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MGMAT Advanced quant - Hybrid problem

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by bubbliiiiiiii » Tue Sep 01, 2015 1:44 am
If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? (1) y is prime (2) z = 9

Manhattan Prep (2015-05-17). GMAT Advanced Quant (Kindle Locations 4099-4101). Manhattan Prep Publishing. Kindle Edition.

OA A
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Pranay
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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Sep 01, 2015 3:00 am
bubbliiiiiiii wrote:If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? (1) y is prime (2) z = 9
The percent increase from x to y is equal to the percent increase from y to z.
Implication:
x/y = y/z
xz = y², where x<y<z.

Statement 1:
If y=2, then xz = 2² = 4, implying that x=1 and z=4.
If y=3, then xz = 3² = 9, implying that x=1 and z=9.
If y=5, then xz = 5² = 25, implying that x=1 and z=25.
In every case, x=1.
SUFFICIENT.

Statement 2:
Since z=9, we get:
(x)(9) = y².
It's possible that x=1 and that y=3.
It's possible that x=4 and that y=36.
Since x can be different values, INSUFFICIENT.

The correct answer is A.
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by bubbliiiiiiii » Tue Sep 01, 2015 4:18 am
The percent increase from x to y is equal to the percent increase from y to z.
Implication:
x/y = y/z
Hi Mitch,

Thanks for responding.

Isn't percentage increase equation be the following?

(x-y)/x = (y-z)/y
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by GMATGuruNY » Tue Sep 01, 2015 5:08 am
bubbliiiiiiii wrote:
The percent increase from x to y is equal to the percent increase from y to z.
Implication:
x/y = y/z
Hi Mitch,

Thanks for responding.

Isn't percentage increase equation be the following?

(x-y)/x = (y-z)/y
If y is 10% greater than x, the, x/y = 10/11.
If z is 10% greater than y, then y/z = 10/11.
Since the fractions in red are equal, we get:
x/y = y/z.

If y is 30% greater than x, the, x/y = 10/13.
If z is 30% greater than y, then y/z = 10/13.
Since the fractions in red are equal, we get:
x/y = y/z.

Implication:
If the percent increase from x to y is equal to the percent increase from y to z, then x/y = y/z.

Algebraic proof:

Percent increase from x to y = (y-x)/x * 100.
Percent increase from y to z = (z-y)/y * 100.
Since the two percent increases are equal, we get:
(y-x)/x * 100 = (z-y)/y * 100
(y-x)/x = (z-y)/y
y/x - x/x = z/y - y/y
y/x - 1 = z/y - 1
y/x = z/y.
Thus:
x/y = y/z.
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by Brent@GMATPrepNow » Tue Sep 01, 2015 5:41 am
Here's a similar challenge question: https://www.beatthegmat.com/challenge-3- ... 76618.html

Cheers,
Brent
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by nikhilgmat31 » Thu Sep 03, 2015 5:14 am
GMATGuruNY wrote:
bubbliiiiiiii wrote:If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? (1) y is prime (2) z = 9
The percent increase from x to y is equal to the percent increase from y to z.
Implication:
x/y = y/z
xz = y², where x<y<z.

Statement 1:
If y=2, then xz = 2² = 4, implying that x=1 and z=4.
If y=3, then xz = 3² = 9, implying that x=1 and z=9.
If y=5, then xz = 5² = 25, implying that x=1 and z=25.
In every case, x=1.
SUFFICIENT.

Statement 2:
Since z=9, we get:
(x)(9) = y².
It's possible that x=1 and that y=3.
It's possible that x=4 and that y=36.
Since x can be different values, INSUFFICIENT.

The correct answer is A.
Mitch, seriously It is awesome question.
I reached at equation y2 = xz

But I answered C by mistake --- your explanation is awesome.
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by Max@Math Revolution » Fri Sep 04, 2015 3:07 am
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 equations ensures a solution.


If x, y, and z are all distinct positive integers and the percent increase from x to y is equal to the percent increase from y to z, what is x? (1) y is prime (2) z = 9

Transforming the original condition and the question by variable approach method we have percentage change =(After-Before)*100/Before, and thus (y-x)*100/x=(z-y)*100/y. multiplying both sides by 100 gives us (y/x)-1=(z/y)-1, y/x=z/y, y^2=xz. The question asks for the value of x=?, and we know that the percentage increases thus x<y<z. Thus, in case of 1) x = 1 if y=prime. Since this is a unique answer, it is sufficient. Therefore the answer is A.


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by Matt@VeritasPrep » Fri Sep 04, 2015 6:23 pm
bubbliiiiiiii wrote: Isn't percentage increase equation be the following?

(x-y)/x = (y-z)/y
You've got the right idea, but remember that percent change is expressed as

100 * (New - Old)/Old

and we know that z > y > x.

So we have

100 * (y - x)/x = 100 * (z - y)/y, or

(y - x)/x = (z - y)/y, or

y*y - x*y = x*z - x*y, or

y*y = x*z
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