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How much is x percent of a certain number?

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Source: — Data Sufficiency |
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by MartyMurray » Sat Jan 09, 2016 10:49 pm
This question is a basic C trap question, one which is set up in such a way that C in a way seems to be the right answer even though C is not actually the right answer.

To answer the question, "How much is x percent of a certain number?", one seemingly would need to know what x is and what the number is. That's what makes this question a C trap.

Statement 1: x = 60

This tells us only what x is and provides no information on the number.

Insufficient.

Statement 2: 2x percent of the number is 24

From this we get no clue regarding the value of the number or of x.

However, if we were to combine this information with the information in Statement 1, we could figure out the value of the number, and then we could multiply the number by .60 to find the answer to the question.

Of course, doing that is unnecessary, because instead we could just divide Statement 2 by 2 to get the following.

x percent of the number is 12.

So, interestingly, we can get the answer to the posed question without knowing what x is or what the number is.

Sufficient.

While this is not a very challenging question, it does exemplify a key point for DS. Often answers to DS questions can be found without finding the values of the variables involved.

The correct answer is B.
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by Poisson » Sat Jun 11, 2016 2:32 pm
Hello,

I could really use some help understanding how statement 2 is sufficient. I don't understand how to get to 12.

I translated the statement as:

(2x/100)*(y)=24

where y is the number. I reduced 2x/100 to get x/50. But I still have the variable y. Please explain how x can be 12?

Thanks so much
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by MartyMurray » Sun Jun 12, 2016 3:49 am
Poisson wrote:Hello,

I could really use some help understanding how statement 2 is sufficient. I don't understand how to get to 12.

I translated the statement as:

(2x/100)*(y)=24

where y is the number. I reduced 2x/100 to get x/50. But I still have the variable y. Please explain how x can be 12?

Thanks so much
Let's use your translation to create a rewrite of the original question. The question is thus the following.

What is (x/100)*(y)?

Your translation of Statement 2 is (2x/100)*(y) = 24.

Divide both sides by 2 to get (x/100)*(y) = 12.

We have answered the question.
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by Poisson » Fri Jul 01, 2016 7:34 am
Marty Murray wrote:
Poisson wrote:Hello,

I could really use some help understanding how statement 2 is sufficient. I don't understand how to get to 12.

I translated the statement as:

(2x/100)*(y)=24

where y is the number. I reduced 2x/100 to get x/50. But I still have the variable y. Please explain how x can be 12?

Thanks so much
Let's use your translation to create a rewrite of the original question. The question is thus the following.

What is (x/100)*(y)?

Your translation of Statement 2 is (2x/100)*(y) = 24.

Divide both sides by 2 to get (x/100)*(y) = 12.

We have answered the question.
Thank you. I had to wrap my head around the step of dividing by 2. Usually, I multiply both sides by the reciprocal or denominator of the fraction to get rid of it. Here in this problem, I needed to see that multiplying by 1/2 will answer the target question.

The takeaway for me is knowing how much I need to manipulate both sides of the equation.

Here's what I ended up doing:

Stem: How much is x percent of a certain number?

(x/100)(y) = xy/100 = ? where y represents the number

My final rephrase was: xy/100 = ?

Please let me know if this final rephrasing is legit?

Next:
Statement 1: (60y)/100 = ?
I still don't know what y is. Eliminate A and D

Statement 2: (2x/100)(y) = 24
I see this as (2x/100)(y/1) = (2xy)/100
Here I've combined my numerators to be 2xy
I now have (2xy)/100 = 24
Now I multiply both sides by 100 to get rid of the fraction
I get 2xy = 2400

I divided out the 2.
(2xy)/2 = 2400/2

Now I get xy = 1200. It still doesn't look like xy/100.

The final step was to divide both sides by 100.

Now I get xy/100 = 12.

Statement 2 is sufficient.
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by Matt@VeritasPrep » Fri Jul 08, 2016 2:30 pm
Poisson, that looks good to me! You've got the process down: start by figuring out how to represent what you're looking for algebraically, then see if S1 or S2 can be transformed into that representation. (In other words, if you want xy/100, determine whether S1 or S2 can be manipulated into xy/100.)
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