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

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Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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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%
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Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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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.
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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New post 01 Jan 2010, 10:42
Would go with B.... i.e. 10%

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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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New post 02 Feb 2011, 11:09
Thanks bunuel, even faster solution than with 2 equasions.
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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shanewyatt wrote:
Can find total price without discount ($81) and price after discount ($72), but not sure where to go from there.

Image


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!
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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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.
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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New post 16 Apr 2011, 13:30
I follow the 10 / 12 split, but how would you end up choosing 10 over 12 using the lucky twin strategy for this question?

VeritasPrepKarishma wrote:
shanewyatt wrote:
Can find total price without discount ($81) and price after discount ($72), but not sure where to go from there.

Image


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!

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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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VeritasPrepKarishma wrote:
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!


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
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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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.

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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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



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%.
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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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New post 17 Apr 2011, 12:20
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?

VeritasPrepKarishma wrote:

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%.

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Re: Disclosed GMAT Exam #42 Discounted Jeans [#permalink]

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gmat1220 wrote:
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?


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%.
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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 08 Mar 2014, 06:05
Option B.
Method of equations
Discount on F=x%
Discount on P=y%
we're given x+y=22
And second equation:5x+4y=100
On simplification y=10%

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 03 May 2014, 03:31
I prefer Bunel's equations, but here's another way:

We buy 3 Fox jeans : 3*15=45.
We buy 2 Pony jeans: 2*18=36.

45*discount fox + 36*discount pony = 9.

Let's start with Answer A.
If the discount on the Pony jeans would be 9% ==> 36*0.09=3.24
Which means discount fox should be 13% ( To match the 22% in total)

12% of 45 = 5,85
And 5,85 + 3.24 = NOT 9 ( The total discount in $)

Let's try answer B. ( I usually start with the most easy percentiles)
10% of 36 = 3,6
12% of 45 = 5,4

3,6+5,4=9 ==> We got a match! Answer B.
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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 01 Aug 2014, 02:35
Without discount, jeans selling price = 15 * 3 + 18 * 2 = 81

Discount = 9

With discount, selling price = 81-9 = 72

Say discount on Pony = x%; so discount on fox = (22-x)%

Setting up equation:

\(\frac{22-x}{100} * (15*3) + \frac{x}{100} * (18*2) = 9\)

x = 10

Answer = B
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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 29 Sep 2015, 03:42
I have a doubt with this question.
if x - pony & y - fox
If the amount saved is 9 then shouldn't the equation be
((3*15)+(2*18)) - ((3*15*x/100)-(2*18*y/100))=9
and x+y=22

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 26 Oct 2015, 01:17
Backsolve is good:

take C (11% each) means (11/100)*15*3+(11/100)*18*2 must be 9, but it is slightly less. So , it is B or D

take D (10% Pony and 12% Fox) means (10/100)*15*3+(12/100)*18*2 is more less than C

so B

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans [#permalink]

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New post 04 Nov 2015, 14:43
I set my question up a bit differently and I am confused as to why I am doing it different / wrong then others.

Lapse in logic along the way, hope someone can point it out.


====== MY METHOD =======
Set total price - discount price = 9

[3*15 + 2*18] - [15*3*y + 2*18*x] = 9

Then I simplified to

72 = 45(22-x)+36x
102=x

Something is off and I am not sure what.

Hope someone can help. Thanks.

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Re: Fox jeans regularly sell for $15 a pair and Pony jeans   [#permalink] 04 Nov 2015, 14:43

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