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The price per pair of brand A jeans is $45 and the price per pair of b

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The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 27 Aug 2018, 15:01
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The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20

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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 27 Aug 2018, 19:43
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carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20



Let the numberr of jeans be A and B, so 45A+65B=560
Let's take the minimum and maximum possible..
If all are of 65 then minimum would be >8 as 8*65=520, still 40$ left
If all are of 45, then max would be 12 as 12*45=540
So our answer has to be 10 or 12..

Now 45A+65B=560....
Let B=1, then 45A+65*1=560......45A=560-65=495....A=495/45=11
So answer 1+11=12

C
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 27 Aug 2018, 19:57
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He cannot buy jeans of brand B only as 560 is not a multiple of 65.
Now by hit and trial we can see if he buys 1 jeans of brand B then the equation becomes
11*45+1*65=560
So, 12 pairs...C is the correct choice

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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 29 Aug 2018, 01:13
chetan2u wrote:
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20



Let the numberr of jeans be A and B, so 45A+65B=560
Let's take the minimum and maximum possible..
If all are of 65 then minimum would be >8 as 8*65=520, still 40$ left
If all are of 45, then max would be 12 as 12*45=540
So our answer has to be 10 or 12..

Now 45A+65B=560....
Let B=1, then 45A+65*1=560......45A=560-65=495....A=495/45=11
So answer 1+11=12

C


chetan2u understood that it could be 12, but how 10? please explain
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 29 Aug 2018, 01:21
1
siddreal wrote:
chetan2u wrote:
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20



Let the numberr of jeans be A and B, so 45A+65B=560
Let's take the minimum and maximum possible..
If all are of 65 then minimum would be >8 as 8*65=520, still 40$ left
If all are of 45, then max would be 12 as 12*45=540
So our answer has to be 10 or 12..

Now 45A+65B=560....
Let B=1, then 45A+65*1=560......45A=560-65=495....A=495/45=11
So answer 1+11=12

C


chetan2u understood that it could be 12, but how 10? please explain


we have seen max possible is 560/45 = 112/9 ~ 12.5 so <12.5
min possible is 560/65 = 112/13~8.7 so >8.7
the choices we have are 8,10,12,14 and 20
Only 10 and 12 are within the max possible and min possible.... this is just to home down to 2 choices

But after solution we get answer as 12
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 29 Aug 2018, 08:05
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carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20


\(45a + 65b = 560\)

\(9a + 13b = 112\)

Now plug in some values for a or b and check { Its better to work with 13 }

\(9*11 + 13 *1 = 112\)

So, The total number of jeans is 12, Answer must be (C)
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 29 Aug 2018, 13:57
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20


#pair of jeans=Money in pocket/unit price
#pairs is greatest when the unit price is the smallest(here numerator is fixed)
So, Mr, Chris has to purchase jeans of brand A since it cheaper than brand B.
So, #greatest pair of jeans could be $560/$45=NOT A WHOLE NUMBER(12.something)
If #pairs of jeans A=11 then cost would be 11*45=495. Now amount left to spend=560-495=$65. Mr. Chris can buy 1 pair jeans of brand B as its unit cost is $65 per pair

So total#pairs=11 of A+ 1 of B=12

Ans. (C)
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 01 Sep 2018, 04:37
1
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20


Dear Moderator,
Found this question under combination section, seems like its has been wrongly tagged.Hope you will do the needful. Thank you.
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 01 Sep 2018, 08:01
stne wrote:
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20


Dear Moderator,
Found this question under combination section, seems like its has been wrongly tagged.Hope you will do the needful. Thank you.


Edited. Thank you.
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Re: The price per pair of brand A jeans is $45 and the price per pair of b  [#permalink]

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New post 03 Sep 2018, 18:57
carcass wrote:
The price per pair of brand A jeans is $45 and the price per pair of brand B jeans is $65. If there is no sales tax and Chris chooses only from among these two brands, what is the greatest number of pairs of jeans that he can buy with exactly $560?

A. 8

B. 10

C. 12

D. 14

E. 20


With $560, he can buy 12 pairs of brand A jeans with $20 left over (notice that 12 x 45 = $540), or he can buy 11 pairs of brand A jeans and 1 pair of brand B jeans with no money left over (notice that 11 x 45 + 65 = $560). Regardless of which option he chooses, the greatest number of pairs of jeans he can buy is 12.

Answer: C
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Re: The price per pair of brand A jeans is $45 and the price per pair of b   [#permalink] 03 Sep 2018, 18:57
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