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If a certain store purchased a computer game and then sold

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If a certain store purchased a computer game and then sold

by BTGmoderatorDC » Fri Sep 27, 2019 4:07 pm
If a certain store purchased a computer game and then sold it for $50, was the store's gross profit from the purchase and sale of the game less than $8?

(1) The store 's gross profit from the purchase and sale of the game was less than 25 percent of the amount for which the store purchased the game
(2) The store 's gross profit from the purchase and sale of the game was greater than 10 percent of the amount for which the store purchased the game

OA E

Source: GMAT Prep
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Source: — Data Sufficiency |
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by deloitte247 » Sun Sep 29, 2019 6:56 am
Store purchased computer game for $50
Question=> Was the store's gross profit from the purchase and sale of the game less than $8?
i.e find out if $50 - cost price < $8
or
If the cost price > $42.
Statement 1: The store's gross profit from the purchase and sale of the game was less than 25 percent of the amount for which the store purchased the game.
This means that;
$50 - cost price < 0.25 of the cost price
- cost price - 0.25[cost price] < -$50
$$\frac{-1.25\left[\cos t\ price\right]}{-1.25}<\frac{-$50}{-1.25}$$
Cost price > $40
If we compare this to the expression in the question stem [cost price > $42], we will notice that there is a definite value for cost price as cost price canbe = 41 which is less than 42.
Also, it can be 43 which is greater than 42. Hence, statement 1 is NOT SUFFICIENT.

Statement 2:
The store's gross profit from the purchase and sale of the game was greater than 10 percent of the amount for which the store purchased the game.
This means that;
$50 - cost price > 0.1 of cost price
-cost price - 0.1 [cost price] - $50
$$\frac{-1\cdot1\left[\cos t\ price\right]}{-1.1}<\frac{-50}{-1.1}$$
Cost price is < $46.
If we compare this to the expression in the question stem [cost price > $42], we will notice that there is no definite value for cost price as cost price can be 44 which is greater than 42. It can also be 40 which is less than 42. Hence, statement 2 is NOT SUFFICIENT.
Combining both statements together;
From statement 1: cost price > $40
From statement 2: cost price < $46
Therefore, $40 < cost price < $46, this means that the cost price = $41. It is less than 42 in the question stem. If cost price = $45, it is greater than 42 in the question stem.
Since the value of cost price is not definite, both statements combined together are NOT SUFFICIENT.

Answer = OPTION E
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