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Math Expert V
Joined: 02 Sep 2009
Posts: 58427
What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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Difficulty:   5% (low)

Question Stats: 95% (00:30) correct 5% (00:48) wrong based on 373 sessions

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What is 11% of x?

(1) 3/8 of x is 24

(2) 5% of x is 3.2

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is 11% of x?

(1) 3/8 of x is 24
(2) 5% of x is 3.2

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), the value of x is unique and sufficient.
For 2), the value of x is also unique and sufficient.
Therefore, the answer is D.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is 11% of x?

(1) 3/8 of x is 24
(2) 5% of x is 3.2

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), the value of x is unique and sufficient.
For 2), the value of x is also unique and sufficient.
Therefore, the answer is D.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Could you please explain more clearly the last paragraph in order to be more specific and clear. As it is now, it is not quite understandable.
Thank you
Arsim
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4017
Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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Top Contributor
Bunuel wrote:
What is 11% of x?

(1) 3/8 of x is 24

(2) 5% of x is 3.2

Target question: What is 11% of x?

Statement 1: 3/8 of x is 24
This statement tells us that (3/8)x = 24
Multiply both sides by 8/3 to get: x = (8/3)(24) = 64
Once we know that x = 64, we can calculate 11% of x
11% of x = 11% of 64 = (0.11)(64) = some distinct value. Of course, we need not actually perform this calculation. We need only recognize that we COULD determine the value of 11% of x
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 5% of x is 3.2
This statement tells us that (0.05)(x) = 3.2
Divide both sides by 0.05 to get: x = 64
Once we know that x = 64, we can calculate 11% of x
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT

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_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4017
Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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1
Top Contributor
Bunuel wrote:
What is 11% of x?

(1) 3/8 of x is 24

(2) 5% of x is 3.2

Here's another approach.

Target question: What is 11% of x?

Statement 1: 3/8 of x is 24
In other words, 37.5% of x is 24
With this information, we can conclude that 75% of x is 48
And 150% of x is 96
And 15% of x is 9.6
And 1.5% of x is 0.96
and so on
So, once we know the value of p% of x, we can determine any other percent of x. (for more on this, watch the video below)
So, using the information in statement 1, we COULD determine the value of 11% of x
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 5% of x is 3.2
With this information, we can conclude that 10% of x is 6.4
We can also conclude that 1% of x is 0.64
So, 11% of x = 6.4 + 0.64 = 7.04
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEOS:

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8027
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2  [#permalink]

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ArsimNuhiu wrote:
MathRevolution wrote:
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is 11% of x?

(1) 3/8 of x is 24
(2) 5% of x is 3.2

In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), the value of x is unique and sufficient.
For 2), the value of x is also unique and sufficient.
Therefore, the answer is D.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Could you please explain more clearly the last paragraph in order to be more specific and clear. As it is now, it is not quite understandable.
Thank you
Arsim

Hi Arsim,

We would love to give you more explanations though it is too much to elaborate in paragraphs.
Hence, we would like you to come visit our website to have a look at our approaches.
Thank you.
_________________ Re: What is 11% of x? (1) 3/8 of x is 24 (2) 5% of x is 3.2   [#permalink] 20 Oct 2016, 17:25
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