If a certain store purchased a computer game and then sold it for $50

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 independent equations ensures a solution.

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

For questions regarding inequalities, if the range of the question includes that of the condition, the condition becomes the answer.
If we modify the question a little, p(profit)=50-c(purchase price).
p=50-c, where p<8.
From condition 1, p<0.25c=c/4 --> 4p<c. If we substitute in c=50-p, 4p<50-p, 5p<50, p<10. This is not sufficient
For condition 2, p>0.1c=c/10 --> 10p>c. If we substitute in c=50-p. 10p>50-p, 11p>50, p>50/11=4.5...., so this is also not a sufficient condition.
Looking at the conditions together, 4.5....<p<10.... So this is still not sufficient as the range of the question does not include the range of the conditions; the answer becomes (E)

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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


either Im missing something or you are missing something =)


(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

gross Profit < 12.5


(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

gross Profit > 5



Im sorry in case I made a careless mistake (Im pretty tired :D)

That's how I solved it.

For the 2 posts above... we don't know the Cost of purchasing the game, only that it was sold for $50. You can use $50 to test (1) but not (2) (see below)

Gross Profit = Revenue - Cost
GP = 50 - C
Question: GP < 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
GP < C/4
Test C=50, GP < 12.5, GP = 50-50 can only be = 0, so this works.
Test C=40, GP < 10, could be 9 or 7 in which case it's insufficient.

(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
GP > C/10
C cannot = 50, because we get GP > 5 but this doesn't make any sense because GP would be 50 - 50 = 0 in this case.
Test C=40, GP > 4, In this case it can be 7 or 9 again, insufficient.

(3) C/10 < GP < C/4
Using C=40 we get 4 < GP < 10 so again not sufficient.

n.b. In my experience it seems that for word problem inequalities in DS (unless there's int constraints) it's more likely than not that both will not be sufficient because the range will include yes or no answers...

gross profit = sale price - cost

\(gross profit = $50 - C\)

$50 - C < $8?

(1) \($50 - C < 0.25C\)
\(50 < 1.25C\)
\(C > 40\)

If C = 41, then the gross profit was more than $8. If C = 44, then gross profit was less than $8. INSUFFICIENT.

(2) \($50 - C > 0.1C\)
\($50 > 1.1C\)
\(C < 45\)
Gross profit could be greater than or less than $8. INSUFFICIENT.

(1&2) Combining the two statements, we learn nothing new. INSUFFICIENT.

Answer is E.

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 > $40

So, 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

Can anyone please explain to me where I'm making a mistake?
egmat Bunuel MathRevolution
I do understand the official solution, just curious as to why what I did does not add up.
Profit = Selling - Buying
P = 50 - B

Is P<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.
So, let B be 4x and P be less than x (less than a quarter of 4x).
x = 50 - 4x
Reminder: boldface x is actually between 0 and x.
(1+4)x=50
x=50/(1+4)=10
Since the number 1 denotes a value between 0 and 1, the denominator must be smaller than 5. In that case x, which is equal to P, must be larger than 10.
What am I doing wrong?