If x and y are integers and x + y = 5, which of the followin

Question

If x and y are integers and x + y = 5, which of the following must be true?

A) x and y are consecutive integers.

B) If x < 0, then y > 0.

C) If x > 0, then y < 0.

D) Both x and y are even.

E) Both x and y are less than 5.

Bunuel · Answer

If x and y are integers and x + y = 5, which of the following must be true? Note that the question asks which of the following MUST be true, not COULD be true. A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4; B. If x < 0, then y > 0: if x is negative then y must be positive so that x+y to equal to positive 5, so this statement must be true; C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4; D. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5; E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1; Answer: B. Hope it's clear.

surendar26 · Answer

In option C if x > 0,then y<0 means x is +ve and y is -ve In option B if x < 0, then y>0 means y is +ve and x is -ve, both are same and satisfying x+y = 5. How option B is right could you explain

Bunuel · Answer

No, these options are not the same.

Option C says: if x is positive then y must be negative which is not necessarily true, take for example x=1 and y=4;

Option B says: if x is negative then y must be positive which must be true: given that y=5-x, so if x is negative then y=5-x=5-(negative)=5+positive=positive.

Hope it's clear.

preetamsaha · Answer

A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4;

B. If x < 0, then y > 0: if x is negative then y must be positive so that x+y to equal to positive 5, so this statement must be true;

C. If x > 0, then y < 0: not necessarily true, for example x=1 and y=4;

D. Both x and y are even: never true, as the sum of two even numbers is even and can not equal to odd number 5;

E. Both x and y are less than 5: not necessarily true, for example x=6 and y=-1;

Answer: B.

CrackverbalGMAT · Answer

In a must be true question, one needs to prove the statement false.

x and y are consecutive integers- We can think of 1+4=5 with 1 and 4 which are not consecutive. Eliminate A.

If x < 0, then y > 0 - Since the sum is positive, then the statement is always true. If one number is negative,the other must be positive to make the sum positive. (Answer)

If x > 0, then y < 0-We can use x = 1 and y =4 to counter the statement. Eliminate C.

Both x and y are even.(Use x=1,y=4 to counter the statement. Eliminate D

Both x and y are less than 5. Take x=5 and y=0 to to counter the statement. Eliminate E.

(option c)
PS-Try to use plugins that can be recycled in other statements.

D.S
GMAT SME

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If x and y are integers and x + y = 5, which of the followin

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