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605-655 (Medium)|   Percent and Interest Problems|   Word Problems|                                    
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A merchant discounted the sale price of a coat and the sale price of a 23 Mar 2022, 03:49
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E
assuming 2 cases for discount percent
    Marked price discount % discount
    coat 90 3% 2.7
    sweater 100 1% 1
    coat > sweater

    Marked price discount % discount
    coat 90 52% 46.8
    sweater 100 50% 50
    coat< sweater
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A merchant discounted the sale price of a coat and the sale price of a 25 Oct 2022, 03:25
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BrentGMATPrepNow
Bunuel
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.

Target question: Which of the two articles of clothing was discounted by the greater dollar amount?

Let's jump straight to....

Statements 1 and 2 combined
Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT

Let x = price of SWEATER before discount
Let x - 10 = price of COAT before discount

Now let's calculate the discount for each item.

Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)

Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)

So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?

Let's test some values.

Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is the SWEATER has the greater discount

Case a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is the COAT has the greater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Hi BrentGMATPrepNow, for St 1, why we are not able to assume sweater discount as 100 here? As I'm thinking like % increase decrease if it had been years here and not coat or sweater? Thanks.
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A merchant discounted the sale price of a coat and the sale price of a 25 Oct 2022, 18:39
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Kimberly77

Hi BrentGMATPrepNow, for St 1, why we are not able to assume sweater discount as 100 here? As I'm thinking like % increase decrease if it had been years here and not coat or sweater? Thanks.
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The given information only tells us that the sale price of the coat and sweater were both discounted buy some amount.

Statement 1 tells us that: The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
There are lots of scenarios that satisfy this information.

For example, it could be the case that the coat was discounted by 12% and the sweater was discounted by 10%
Or it could be the case that the coat was discounted by 13% and the sweater was discounted by 11%
Or it could be the case that the coat was discounted by 14% and the sweater was discounted by 12%
Or it could be the case that the coat was discounted by 15% and the sweater was discounted by 13%
Or it could be the case that the coat was discounted by 16% and the sweater was discounted by 14%
.
.
.
etc
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A merchant discounted the sale price of a coat and the sale price of a 25 Oct 2022, 21:03
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Thank you for posting this solution: no algebra, no testing of values, almost no numbers at all.
    If a greater discount percentage was applied to the more expensive item, then the discount amount on that item would clearly be greater.

    But the extra 2% discount is on the cheaper item... and there's no way to know "if that's more than enough to compensate for the missing 2% on the more expensive item"

Posted from my mobile device
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A merchant discounted the sale price of a coat and the sale price of a 26 Oct 2022, 12:23
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BrentGMATPrepNow
Kimberly77

Hi BrentGMATPrepNow, for St 1, why we are not able to assume sweater discount as 100 here? As I'm thinking like % increase decrease if it had been years here and not coat or sweater? Thanks.

The given information only tells us that the sale price of the coat and sweater were both discounted buy some amount.

Statement 1 tells us that: The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
There are lots of scenarios that satisfy this information.

For example, it could be the case that the coat was discounted by 12% and the sweater was discounted by 10%
Or it could be the case that the coat was discounted by 13% and the sweater was discounted by 11%
Or it could be the case that the coat was discounted by 14% and the sweater was discounted by 12%
Or it could be the case that the coat was discounted by 15% and the sweater was discounted by 13%
Or it could be the case that the coat was discounted by 16% and the sweater was discounted by 14%
.
.
.
etc
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Great explanation thanks BrentGMATPrepNow
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A merchant discounted the sale price of a coat and the sale price of a 25 Dec 2022, 03:11
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BrentGMATPrepNow
Bunuel
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.

Target question: Which of the two articles of clothing was discounted by the greater dollar amount?

Let's jump straight to....

Statements 1 and 2 combined
Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT

Let x = price of SWEATER before discount
Let x - 10 = price of COAT before discount

Now let's calculate the discount for each item.

Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)

Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)

So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?

Let's test some values.

Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is the SWEATER has the greater discount

Case a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is the COAT has the greater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Hi BrentGMATPrepNow, regarding St.2 , p+2 = percent discount on COAT, not sure why is not C = 1.02P since is 2 percentage points greater than the percent discount on the sweater?
Thanks Brent
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A merchant discounted the sale price of a coat and the sale price of a 27 Dec 2022, 11:16
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Kimberly77
BrentGMATPrepNow
Bunuel
A merchant discounted the sale price of a coat and the sale price of a sweater. Which of the two articles of clothing was discounted by the greater dollar amount?

(1) The percent discount on the coat was 2 percentage points greater than the percent discount on the sweater.
(2) Before the discounts, the sale price of the coat was $10 less than the sale price of the sweater.

Target question: Which of the two articles of clothing was discounted by the greater dollar amount?

Let's jump straight to....

Statements 1 and 2 combined
Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT

Let x = price of SWEATER before discount
Let x - 10 = price of COAT before discount

Now let's calculate the discount for each item.

Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)

Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)

So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?

Let's test some values.

Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is the SWEATER has the greater discount

Case a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is the COAT has the greater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Hi BrentGMATPrepNow, regarding St.2 , p+2 = percent discount on COAT, not sure why is not C = 1.02P since is 2 percentage points greater than the percent discount on the sweater?
Thanks Brent
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I suggest that you try testing some different values for P and C confirm your hypothesis.
Let me know what you get.
Also, be sure to clearly define what P and C represent
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A merchant discounted the sale price of a coat and the sale price of a 27 Dec 2022, 13:16
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Thanks BrentGMATPrepNow. C = Coat, P = %
As there's no exact discount being given but only 2 percentage points greater than the percent discount on the sweater therefore we can only conclude it as p+2 = percent discount on COAT? Is that correct Brent? Thanks
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A merchant discounted the sale price of a coat and the sale price of a 29 May 2024, 20:42
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­Coat = C -> Discount by a%
Sweater = S -> Discount by b%
Is C∗a100𝐶∗𝑎100 > or < S∗b100𝑆∗𝑏100?

1) x = y + 2
We do not know the price. Insufficient.

2) C = S - 10
We do not know the discount %. Insufficient.

1+2)
x = y +2
C = S - 10
x = 10% and y = 8%
C = 10, S = 20
S∗b100𝑆∗𝑏100 = 1.6
C∗a100𝐶∗𝑎100 = 1

But if x = 52%, y = 50%
C = 1000, S = 1010
S∗b100𝑆∗𝑏100 = 505
C∗a100𝐶∗𝑎100 = 520

2 different values. Insufficient.

E is the answer
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A merchant discounted the sale price of a coat and the sale price of a 09 Apr 2025, 07:00
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chetan2u
Psk13
c=s-10
x=y+2

case 1: c=90 s=100
x=4% y 2%
discount on coat = 90*4%=3.6
discount on sweater = 100*2%=2

coat>sweater

case 2: c= 490 s =500
x=12% y=10%
discount on coat = 490*12%=58.8
discount on sweater=500*10%=50
coat >sweater
why am i getting same scenarios
are there any constraints on taking the sample values?

Take scenarios where 10 is a big amount as compared to x and y..
say x = 5 and y =15...
4% 0f 5 = 0.2 and 2% of 15 = 0.3, so s>c..
similarly there will be many other values
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Hi chetan2u,

Thanks for the explanation. But can you please give the reason, why we should take a value where 10 is a big amount as compared to x and y? i did get the right answer... but i had to test 3/4 values to get insufficiency for both statements combined...Hence asking...
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A merchant discounted the sale price of a coat and the sale price of a 24 Jul 2025, 18:17
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If the same question had asked for discounted price, Would the option C be right?
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A merchant discounted the sale price of a coat and the sale price of a Updated on: 05 Oct 2025, 01:32
Originally posted by anushree01 on 05 Oct 2025, 01:09.
Last edited by Bunuel on 05 Oct 2025, 01:32, edited 1 time in total.
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If they had given : More discount is on more expensive item only then we could conclusively say that the expensive item will be cheaper.
But since even on combining A & B both --> we dont get that.
So Answer is E
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A merchant discounted the sale price of a coat and the sale price of a 20 Jun 2026, 12:52
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Hey Brent, thank you for your explanation. Is there a way/method to pick two values to test here?
BrentGMATPrepNow


Target question: Which of the two articles of clothing was discounted by the greater dollar amount?

Let's jump straight to....

Statements 1 and 2 combined
Let p = percent discount on SWEATER
So, p+2 = percent discount on COAT

Let x = price of SWEATER before discount
Let x - 10 = price of COAT before discount

Now let's calculate the discount for each item.

Discount on SWEATER = (p/100)(x)
Discount on COAT = (p+2/100)(x - 10)

Let's make things easier on ourselves by multiplying both values by 100 to get:
Discount on SWEATER = (p)(x)
Discount on COAT = (p + 2)(x - 10)

So, which value is greater?
Is (p)(x) greater than (p + 2)(x - 10)? Or is (p + 2)(x - 10) greater than (p)(x)?

Let's test some values.

Case a: p = 8 and x = 11.
In this case, (p)(x) = (8)(11) = 88 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(11 - 10) = (10)(1) = 10 (= discount on COAT)
So, the answer to the target question is the SWEATER has the greater discount

Case a: p = 8 and x = 110.
In this case, (p)(x) = (8)(110) = 880 (= discount on SWEATER)
And (p + 2)(x - 10) = (8 + 2)(110 - 10) = (10)(100) = 1000 (= discount on COAT)
So, the answer to the target question is the COAT has the greater discount

Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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A merchant discounted the sale price of a coat and the sale price of a 26 Jun 2026, 09:14
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Hi AnushkaKala,

Yes, there's a clean method, and it beats picking numbers at random (which is why some posters above kept landing on the same answer, e.g., Psk13 getting "coat > sweater" twice).

The trick is to find the break-even point first - the case where the two dollar discounts are exactly equal - and then pick one value on each side of it.

Step 1: Set the two discounts equal

Using the combined info (coat is $10 cheaper and gets 2% more discount), let the sweater price be S and its discount be d%:

- Sweater discount = d% of S
- Coat discount = (d+2)% of (S - 10)

Set them equal and simplify, and you get the boundary: S = 5d + 10.

Step 2: Pick a discount, then straddle the boundary

Say d = 2 (sweater 2%, coat 4%). The break-even price is S = 5(2) + 10 = 20.

Check it: sweater = 2% of 20 = 0.40; coat = 4% of 10 = 0.40. Equal - good, that's the pivot.

Now step to each side:

- S = 30: sweater = 2% of 30 = 0.60; coat = 4% of 20 = 0.80 - coat wins.
- S = 15: sweater = 2% of 15 = 0.30; coat = 4% of 5 = 0.20 - sweater wins.

Same two statements, two opposite answers - not sufficient - E.

Why random guessing kept failing

If you pick a large price (like $1000), the $10 gap is tiny, so the higher-percent coat almost always wins - you'll keep getting the same answer. To flip the result, you need a price where $10 is a big chunk of the total (chetan2u's point about "10 being large compared to the prices").

Takeaway: when you must show insufficiency, hunt for the equality case, then test one value above and one below it. That guarantees you find both answers fast instead of fishing.

Answer: E

AnushkaKala
Hey Brent, thank you for your explanation. Is there a way/method to pick two values to test here?

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