A merchant discounted the sale price of a coat and the sale price of a

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 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.

Statement 1 and 2 are clearly insufficient.

Combine both statement, we have

Price for coat = C
Percent discount for coat = X

Price for sweater = C+2
Percent discount for sweater = X-2

So, the question asks whether
\(\frac{(X-2)(C+10)}{100} > \frac{XC}{100}\)

Multiply both side by 100

\((X-2)(C+10) > XC\)

Simplify the equation, we get

Is \(10X > 2C + 20\) ?

Since it depends on 2 variables, we cannot conclude which of the two articles was discounted by greater dollar amount.

Am I doing it right?

(1) not sufficient; we dont't have dollar amounts
(2) Sweter: P dollars, Coat P-10 clearly not sufficient, as no info about %of a discount
(1+2) Still not sufficient Price could be 20$ or 1000000$ which will give us differnt results....
Answer (E)

Let Pc and Ps, Dc and Ds be prices, percentage discounts for Coat and Sweater respectively.

So the question is Pc*Dc>Ps*Ds or Pc*Dc<Ps*Ds?
It’s a clever question but if we get rid of all the verbiage it could be stripped down to:
Is Pc*Dc>Ps*Ds
St1) Dc>Ds
St2) Pc<Ps
Since two statements put together don’t give us a certain direction of inequality we cant answer the question. Ans E
For details see below-

St1) Dc=Ds+2--> Pc*(Ds+2)>Ps*Ds? INSUF as we dont know the values of Pc and Ps. To be precise we need to know if Pc>Ps*Ds/(Ds+2)?
St2) Pc=Ps-10 --> (Ps-10)*Dc>Ps*Ds? INSUF as we dont know the values of Dc and Ds. To be precise we need to know if Dc>Ds*Ps/(Ps-10)?
St1+St2) since Dc=Ds+2 doesnt help us answer Dc>Ds*Ps/(Ps-10)? or Pc=Ps-10 doesnt help us answer if Pc>Ps*Ds/(Ds+2)? INSUF
Ans E

Clearly both statements alone are insuff..
So needed to check 2 different values of sweater with very much difference for getting a quick answer.
I will check for a price of $20 and another for $1000 for a given discount of 10% (check easy number for fast calculation)
for sweater @ $20 discount is $2 thus price of coat is $10 less=$10 and discount is 12 %( as discount on the coat was 2 percentage points greater) of it is $1.2.
discount amount of sweater > discount amount of Coat.
similarly for a sweater price of $ 1000 will have a discount $100
And discount of coat is 12% of 990 =118.....
discount amount of sweater < discount amount of Coat.

Ans E.

Coat = C -> Discount by a%
Sweater = S -> Discount by b%
Is \(\frac{C*a}{100}\) > or < \(\frac{S*b}{100}\)?

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
\(\frac{S*b}{100}\) = 1.6
\(\frac{C*a}{100}\) = 1

But if x = 52%, y = 50%
C = 1000, S = 1010
\(\frac{S*b}{100}\) = 505
\(\frac{C*a}{100}\) = 520

2 different values. Insufficient.

E is the answer.
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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 experts, please provide your inputs on my analysis

The way I solved this,

Given :

let the selling price of the coat be $X

let the selling price of the sweater be $Y

Statement 1: If Y - a% of Y, then X - (a+2)% of X ... we need to compare a%ofY and (a+2)%ofX .. clearly we need X and Y to reach the desired result, and we don’t have X and Y.. hence not sufficient

Statement 2: Y=X+10 — clearly not sufficient

Combining Statement 1 and Statement 2, we need to compare

(a+2)% of X, which is equal to (aX)/100 + 2x/100

And

a% of (X+10), which is equal to (aX)/100 + 10a/100

So which of the above two is greater depends on 2X/100 and on 10a/100 .. we don’t have both “a” and “X”, hence what impact would both 2X/100 and 10a/100 have on aX/100 can’t be uniquely determined. Hence the answer E

PS: we can also consider certain values and get to the correct answer, BUT I find putting values both risky and time consuming

chetan2u VeritasKarishma Bunuel

Apologies if I have missed a few names of the experts, please feel free to provide your inputs

Looking forward to hearing from you guys

Best regards,

Posted from my mobile device

Yes, the method is correct. Only point is that $ and $Y are not the selling price but marked price. SP would be after the discount.
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Dollar amount of discount depends on both, the marked price and the discount percentage. So neither statement alone is sufficient.

Taking both statements together,

Coat - Sale price is $10 less and discount is 2% more.

Think about the instance when the discount dollar amount will be the same.

Say discount percentages are 4% and 2% for coat and sweater respectively.
When will 4% of something be equal to 2% of something else? When the amounts are in the ratio 1:2. Since we want the difference between them to be 10, the amounts would be 10 and 20 for marked price of coats and sweaters respectively.
So 4% of 10 is 4 and 2% of 20 is 4.

Now if the amounts are 5 and 15 for example, the dollar amount of discount on coats is lower.
but if the amounts are 20 and 30, the dollar amount of discount on coats is higher.

Hence, the given information is not sufficient.

Answer (E)

Use of too many variables eats up your time and makes you lose the plot.
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VeritasKarishma -- this is really amazing insight ..

Is there a blog post specifically on this issue perhaps ?

I understand the concept here but i need to do some more questions in order to get this imbibed completely

I am afraid on test day, with the added pressure of test anxiety + timings = i may not able to think logically like this unless i practice more questions using this concept or just reading a blog post

Any links or posts towards this would be helpful

Thank you !

jabhatta2 - Such a method involves clarity about ratios, percentages, markup-discount, transition points and the need to solve questions logically. If someone asks me whether x will always be greater than y, I will try to make them equal and then see why x cannot be less than y. There is no one single concept behind it. GMAT will keep making innovative questions testing multiple concepts. Your best hope would be to throw away your scratch pad and then try to work logically.
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Solution:

Question Stem Analysis:

We need to determine which of the two articles of clothing, the coat or the sweater, was discounted by the greater dollar amount.

Statement One Alone:

Statement one alone is not sufficient to answer the question since it depends on the original prices of the coat and sweater. If they had the same price originally, then the coat would have a greater dollar amount discount. However, if the sweater had a higher price than the coat, the sweater could have a greater dollar amount discount. For example, if the coat was $30 originally and the discount was 10%, the coat was discounted by $3. However, if the sweater was $40 originally and the discount was 8%, the sweater was discounted by $3.20.

Statement Two Alone:

Statement two alone is not sufficient to answer the question since it depends on the percentages of discount of the coat and sweater. If they had the same percentage, then the sweater would have a greater dollar amount discount. However, if the coat had a higher percentage discount than the sweater, the coat could have a greater dollar amount discount. For example, if the sweater was $100 originally and the discount was 8%, the sweater was discounted by $8. However, if the coat was $90 originally and the discount was 10%, the coat was discounted by $9.

Statements One and Two Alone:

Even with the two statements, there is still not enough information to answer the question since we can use the same examples that we used in statements one and two. In statement one, we see that given that the original price sweater was $10 more than that of the coat, and the percent discount of the coat is 2% more than that of the sweater, so the sweater had a greater dollar amount discount ($3.20 vs. $3). However, in statement two, given the same conditions, the coat had a greater dollar amount discount ($9 vs. $8).

Answer: E

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Answer: Option E

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Bunuel chetan2u I followed the official explanation but I am not able to grasp even I could see that E is correct option after playing with numbers. Can you give inputs on this. Is there any general principle of this or why its actually occurring because there is only a difference of 10 in amount.

Here is a a systematic way to solve this problem along with an understanding of how to solve such problems. The trick is to first calculate the "cost price" because the cost of raw materials is usually fixed.

Step 1: Express / find cost price
Step 2: Apply cost price to the second equation
Step 3: Solve the problem


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assume

coat 100$
sweater 110$


1) coat 2% and sweater 0% >> 2 vs 0 >> ">" (2>0)
2) coat 100% and sweater 98% >> 100 vs 110-2.2 >> "<" (100<107.8)

So E