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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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20 Apr 2018, 01:34
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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.

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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Updated on: 20 Apr 2018, 02:06
1
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.

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 _________________ Kindly press the +1Kudos if you like the explanation. Thanks a lot!!! 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. Intern Joined: 09 Jun 2012 Posts: 26 Location: India Re: A store sells only two types of shirts - branded and non-branded [#permalink] ### Show Tags 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 _________________ Please press +1 Kudos if you find my post/reply helpful Manager Joined: 03 Oct 2016 Posts: 122 Re: A store sells only two types of shirts - branded and non-branded [#permalink] ### Show Tags 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). _________________ Non-Allergic To Kudos Intern Joined: 10 May 2016 Posts: 17 Location: India GMAT 1: 690 Q49 V35 GPA: 3.9 Re: A store sells only two types of shirts - branded and non-branded [#permalink] ### Show Tags 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. Intern Joined: 03 Jan 2015 Posts: 4 Re: A store sells only two types of shirts - branded and non-branded [#permalink] ### Show Tags 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.

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

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

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26 Nov 2018, 07:48
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souvik101990 wrote:
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.

Given: 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.
Let B = # of branded shirts sold
Let N = # of non-branded shirts sold
If a TOTAL of 30 shirts were sold, we can write: N + B = 30

Target question: What is the value of B?

Statement 1: The store sold more than 20 branded shirts on that day.
All we know so far is that N + B = 30
So, it's possible that B = 21, B = 22, B = 23, etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: On that day, the total sales from shirts were between $1604 and$1674.
Branded shirts cost $60 each, and all the non-branded shirts cost$20 each
We can write: 20N + 60B = TOTAL sales
This means: 20N + 60B = some value between $1604 and$1674

Let's see if we can also use the fact that N + B = 30 to help us answer the target question.
We can rewrite 60B as 20B + 40B and see what happens.
We get: 20N + 20B + 40B = some value between $1604 and$1674
Factor first two terms to get: 20(N + B)+ 40B = some value between $1604 and$1674
Replace N + B with 30 to get: 20(30)+ 40B = some value between $1604 and$1674
Evaluate: 600 + 40B = some value between $1604 and$1674
Subtract 600 from both sides to get: 40B = some value between $1004 and$1074

IMPORTANT: B is a POSITIVE INTEGER.
If B = 25, then 40B = 40(25) = 1000, which is NOT between $1004 and$1074
If B = 26, then 40B = 40(26) = 1040, which IS between $1004 and$1074
If B = 27, then 40B = 40(27) = 1080, which is NOT between $1004 and$1074

So, there's only 1 possible value that satisfies statement 2.
The answer to the target question is B = 26
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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

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27 Nov 2018, 19:45
souvik101990 wrote:
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.

$$30\,{\text{units}}\,\,\,\left\{ \begin{gathered} \,B\,\,{\text{branded}}\,{\text{,}}\,\,{\text{\ 60}}\,\,{\text{each}} \hfill \\ \,N\,\,{\text{non - branded}}\,{\text{,}}\,\,{\text{\ 20}}\,\,{\text{each}} \hfill \\ \end{gathered} \right.$$

$$? = B$$

$$\left( 1 \right)\,\,B > 20\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {B,N} \right) = \left( {21,9} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 21 \hfill \\ \,{\text{Take}}\,\,\left( {B,N} \right) = \left( {22,8} \right)\,\,\,\, \Rightarrow \,\,\,\,? = 22 \hfill \\ \end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.$$

$$\left( 2 \right)\,\,1604 < 60B + 20\left( {30 - B} \right) < 1674\,\,\,\,\,\,\left[ \ \right]$$

$$1604 < 40B + 600 < 1674$$

$$25 \cdot 40 + 4 = 1004 < 40B < 1074 = 26 \cdot 40 + 34$$

$$25 + \frac{4}{40} < B < 26 + \frac{34}{40}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = B = 26\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{SUFF}}.$$

This solution follows the notations and rationale taught in the GMATH method.

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

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08 Dec 2018, 02:05
B Branded, N Not branded
B+N=30 --- (a)

Total Sales must be: 60B+20N= 40B+20(B+N)= 40B+20*30=40B+600 --- (b)

1. B>20
B can be 21, 22,...
No eqn. that puts any restriction on value of B
Not sufficient

2. 1604< Total Sales < 1674
From b, 1604 < 40B+600 < 1674
It is possible for only one value of B, i.e. 26
Hence, sufficient.

Option: B
Re: A store sells only two types of shirts - branded and non-branded   [#permalink] 08 Dec 2018, 02:05
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