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Percent Change

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by Rudy414 » Fri Mar 22, 2013 1:35 pm
The average of three distinct positive integers x, y, and z is 64. If a new number d is add, will the percent increase exceed 13%?

1) d is twice the value of one of the original numbers

2) d is half the value of the largest of the original numbers

B

I actually got the answer right, but I am not sure if my math is correct or if I just got lucky.

Here is how I solved it:

1. (x+y+z)/3 = 64 -> x+y+z = 192
2. 13% of 192 is approximately 23. So, in order for d to be at least a 13% increase, d > 23
3. The most extreme number combinations are 189+1+2, in which case (for statement 2) d=94.5, and 63+64+65, in which case d=32.5. Since both are greater than 23, the percent increase is greater than 13%.

Does this make sense or am I missing something?

Thank you
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Source: — Data Sufficiency |

by Anju@Gurome » Fri Mar 22, 2013 2:25 pm
Rudy414 wrote:The average of three distinct positive integers x, y, and z is 64. If a new number d is add, will the percent increase exceed 13%?

1) d is twice the value of one of the original numbers
2) d is half the value of the largest of the original numbers
"percent increase" of what? The sum or the average?

If it is percent increase of the sum
The new sum must be 64*3*(1.13) ≈ 217
Hence, for the percent increase of sum to exceed 13%, d must be greater than or equal to (217 - 192) = 25

Statement 1: Let us assume x = 1, y = 2, and z = 189
Now,
  • if d = 2x ---> d = 2 < 25
    but
    if d = 2z ---> d = 378 > 25
Not sufficient

Statement 2: The minimum possible value of the largest of the original three integers is 65. As 65/2 = 32.5 > 25, the half of the largest of the original three integers will be always greater than 25.
Hence, d > 25

Sufficient
[spoiler]
The correct answer is B.[/spoiler]
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
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by Anju@Gurome » Fri Mar 22, 2013 2:31 pm
If it is percent increase of the average
The new sum must be 64*(1.13)*4 ≈ 289
Hence, for the percent increase of sum to exceed 13%, d must be greater than (289 - 192) = 97
So, the question is whether d > 97 or not.

Statement 1: Let us assume x = 1, y = 2, and z = 189
Now,
  • if d = 2x ---> d = 2 < 97
    but
    if d = 2z ---> d = 378 > 97
Not sufficient

Statement 2: The maximum possible value of the largest of the original three integers is 189. As 189/2 = 94.5 < 97, the half of the largest of the original three integers will be always less than 97.
Hence, d < 97

Sufficient

The correct answer is B.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
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by Rudy414 » Fri Mar 22, 2013 2:59 pm
It didn't say the percent increase of the average or the sum. I suppose the question is talking about the percent change of the average since it gave the original average, as opposed to giving the original sum.

Either way, I just wanted to make sure my logic was sound, and it sounds like you confirmed it. I just need to be careful of the scope (i.e., solving for the sum or the average).

Thank you.
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by hemant_rajput » Sat Mar 23, 2013 9:31 am
Hi Rudy,
"percent increase" of what? The sum or the average?
The point that Anju made is quite important. The question you posted is ambiguous; As every GMAT experts says don't practice from books which doesn't comply with GMAT Standards because it will not only throw your skills in wrong direction but also it is possible that you may pick wrong habits(grammatical mistakes) while solving those questions.

Believe me, I've done that mistake for a long time and I can tell you it was not worth it.
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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