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Which of the positive integers x or y is greater?

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Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 18:51
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:30) correct 43% (01:37) wrong based on 21 sessions

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GMATBusters’ Quant Quiz Question -9


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Which of the positive integers x or y is greater?

(1) y = 2x
(2) 2x + 5y = 12

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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 18:52
(1) y = 2x
since both are positive integers and y is double of x. Hence, y is greater than x
SUFFICIENT
(2) 2x + 5y = 12
There is only one positive integral solution of this equation x= 1, y = 2.
Hence, y is greater than x.
SUFFICIENT

Answer D
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 19:39
Which of the positive integers x or y is greater?

(1) y = 2x
(2) 2x + 5y = 12

Given:
Both X and Y are Positive and both Integers

We do not need to include 0 or decimals in our calculations.

(1) y=2x
Positive Integer Y is equal to twice the positive integer X.

This clearly says that Y > X. Option 1 is sufficient. Eliminate B,C and E.

(2) 2x + 5y = 12
Since both X and Y are integers and both positive. The only values that would work here is X = 1 and Y = 2 and this gives Y > X - Option 2 alone is sufficient. Eliminate A, C and E.

Both the options are sufficient alone.

Ans: D
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 20:00
1) Since both x and y are positive integers and y=2x, y is greater than x (the only case where this is not applicable is with negative integers).
Clearly, this statement is sufficient.
2) from 2x+5y=12, it is clear that y has to be even and less or equal than two. Therefore, the only set of numbers that satisfy the equation are x=1 and y=2.
Clearly, this statement is sufficient.
Answer: D
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 20:09
Since x and y are positive integers, so for 1) x = 2y means x is always greater than y. sufficient.

and for 2) only one value for both x and y will satisfy the equation. so its also sufficient.

D is the answer.
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 20:31
Qs: x> y or y>x
Given : x and y are positive integer.

(1) y = 2x

we can see that y is a multiple of x and both are positive so y will be always greater than x. hence y>x
if x =2, y = 4
if x=10, y= 20 , so y>x
sufficient to answer.

(2) 2x + 5y = 12
we can see that y is a multiple of 5 so unit digit will be always 0 or 5. x is a multiple of 2 so unit digit may be 2, 4, 6, etc. but the summation of equation is given as 12 so unit digit of only zero and 2 are possible here for x and y in case. by this logic let us check the values,
if y=2 then x= 1, 2x +5y = 12
other values are not possible. also both are positive values.
so y> x - sufficient to answer.

Answer is D.
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 21:52
x=y= Positive integer.

Question : Greater (x,y)=?

Statement 1: y=2x

x=1 y=2
x=2 y=4
x=3 y=6
y is greater value. Sufficient.

Statement 2: 2x+5y=12
y=1 not possible. Gives us a non integer value of x.
y=2 x=1 works. y is greater.
x=2,3,4,5 doesn't work. x=6 gives us y as 0 still doesnt work.

So only one solution. Hence Sufficient.

Answer D
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 01 Feb 2020, 21:59
Statement 1: y= 2x,

Since its mentioned that both integers are positive, means whatever be the value of x, y will be 2 times greater, so the statement is Sufficient

Statement 2: 2x+5y =12

Since nothing is mentioned about the values of x & y, and its only 1 equation with 2 unsolved variables, we cannot deduce anything so the statement is Insufficient.

Answer is A.
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Re: Which of the positive integers x or y is greater?  [#permalink]

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New post 02 Feb 2020, 01:20
since given that x, y are integers so we need not consider 0
#1
y=2x ; y>x always sufficient
#2
2x + 5y = 12
x=2,y=2 x=y sufficient

IMO D:
in DS in case of option D ; the value of answer need to be same in both stmtns...

Which of the positive integers x or y is greater?

(1) y = 2x
(2) 2x + 5y = 12
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Re: Which of the positive integers x or y is greater?   [#permalink] 02 Feb 2020, 01:20

Which of the positive integers x or y is greater?

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