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# If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4

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Math Expert
Joined: 02 Sep 2009
Posts: 47983
If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 04:35
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Difficulty:

15% (low)

Question Stats:

87% (01:12) correct 13% (01:46) wrong based on 30 sessions

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If x/2 = 3/y, is x less than y?

(1) y >= 3

(2) y <= 4

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If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 04:42
Bunuel wrote:
If x/2 = 3/y, is x less than y?

(1) y >= 3

(2) y <= 4

$$\frac{x}{2} = \frac{3}{y}$$ can be re-written as xy = 6

1. If y >= 3, the minimum value that y can take is 3.
For that value, x will be 2. x will always be less than y (Sufficient)

2. If y <= 4, y could also take the value of 2.
In this case, the value of x will be 3 making x greater than y.
However, y will be greater than x when y = 3 and x = 2 (Insufficient) (Option A)
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If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 04:44
Bunuel wrote:
If x/2 = 3/y, is x less than y?

(1) y >= 3

(2) y <= 4

St1:- y >=3

when $$y_{min}=3$$, then x=2. For every value of y>3, x would reduce further and it will be always less than y
so, x>y.
Sufficient.

St2:- y<=4

when y=3, then x=2; implies y>x
when y = 2, then x=3, implies x>y.
Insufficient.

Ans. (A)
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Joined: 31 Oct 2013
Posts: 479
Concentration: Accounting, Finance
GPA: 3.68
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Re: If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 04:49
Bunuel wrote:
If x/2 = 3/y, is x less than y?

(1) y >= 3

(2) y <= 4

Given

x/2 = 3/y

xy = 3*2

we are asked to determine which one is greater between x and y.

Statement 1 :

y >= 3.

As we already know that xy = 6 and y>=3, x has to be less than or equal to 2.

So, x<y. Sufficient.

Statement 2 :

y<=4

It means y could be 1 or 2 as well. As xy = 6 and y could be 1 or or 3 it is impossible to determine whether x or y is greater. NOT sufficient.

Thus the best answer is A.
Senior Manager
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Posts: 381
Re: If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 05:05
Given, xy = 6.
1. y = 3, 4, 5...... Answer would be yes for all the following values.
Hence, sufficient.

2. y = 4, 3 answer would be yes. But if y = 2, x = 3. Thus, x>y. Thus, answer is no.

Hence, insufficient.

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Concentration: Finance, Healthcare
Re: If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4  [#permalink]

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13 Jul 2018, 11:44
(1) y >= 3: min y value is 3 => x= 2 < 3 (sufficient)

(2) y <= 4: y could be negative or positive (insufficient)

Re: If x/2 = 3/y, is x less than y? (1) y >= 3 (2) y <= 4 &nbs [#permalink] 13 Jul 2018, 11:44
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