, y=3, z=2) satisfy the given inequalities, whereas x and y relation is not unique.

Answer:  (E)

adkikani · Answer

Bunuel   niks18   amanvermagmat

Combining both statements, can we subtract (2) from (1)?

0 < y-x

Adding x to both sides:
x<y.

Bunuel · Answer

No. You can only apply subtraction when their signs are in the opposite directions: If a>b and c and < ) --> a-c>b-d (take the sign of the inequality you subtract from). Example: 3<4 and 5>1 --> 3-5<4-1 . 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 . For more check Manipulating Inequalities .

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Is x < y? (1) z < y (2) z < x

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