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# If 3*x = 2*y = 5, then 24*x*(y^2) =

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Math Expert
Joined: 02 Sep 2009
Posts: 61289
If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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03 Mar 2019, 23:45
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Difficulty:

5% (low)

Question Stats:

84% (01:05) correct 16% (01:58) wrong based on 49 sessions

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If 3*x = 2*y = 5, then 24*x*(y^2) =

A. 250
B. 500
C. 750
D. 1000
E. 1250

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Re: If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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03 Mar 2019, 23:49
Bunuel wrote:
If 3*x = 2*y = 5, then 24*x*(y^2) =

A. 250
B. 500
C. 750
D. 1000
E. 1250

we can say
x=5/3 ; y= 5/2
24*x*(y^2)=
IMO A 250
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3239
If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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03 Mar 2019, 23:52

Solution

Given:
• $$3 * x = 2 * y = 5$$

To find:
• The value of the expression $$24 * x * y^2$$

Approach and Working:
We can rewrite the given expression as following:
• $$24 * x * y^2 = 3x * 4y^2 * 2 = 3x * (2y)^2 * 2 = 5 * (5)^2 * 2 = 5 * 25 * 2 = 250$$

Hence, the correct answer is option A.

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Re: If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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03 Mar 2019, 23:54
Bunuel wrote:
If 3*x = 2*y = 5, then 24*x*(y^2) =

A. 250
B. 500
C. 750
D. 1000
E. 1250

NOTE:

3x = 2y = 5.

Given ,

$$24 (x) (y)^2$$

= 3 * 2 * 2 * 2 *x * y * y.

= 3x * 2y * 2y * 2

= 5 * 5 * 5 * 2

= 125 * 2

= 250.
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Re: If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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04 Mar 2019, 02:55
24*x*(y^2) = 2. 3x. (2y)^2 = 2.5.(5)^2=10.25=250 ..... Ans A
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Re: If 3*x = 2*y = 5, then 24*x*(y^2) =  [#permalink]

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06 Mar 2019, 19:16
Bunuel wrote:
If 3*x = 2*y = 5, then 24*x*(y^2) =

A. 250
B. 500
C. 750
D. 1000
E. 1250

Since 3x = 5, x = 5/3. Similarly, since 2y = 5, y = 5/2.
Therefore,

24x(y^2) = 24(5/3)(5/2)^2 = 40(25/4) = 10(25) = 250

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Re: If 3*x = 2*y = 5, then 24*x*(y^2) =   [#permalink] 06 Mar 2019, 19:16
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