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# What is the value of 16xy^2+32x^2y?

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Math Expert
Joined: 02 Aug 2009
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What is the value of 16xy^2+32x^2y?  [#permalink]

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24 Feb 2017, 07:44
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45% (medium)

Question Stats:

68% (02:12) correct 32% (01:51) wrong based on 144 sessions

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What is the value of $$32xy^2+16x^2y$$?

(1) $$(x+2y)^2=64$$
(2) x=2y

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of 16xy^2+32x^2y?  [#permalink]

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24 Feb 2017, 08:13
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Top Contributor
chetan2u wrote:
What is the value of $$32xy^2+16x^2y$$?

(1) $$(x+2y)^2=64$$
(2) x=2y

Great question!

Target question: What is the value of 32xy² + 16x²y?
After scanning the two statements, I see that we might benefit from rephrasing the target question.
32xy² + 16x²y = 16xy(2y + x)
So.....
REPHRASED target question: What is the value of 16xy(2y + x)?

Statement 1: (x+2y)² = 64
This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 8, in which case 16xy(2y + x) = 0
Case b: x = 1 and y = 7, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 2y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 0 and y = 0, in which case 16xy(2y + x) = 0
Case b: x = 2 and y = 1, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x+2y = 8 OR x+2y = -8
Statement 2 tells us that x = 2y

So, we have two possible systems of equations:
x+2y = 8
x = 2y

AND
x+2y = -8
x = 2y

If we solve the first system, we get: x = 4 and y = 2, in which case 16xy(2y + x) = 16(4)(2)[2(2) + (4)] = some POSITIVE number
If we solve the second system, we get: x = -4 and y = -2, in which case 16xy(2y + x) = 16(-4)(-2)[2(-2) + (-4)] = some NEGATIVE number
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

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Re: What is the value of 16xy^2+32x^2y?  [#permalink]

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16 Jul 2017, 13:35
What is the value of $$32xy^2+16x^2y$$?

$$32xy^2+16x^2y$$

$$= 16xy(2y+x)$$

(1) $$(x+2y)^2=64$$

This gives value of $$(x+2y)^2$$, however, we are not having value for $$xy$$

Hence, (1) ===== is NOT SUFFICIENT

(2) $$x=2y$$

Once again this gives us an equation in "$$y$$" and as we are not having the value of $$y$$, we will not be able to determine the value.

Hence, (2) ===== is NOT SUFFICIENT

Combining (1) & (2)

EVen after combining we cannot determine the value of the equation = $$= 16xy(2y+x)$$

Hence, (1) & (2) ===== is NOT SUFFICIENT

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Re: What is the value of 16xy^2+32x^2y?  [#permalink]

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20 Dec 2017, 06:14
GMATPrepNow wrote:
chetan2u wrote:
What is the value of $$32xy^2+16x^2y$$?

(1) $$(x+2y)^2=64$$
(2) x=2y

Great question!

Target question: What is the value of 32xy² + 16x²y?
After scanning the two statements, I see that we might benefit from rephrasing the target question.
32xy² + 16x²y = 16xy(2y + x)
So.....
REPHRASED target question: What is the value of 16xy(2y + x)?

Statement 1: (x+2y)² = 64
This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 8, in which case 16xy(2y + x) = 0
Case b: x = 1 and y = 7, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 2y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 0 and y = 0, in which case 16xy(2y + x) = 0
Case b: x = 2 and y = 1, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x+2y = 8 OR x+2y = -8
Statement 2 tells us that x = 2y

So, we have two possible systems of equations:
x+2y = 8
x = 2y

AND
x+2y = -8
x = 2y

If we solve the first system, we get: x = 4 and y = 2, in which case 16xy(2y + x) = 16(4)(2)[2(2) + (4)] = some POSITIVE number
If we solve the second system, we get: x = -4 and y = -2, in which case 16xy(2y + x) = 16(-4)(-2)[2(-2) + (-4)] = some NEGATIVE number
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

I thought that in GMAT, any squared root takes only the positive value not the negative.

(x+2y)^2=64 Take square root of both sides we get
x+2y=8

Why you included -8 here?
Math Expert
Joined: 02 Aug 2009
Posts: 7025
Re: What is the value of 16xy^2+32x^2y?  [#permalink]

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20 Dec 2017, 06:23
Zoser wrote:
GMATPrepNow wrote:
chetan2u wrote:
What is the value of $$32xy^2+16x^2y$$?

(1) $$(x+2y)^2=64$$
(2) x=2y

Great question!

Target question: What is the value of 32xy² + 16x²y?
After scanning the two statements, I see that we might benefit from rephrasing the target question.
32xy² + 16x²y = 16xy(2y + x)
So.....
REPHRASED target question: What is the value of 16xy(2y + x)?

Statement 1: (x+2y)² = 64
This tells us 2 things: EITHER x+2y = 8 OR x+2y = -8
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 8, in which case 16xy(2y + x) = 0
Case b: x = 1 and y = 7, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = 2y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 0 and y = 0, in which case 16xy(2y + x) = 0
Case b: x = 2 and y = 1, in which case 16xy(2y + x) = some value other than 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that EITHER x+2y = 8 OR x+2y = -8
Statement 2 tells us that x = 2y

So, we have two possible systems of equations:
x+2y = 8
x = 2y

AND
x+2y = -8
x = 2y

If we solve the first system, we get: x = 4 and y = 2, in which case 16xy(2y + x) = 16(4)(2)[2(2) + (4)] = some POSITIVE number
If we solve the second system, we get: x = -4 and y = -2, in which case 16xy(2y + x) = 16(-4)(-2)[2(-2) + (-4)] = some NEGATIVE number
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

I thought that in GMAT, any squared root takes only the positive value not the negative.

(x+2y)^2=64 Take square root of both sides we get
x+2y=8

Why you included -8 here?

there are two different things....
$$\sqrt{64}$$ will laways be positive and will be 8..
but $$x^2=64$$ will have two values of x since $$8^2=(-8)^2=64$$
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of 16xy^2+32x^2y? &nbs [#permalink] 20 Dec 2017, 06:23
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