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A store sells only two types of shirts - branded and non-branded

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A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 20 Apr 2018, 01:34
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[header3]GST Week 2 Day 4 e-GMAT Question 4/header3]
Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirt that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.

2. On that day, the total sales from shirts were between $1604 and $1674.

Answer Choices

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.

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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post Updated on: 20 Apr 2018, 02:06
souvik101990 wrote:

GST Week 2 Day 4 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirt that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.

2. On that day, the total sales from shirts were between $1604 and $1674.

Answer Choices

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.




Statement (1) ALONE is NOT sufficient,

Only option (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient as can be seen in the table below

B U B Price Unbranded Price Total

30 Branded and 0 Unbranded Total Price is (30*60) + 0 $1800

29 Branded and 1 Unbranded Total Price is (29*60) + (20*1) $1760

28 Branded and 2 Unbranded Total Price is (28*60) + (20*2) $1720

27 Branded and 3Unbranded Total Price is (27*60) + (20*3) $1680

26 Branded and 4 Unbranded Total Price is (26*60) + (20*4) $1640

25 Branded and 5 Unbranded Total Price is (25*60) + (20*5) $1600

24 Branded and 6 Unbranded Total Price is (24*60) + (20*6) $1560



Only Branded quantity of 26 and Unbranded quantity of 4 satisfy condition of statement (2)

Hence option B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficien is the answer
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Originally posted by houston1980 on 20 Apr 2018, 01:54.
Last edited by houston1980 on 20 Apr 2018, 02:06, edited 1 time in total.
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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 20 Apr 2018, 02:05
Correct Answer - B

Price of a branded shirt = $60
Number of branded shirts= B
Number of non-branded shirts= N
Price of a Non-Branded shirt = $20

total shirts sold on a day = 30
B + N= 30

To find- B

1. B>20 . It can be any number greater than 20 , so Not sufficient

2. 1604< T <1674
Let total sales = T
T= (60 * B) + (20 * N)
By maximizing B(as it has the greater price), we get only one value for T which is between 1604 and 1674.

Sufficient
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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 20 Apr 2018, 05:09
souvik101990 wrote:

GST Week 2 Day 4 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirt that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.
2. On that day, the total sales from shirts were between $1604 and $1674.

Answer Choices

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.


Let branded shirts =X and non-branded shirts =Y. Given, X+Y=30 and we are asked to find X.

1. The store sold more than 20 branded shirts on that day. --->>> Clearly Not Sufficient.
2. On that day, the total sales from shirts were between $1604 and $1674. --->>> this leads to the below equation.

1604 < 60X+20Y < 1674
1604 < 60X+20(30-X) < 1674 ---- Substituting Y=30-X
1604 < 60X+600-20X < 1674
1004 < 40X < 1074
25.1 < X < 26.85

As, shirt has to be an integer X will be 26 and Y=30-26=4.
Validation: Confirm the total sales of shirts by putting the values 26*60+20*4=1560+80=1640 which is between 1604 and 1674.

Hence, statement 2 is sufficient.

Answer (B).
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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 21 Apr 2018, 14:49
souvik101990 wrote:

GST Week 2 Day 4 e-GMAT Question 1


Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and e-GMAT Quant Online Course . See the GMAT Spring Training Thread for all details


A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirt that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.

2. On that day, the total sales from shirts were between $1604 and $1674.

Answer Choices

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D) EACH statement ALONE is sufficient.

E) Statements (1) and (2) TOGETHER are NOT sufficient.



The correct answer is Option B

Here is the solution:

From the question we can gather that Branded (B) and Non-Branded (B) sum up to 30 units. So B+NB=30 . Another important thing we get from the question is that both B and NB are positive integers.
Now lets consider the options:
1) NB>20 - This is of no help as there are multiple cases that fulfil this. Hence option A & D are eliminated.
2) Mathematically, the statement will look something like - 1604< 60B+20NB < 1674 or 1604< 20(3B+NB) < 1674
So 20(3B+NB) can only 1620 or 1640 or 1660. Now we have two equations and two variables. On solving, we further realise that 20(3B+NB) can only be 1640, such that B and NB are positive integers.

Hence, option B.
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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 23 Apr 2018, 06:48
A store sells only two types of shirts - branded and non-branded. All the branded shirts are priced at $60 per unit and all the non-branded shirts are priced at $20 per unit. On a certain day, the store sold a total of 30 shirts. What is the number of branded shirt that the store sold on that day?

1. The store sold more than 20 branded shirts on that day.

2. On that day, the total sales from shirts were between $1604 and $1674.

Let the number of branded shirts sold be x. Since 30 shirts were sold in total, number of Non branded shirts sold was 30-x. The question asks to find: x

Total sales from sales of shirts = 60(x) + 20(30-x) = 40 x + 600 = 40 (x+15). Since x is an integer greater than 0, the total sales should be a multiple of 40.

Step 1 - Evaluate statement (1) independently:- Store sold more than 20 branded shirts => x >20. Clearly, there is no unique value of x. Statement (1) is insufficient.

Step 2 - Evaluate statement (2) independently:- total sales from shirts were between $1604 and $1674. From our pre-thinking step, we know that total sales should be a multiple of 40. Clearly, there is only one multiple of 40 between between $1604 and $1674 i.e. $1640. Hence x = 1640/40 - 15 = 26. Hence, statement (2) is sufficient.

Step 3 - Evaluate statements (1) and (2) combines:- There is no need of this step as statement (2) alone is sufficient.

Hence answer is choice B :)
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Re: A store sells only two types of shirts - branded and non-branded  [#permalink]

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New post 23 Apr 2018, 07:57
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Re: A store sells only two types of shirts - branded and non-branded &nbs [#permalink] 23 Apr 2018, 07:57
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