If x and y are prime integers and x

Question

If x and y are prime integers and x < y, which of the following cannot be true?

A.  x  is even

B.  x + y  is odd

C.  xy  is even

D.  y + xy  is even

E.  2x + y  is even

IanStewart · Answer

If x and y are prime, and x < y, then maybe x is 2, or maybe x is odd, but y certainly is not 2. So y must be odd. In answer E, we're clearly adding y to an even number 2x, and if y is odd, 2x + y will always be odd, so E cannot be true.

Answers A through C will be true if x = 2, and answer D will be even if x is odd (because answer D is equal to y(x + 1), and x+1 is even if x is odd).

GMATinsight · Answer

in  cannot be true  questions, our Aim is always to eliminate the incorrect options

A.  x  is even  INCORRECT  because x can be 2

B.  x + y  is odd  INCORRECT  because x can be 2 and y 3 such that x+y = 5

C.  xy  is even  INCORRECT  because x can be 2 and tehn xy will be even

D.  y + xy  is even  INCORRECT  because x can be 3 in which case y(1+x) will be even

E.  2x + y  is even  CORRECT  because 2x is always even and y is always odd i.e. 2x+y = e+o = odd

Answer: Option E

Abhishek009 · Answer

Let  x = 2  &  y = 3

(A) 2 ; Possible
(B) 2 + 3 = 5; Possible
(C) 2*3 = 6 ; Possible
(D) 2 + 2*3 = 8 ; Possible
(E) 2*2 + 3 = 7 ; Not possible

Answer must be (E)

TestPrepUnlimited · Answer

A: x = 2 is allowed. Can be true.

B: x = 2 then add any y to get an odd sum. Can be true.

C: x = 2 then multiply by any y to get an even number. Can be true.

D:  y*(x + 1)  is even, let x be odd so that x + 1 is even. Can be true.

E: y is forced to be odd as y cannot be 2. Then 2x + y must be even + odd = odd. Cannot be true.

Ans: E

e3thekid · Answer

We are looking for an option that CANNOT be true.

If x and y are prime numbers, and x<y:

Let’s say x = 2 and y = 3

x is even; x = 2, can be true. Eliminate A

x + y is odd; x = 2 and y = 3, can be true. Eliminate B

xy is even; if we x = 2 and it’s the only even prime, the product of xy is even, can be true. Eliminate C

y + xy is even; if x = any prime other than 2 and y is a larger prime, this would result in an odd + odd which is even, can be true. Eliminate D

E. 2x + y is even; no matter what prime we assign to x, 2x will be an even number. Then y would be a be larger prime, so even + odd can never result in an even number. CANNOT be true.

Option E

If x and y are prime integers and x < y, which of the following cannot

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