GIVEN:• A certain store purchased a computer game.
• The store sold the computer game for $50.
- Selling Price (SP) of the computer game = $50
Note: We are not told about the store’s cost (CP) of purchasing the computer game.
Now, let’s look at what the question asks.
ASKED:Was the store’s profit from selling and purchasing the game less than $8?
Let’s
translate all this English to Math. The question asks:
•
Is SP – CP < $8?• Is $50 – CP < $8 --- (since SP is given as $50)
• Is CP > $50 - $8?
=>
Is Cost Price (CP) > $42? ------ (1)See how we
simplified the question so much! It now just depends on the missing Cost Price (CP).
We need to analyze each statement individually, and then together if needed, and see whether they give us a clear answer to the question in (1).
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.Translating Statement 1:
- Gross Profit from the sale-purchase of the game < 25% of the CP
Since Profit = SP – CP, statement 1 tells us that SP – CP < 25% of CP
o SP < CP + 25% of CP
o 50 < CP + 0.25CP (since SP = $50)
o 50 < 1.25CP
Therefore, CP > $50/1.25 =>
CP > $40So, from Statement 1, we got that CP > $40.
But is it greater than $42 as the question asks?We cannot comment on that! The Cost Price may be $41 or $43.5 , or for that matter, anything greater than $40 and less than $50. (Less than $50 is needed because that is the SP, and we are making a profit!)
Hence, Statement 1 alone is insufficient.
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.
Translating Statement 2:
- Profit from the sale-purchase of the game > 10% of CP
Again, since Profit = SP – CP, we have SP – CP > 10% of CP
o SP > CP + 10% of CP
o 50 > CP + 0.1CP
o 50 > 1.1CP
o CP < SP/1.1
Therefore, CP < $50/1.1 =>
CP < $45 approximately.So, from Statement 2 we know that CP < $45.
But is it greater than $42 as the question asks?We still cannot comment on that. The Cost Price may be $39 or $42.4 , or for that matter, anything less than $45.
Hence, Statement 2 alone is insufficient.
STATEMENT 1 & 2 COMBINED:From Statement 1 & 2, we get that:
$40 < CP < $45(approximately)But again, can we tell with certainty whether CP is greater than $42 as the question asks?NO! The Cost Price may be anything in the range of 40 to 45, both exclusive.
Hence, Statement 1 & 2 together are insufficient as well.
Hence,
Correct Choice: E Best Regards,
Ashish Arora
Quant Expert,
e-GMAT _________________