markup price

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hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Sun Jun 17, 2012 9:52 pm

If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item's final price (after both changes) greater than its original price?

(1) m > d + 10

(2) m = 1.5d

OA is E

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Source: Beat The GMAT — Data Sufficiency | Sun Jun 17, 2012 9:52 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 18, 2012 3:47 am

hey_thr67 wrote:If the original price of an item in a retail store is marked up by m percent and the resulting price is then discounted by d percent, where m and d are integers between 0 and 100, is the item's final price (after both changes) greater than its original price?

(1) m > d + 10

(2) m = 1.5d

OA is E

Let the original price = 100.
Then the markup = (m/100)*100 = m.
The resulting price = 100+m.
The subsequent discount = d/100*(100+m) = d + md/100
Thus, the total percent change = percent increase - percent decrease = m - d - md/100.
For the final price to be greater than the original price, the total percent change must be positive.

Question rephrased:
Is m - d - md/100 > 0?

Statement 1: m - d >10
For the sake of efficiency, plug in values that also satisfy the condition in statement 2: m = 1.5d.
Be sure to try EXTREMES.
Easy values for d:
10, 20, 30, 40, 50, 60...
Resulting in the following possible values for m = 1.5d:
15, 30, 45, 60, 75, 90...
The following extremes satisfy m-d > 10:
d=30, m=45 and d=60, m=90.

If d=30 and m=45, then m - d - md/100 = 45 - 30 - (45*30)/100 = 1.5.
If d=60 and m=90, then m - d - md/100 = 90 - 60 - (90*60)/100 = -24.
Since in the first case the percent change is positive, and in the second case the percent change is negative, the two statements combined are INSUFFICIENT.

The correct answer is E.

It is helpful to know the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total percent change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total percent change = x - y - xy/100.

Last edited by GMATGuruNY on Mon Jun 18, 2012 10:35 am, edited 1 time in total.

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 amFollowed by: 6 members; Thanked: 16 times

by dhonu121 » Mon Jun 18, 2012 3:58 am

Hi Mitch,
Correct me if I am wrong, but we could have solved this algebraically as well without guessing those numbers.

For the first case we need to put m=1.5d in the equation and for the second case we need to put m=d+10 in the equation.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 18, 2012 10:49 am

dhonu121 wrote:Hi Mitch,
Correct me if I am wrong, but we could have solved this algebraically as well without guessing those numbers.

For the first case we need to put m=1.5d in the equation and for the second case we need to put m=d+10 in the equation.

The values that I plugged in were not derived by guessing.
Please revisit my post above, in which I've fleshed out the reasoning.
Algebra could certainly be used here, but I'm not sure that the resulting solution would be more efficient.
Generally, algebra works best when trying to prove sufficiency.
To prove insufficiency, plugging in values typically is easier and quicker.

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dhonu121: Master | Next Rank: 500 Posts; Posts: 316; Joined: Sun Aug 21, 2011 6:18 amFollowed by: 6 members; Thanked: 16 times

by dhonu121 » Mon Jun 18, 2012 9:25 pm

GMATGuruNY wrote: Generally, algebra works best when trying to prove sufficiency.
To prove insufficiency, plugging in values typically is easier and quicker.

Thanks. I was generally not sure as to when to use numbers and when to use algebra. This above would help.

If you've liked my post, let me know by pressing the thanks button.

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