Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell

Question

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%

x discount on Pony jeans, (0.22 - x) discount on Fox jeans.

Set the equation: 3*15(0.22 - x) + 2*18x = 9 --> x = 0.1 = 10%.

Answer: B.

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%

Bunuel · Accepted Answer

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%

x discount on Pony jeans, (0.22 - x) discount on Fox jeans.

Set the equation: 3*15(0.22 - x) + 2*18x = 9 --> x = 0.1 = 10%.

Answer: B.

A. 9%
B. 10%
C. 11%
D. 12%
E. 15%

x discount on Pony jeans, (0.22 - x) discount on Fox jeans.

Set the equation: 3*15(0.22 - x) + 2*18x = 9 --> x = 0.1 = 10%.

Answer: B.

KarishmaB · Answer

Note: When I look at this question, my first instinct is to check if the split is 10% and 12%. The reason is that it is a lucky twin... i.e. when I split 22% to get one part as 10%, the other is 12%. When one part is 9%, the other is 13% (not there in options). When one part is 15%, the other is 7% (not there in options). 11% cannot be because the discount rates are different. I am not saying this strategy will always work, but this is what I will always start with because it has the maximum probability of being correct.

Why? Because it is the tendency of the question setter to give one option as 12% too even if the correct answer is 10% because it is a pit for someone who is careless. Say, one found that the 22% is split into 10 and 12 but while answering the question, made a mistake of marking the discount on Fox jeans rather than Pony jeans... Bang!

So watch out for lucky twins especially in probability questions!

craky · Answer

Thanks bunuel, even faster solution than with 2 equasions.

subhashghosh · Answer

Let x be the discount on Fox Jeans
Let y be the discount on Pony Jeans

x + y = 22

x/100* 15 * 3 + y/100 * 18 * = 9

Solving these we get y = 10, so the answer is B.

Yalephd · Answer

I follow the 10 / 12 split, but how would you end up choosing 10 over 12 using the lucky twin strategy for this question?

IanStewart · Answer

That might sound plausible, and I've certainly read about the 'trick' of identifying 'twin' answer choices many times, but in practice it is completely pointless to look for twinned answer choices. I looked at all the official questions in the OG and the Official Quant Review to see how often you'd answer correctly if you always guessed that a 'twin' answer was correct. It turns out you'd do (very slightly) worse by guessing a 'twin' than if you just guessed at random. I posted details here: spaceland-prep-strategy-question-110923.html

Spidy001 · Answer

Let x and y are discount rates on Fox and Pony jeans respectively.

=> 3(15)(x) + 2*18(0.22-x) = 9

=> x = 12% and y =10%

Answer is B.

KarishmaB · Answer

It is a guess. The way it helps me is that I will first check for the 10/12 split. If it doesn't work out, I will check the other options. You have to solve to get to the right answer. 
Say if the % offered on Pony jeans ($18) is 10%, I am getting a discount of 1.8 on each pair of jeans. If I am getting 12% discount on Fox jeans($15), I am saving $1.8 on each pair of Fox jeans (you can calculate this orally and quickly - 10% of 15 is 1.5; 1% of 15 is 0.15 so 2% is 0.3, hence 12% of 15 is 1.5+0.3 = $1.8. If it seems too cumbersome, it is only because of lack of practice; it actually happens in a flash once you are used to it!) 
On 3 pairs of Fox jeans and 2 pairs of Pony jeans, I will save 5*1.8 = $9
Since $9 is the given discount, our assumption is correct and the discount of Pony jeans must be 10%.

gmat1220 · Answer

Karishma

Considering the weights - 3 and 2 (3 pairs of fox and 2 pairs of pony) - that he saved (12/10 discount) more by buying more of the fox jeans than pony jeans ? Is this thinking correct? i.e. more discount on the fox.

Or the opposite

He could have saved more by more discount on the pony - since the pony is priced for $3 more ($18 per pair) Hence we must rule out the option D before guessing option B. What do you think?

KarishmaB · Answer

I think the way you are thinking is pretty great but I did not understand what is 12/10 discount.

If you want to consider weights, say, if you know that the answer is either 10-12 or 12-10, you can think this way:
3 Fox jeans price = $45
2 Pony jeans price = $36
So you got a discount of $9 on $81 which is 1/9 i.e. 11.11% discount. Since Fox jeans total cost price is higher than Pony jeans total cost price, the discount of Fox jeans must be 12% and that of Pony jeans must be 10% to give an average discount of 11.11% i.e. a value closer to 12% than to 10%.

ScottTargetTestPrep · Answer

At the regular prices, 3 pairs of Fox jeans and 2 pairs of Pony jeans would cost 3 x 15 + 2 x 18 = 45 + 36 = $81. Since a total of $9 is saved at the discounted prices, the cost of the same 5 pairs of jeans is now $72. Since the sum of the 2 discount rates is 22%, we can let n/100 = the discount rate of Pony jeans and (22 - n)/100 = the discount rate of Fox jeans and create the equation:

3 x 15 x (1 - (22 - n)/100) + 2 x 18 x (1 - n/100) = 72

Multiplying the equation by 100, we have:

45 x (100 - (22 - n)) + 36 x (100 - n) = 7200

45 x (78 + n) + 3600 - 36n = 7200

3510 + 45n - 36n = 3600

9n = 90

n = 10

Thus, the discount rate of Pony jeans is n/100 = 10/100 = 10%.

Answer: B

rickyric395 · Answer

Hey  Spidy001  9$ is saved money so isn't the 2nd equation be original price - discounted price = saved money ?

rickyric395 · Answer

Hey  Bunuel  , saved money is 9$ , then isn't that should be original price - discounted price = saved money . What am I missing ?

Bunuel · Answer

Yes, you could do that way too:

(3*15 + 2*18) - (3*15*(1 - (0.22 - x)) + 2*18*(1 - x)) = 9

If you simplify the above you get the same equation I have:

3*15(0.22 - x) + 2*18x = 9

My equation, represents the following:

Amount of the discount on Fox jeans + Amount of the discount on Pony jeans = $9.

Does this help?

rickyric395 · Answer

Hey  Bunuel , from the stem , I formed 2 equations 1)  x+y=22  2)  3*15*(1-\frac{x}{100}) + 2*18*(1-\frac{y}{100}) 
But I guess i have made some mistake. Can you please point it to me?

Bunuel · Answer

There is no second  equation  in your post. What does this  expression  represent:  3*15*(1-\frac{x}{100}) + 2*18*(1-\frac{y}{100})  ?

rickyric395 · Answer

Sorry , I missed writing the complete 2nd equation.
1st eqn is  x+y=22  ----- (from sum of rate of discount as 22)
2nd eqn is  3*15*(1-\frac{x}{100}) + 2*18*(1-\frac{y}{100})=9  ----- (money saved is 9$)

Bunuel · Answer

If the discount on Pony jeans is say 10%, then 2*18*0.10 gives the amount of the discount, while 2*18*(1 - 0.1) gives the amount paid. You are mixing these two.

Kinshook · Answer

@shanewyattGiven: Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans.

Asked:  If the sum of the two discounts rates is 22 percent, what is the discount rate on Pony jeans?
Let  the discount rate on Pony jeans be x%.
The discount rate on Fox jeans = 22% - x%

3*15*(.22-x%) + 2*18*x% = 9
9.9 - .45x + .36x = 9
.09x = .9
x = 10%

IMO B

Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell

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Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell

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