The original price of a computer was increased by x% to reach its

Question

The original price of a computer was increased by x% to reach its current price. If Elena used a coupon that allowed her to purchase the computer at a y% discount off the current price, was the price at which she purchased the computer less than the original price of the computer?

(1) x = 12 and y < 12
(2) y > 9

(1) x = 12 and y < 12
(2) y > 9

MartyMurray · Accepted Answer

The original price of a computer was increased by x% to reach its current price. If Elena used a coupon that allowed her to purchase the computer at a y% discount off the current price, was the price at which she purchased the computer less than the original price of the computer?

Statement (1)

(1) x = 12 and y < 12

Notice that x = 12 percent of the original smaller price and y < 12 percent of the current larger price.

For example, if we let the original price be 100, then x percent of the original price = 12, the current price = 112, and y percent of the current price < 0.12 x 112, meaning y percent of the current price < 13.44

So, y percent of the current price could be, for instance, 1 or 13, meaning the coupon could have subtracted 1 or 13 from 112 with the result that the price paid by Elena may have been greater or less than the original price of the computer.

Insufficient.

Statement (2)

(2) y > 9

Since we have no idea what x is, this statement is clearly insufficient.

Statements Combined

We have the following:

x = 12

9 < y < 12

Let the original price be 100.

100 + x(100) = 100 + 0.12(100) = 112

If y is just over 9, 112 - y(112) = 112 - just over 0.09(112) = 112 - just over 10.08 > 100

If y is just under 12, 112 - y(112) = 112 - just under 0.12(112) = 112 - just under 13.44 < 100

Insufficient

The correct answer is (E).

egmat · Answer

Here is a  detailed video solution  for this interesting question.
See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=yx9RcmxQSLo

Let us know if you have any questions.

gmatophobia · Answer

Net percentage change is given by x - y -\frac{xy}{100} Question : x - y -\frac{xy}{100} < 0 100(x - y) -xy < 0 Statement 1 (1) x = 12 and y < 12 x - y is positive. 100(x - y) < xy As we do not know the exact value of x and y, we cannot conclude on the inequality. Hence, the statement alone is not sufficient. We can eliminate A and D. Statement 2 (2) y > 9 Not sufficient, as we do not know the value of x. Eliminate B. Combined x = 12 and 9 < y < 12 Case 1: y \approx 12 100(x - y) \approx 0 100(x - y) - xy < 0 In this case, the net percentage change is negative. Case 2: y \approx 9 100(12 - 9) \approx 300 300 - 108 > 0 In this case, the net percentage change is positive. As we have two contradicting results, the statements combined are not sufficient. Option E

chetan2u · Answer

When you increase A by say 10%, and then reduce by same %, 10%, the reduction includes not only 10% on x but also 10% on the increased amount, which is 10% of A. Thus, increasing by x% and reducing by x% would surely give a smaller amount. => y\geq x will give you a decreased amount. But if y10+\frac{80}{112} will give lower value than initial amount. Here, y could be 10 or 11 giving different answers. Insufficient (2) y > 9 Nothing about x. Insufficient Combined. y can still be 10 or 11, giving different answers. Insufficient E

GMATGuruNY · Answer

Let the original price = 100.

Statements combined:
Current price = 100 + 12% of 100 = 112

Case 1: y = just a bit less than 12
12% of 112 = (10% of 112 + 2% of 112) = 11.2 + 2.24 = 13.44
Implication:
Since the discount must actually be LESS than 12%, the discount in dollars must be LESS than 13.44.
If the discount = 13, we get:
Purchase price = 112 - 13 = 99
Since the purchase price is less than the original price, the answer to the question stem is YES.

Case 2: y = just a bit more than 9
9% of 112 = (0.09)(112) = 10.08
Implication:
Since the discount must actually be more MORE 9%, the discount in dollcars must be MORE than 10.08.
If the discount = 11, we get:
Purchase price = 112 - 11 = 101
Since the purchase price is NOT less than the original price, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

E

Fish181 · Answer

Pick a number for the price of the computer. I chose $100.

1) x = 12%

Therefore new price is $112.

At y = 11%, you would say   * 112 = 99. So yes it's less.
Choose anything less than 12 for y. I chose 0.
At y=0%, the price is 112 so no.

You have a yes/no so insufficient.

2)

We don't know what x is. The computer's price could've been increased by 1% or 1000000000000% percent. Since we know y > 9 then there are cases where it DOES and DOESN'T work.

You have a yes/no so insufficient.

E

KarishmaB · Answer

Essentially, this is a mark-up discount question and requires only 1 calculation. Consider the original price to be the cost price. The price is marked up by x% and then a discount of y% is given. The question is whether there was a loss or not.

(1) x = 12 and y < 12

This I know is not sufficient. Mark up of 12% is on cost price and discount is given on the greater marked up price. So a lower discount will wipe out the entire mark up. But we don't know how much lower y actually is.
Not sufficient.

(2) y > 9

No value for x so certainly not sufficient.

Both together, let me find the value of y for which there will be no profit no loss i.e. she purchased the computer at original price.

(1 + \frac{12}{100}) * DiscountMultiplier = 1

Discount Multiplier = \frac{100}{112}

If y were 9, discount multiplier would be  \frac{91}{100}

Now the question is, which is greater:  \frac{100}{112} or \frac{91}{100}

When I increase 100 (the denominator of second fraction) by 12%, I get 112, the denominator of first fraction. When I increase 91 (the numerator of 2nd fraction by 9 which is 10% of 91, I already get the numerator of first fraction.
It means first fraction is smaller than second fraction. Hence I need a greater discount than y = 9 so that the selling price = cost price. Since y > 9, it is possible that selling price is more than cost price, equal to cost price or less than cost price.

Hence this not sufficient and  answer is (E)

If the last part is a bit too un-intuitive, think of it this way:

Discount percentage is  \frac{12}{112} * 100 = 10.something = y

So if y = 9.5% say, then her purchase price is higher than original price but if y = 11%, then her purchase price is lower than original price. Since both values of y are acceptable as per the 2 statements, we cannot say whether her purchase price was lower than original price.

Answer (E)

Method 2:

Alternatively think of this as successive percentage changes. You increase something by x% and then reduce it by y%. When will the overall impact be nothing? 
If x = 12% 
 \frac{112}{100} * \frac{100}{112}  will give us 1 i.e. no change.

100/112 is a decrease of 12/112 which is 10.something percent. 
So if y = 9.5% say, then her purchase price is higher than original price but if y = 11%, then her purchase price is lower than original price. Since both values of y are acceptable as per the 2 statements, we cannot say whether her purchase price was lower than original price.

Note that both methods are actually the same. They are just different ways of thinking about it. After all, mark up is an application of successive percentage changes. 
The concept of multiplier is  discussed in this video. 
Successive percentage changes are  discussed here.

GMATCoachBen · Answer

This is a key principle that will help you avoid this kind of trap on other questions. Many people will wrongly assume that a 10% increase and 10% decrease will cancel each other out. As we become more mindful and proactively avoid these potential traps, we gain a huge advantage over the competition!

samarpan.g28 · Answer

Let the original price be p. Final price after price increase and discount becomes x*(100+x/100)*(100-y/100).

From statement 1, x is fixed but we will get different values of the final price for y<12. Insufficient.
In statement 2, x is unknown. Insufficient.

Combining 1 and 2, if we consider y=10, the final price becomes 1.008p -> greater than p.
If we consider y=11, the final price becomes 0.9968p -> less than p. Insufficient. Option (E) is correct.

Nitin93 · Answer

Stm1 :
-> Let the original price = 100
-> Since x= 12, current price becomes 112
Finding the boundary value of y at which purchase price = original price
-> 112 * (1-y/100) = 100
-> 1 - y/100 = 100/112
-> y/100 = 12/112
-> y = 1200/112 = 10.xy

y must be greater than 10.xy for purchase price to be less than original price
Given y< 12
1) If y=11 -> answer is Y
2) If y=10 -> answer is N

Not sufficient

Stmt 2 : y>9
-> Since x is not given, markup can be anything. Clearly not sufficient

Stmt 1 + 2
-> 9<y<12 -> again y can be 11 (answer : Y) or 10 (answer : N).
-> Not sufficient

Answer : E

Borrat · Answer

let original price be p.

Current price = p((100 + x)/100)
Elena’s price = ((100 - y)/100) · p((100 + x)/100)

We want: ((100 - y)/100) · ((100 + x)/100) · p < p or (100 - y)(100 + x) < 10,000

x = 12, y < 12

(100 - y)(112) < 10,000 = 11200 - 112y < 10,000
If y = 1: 11088 < 10000 → No
If y = 11: 9968 < 10000 → Yes
Not sufficient.

y > 9
Alone: not sufficient.

1) and 2) together

x = 12, and 9 < y < 12

If y = 11 → Yes
If y = 10 → No

Still not sufficient.

Answer: E

The original price of a computer was increased by x% to reach its

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The original price of a computer was increased by x% to reach its

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards