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Store S sold a total of 90 copies of a certain book during [#permalink]

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06 Dec 2009, 10:40

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Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

(1) Last week Store S sold 8 copies on Thursday (2) Last week Store S sold 38 copies on Saturday

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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06 Dec 2009, 11:56

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Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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06 Dec 2009, 12:33

kp1811 wrote:

Hussain15 wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

1) Last week Store S sold 8 copies on Thursday 2) Last week Store S sold 38 copies on Saturday

Store S sold a total of 90 copies of a certain book during the 7 days of last week, and it sold different number of copies on any two of the days. If for the 7 days store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did store S sell more than 11 copies on Friday?

1. Last week store S sold 8 copies of the book on Thursday

2. Last week store S sold 38 copies of the book on Saturday

This Q has been discussed multiple times. My question is "which statement in the Question tells that each day they sold different number of books" _________________

Re: GMAT Prep Q - clarification on OA [#permalink]

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01 Aug 2010, 10:54

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It says in the question stem that they didn't sell the same number of books on any two of the days. This means that they didn't sell same number of books on any day.

Re: GMAT Prep Q - clarification on OA [#permalink]

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02 Aug 2010, 20:38

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abhisheksh wrote:

I didn't get it how B is sufficient enough... Can you please provide solution link to this question.

As per the question M +Tu +W +Th + Fr + Sa +Su =90 and M,Tu,W,Th,Su < F< Sa

1) If Thursday sold 8 copies For values of Th=8,W=7,Tu=6,M=5,Su=4,F=10,Sa=50 (Fr <11) For values of Th=8,W=7,Tu=6,M=5,Su=4,F=12,Sa=48 (Fr >11). Hence not sufficient. 2) If Saturday sold 38 copies M +Tu +W +Th + Su + Fr = 52 Since the second highest number of books were sold on Friday and no two days sold the same number of books. If Friday sold <=11 books The maximum value of M +Tu +W +Th + Su is 10+9+8+7+6 which makes max value of M +Tu +W +Th + Su + Fr = 51 (< 52). So Friday should have definitely sold more than 11 books. Hence sufficient.

So answer is B _________________

___________________________________ Please give me kudos if you like my post

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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08 Jan 2011, 20:08

Bunuel wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Answer: B.

Hope it's clear.

Hi Bunnel, I interpreted the question that except friday and saturday the number of books sold on all the other days were same. Since it is given the number of books sold were different on any 2 days?. Shouldnt the question be on all the days the number of books sold were different?.. Please clarify....

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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09 Jan 2011, 04:13

Expert's post

saisriram wrote:

Bunuel wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Answer: B.

Hope it's clear.

Hi Bunnel, I interpreted the question that except friday and saturday the number of books sold on all the other days were same. Since it is given the number of books sold were different on any 2 days?. Shouldnt the question be on all the days the number of books sold were different?.. Please clarify....

No, your interpretation is not correct, we are told that "(store) sold different numbers of copies on any 2 days", so there are no 2 days on which it sold the same number of copies --> store sold different number of copies on each day. _________________

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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10 Jan 2011, 22:18

Bunuel wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Answer: B.

Hope it's clear.

Hello Bunnel, The explanation is very clear..Just would like to ask one Q.. It is mentioned: Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days and to explain this you have taken 0,1,2,3,4 to explain... But I am just wondering can we take 0 in this case because he has sold some copies and its different from that of the other days..I think we should start from 1,2,3,4,5. (The answer does not depend on this query but I am just asking out of curiousity)

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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11 Jan 2011, 00:38

Expert's post

jullysabat wrote:

Bunuel wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Answer: B.

Hope it's clear.

Hello Bunnel, The explanation is very clear..Just would like to ask one Q.. It is mentioned: Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days and to explain this you have taken 0,1,2,3,4 to explain... But I am just wondering can we take 0 in this case because he has sold some copies and its different from that of the other days..I think we should start from 1,2,3,4,5. (The answer does not depend on this query but I am just asking out of curiousity)

I think the store could have sold zero copies on any day (except Friday and Saturday). Why not? Nothing in the stem indicates that the # of sold copies were more than zero. _________________

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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11 Jan 2011, 09:37

Bunuel wrote:

jullysabat wrote:

Bunuel wrote:

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?

Given: (Any of other five days different sales)<Fri<Sat(max) and Sun+Mon+Tue+Wed+Thu+Fri+Sat=90.

Question: is Fri>11?

(1) Last week Store S sold 8 copies on Thursday --> Sun+Mon+Tue+Wed+8+Fri+Sat=90 --> if the sales before Friday were: 0+1+2+3+8(Thu)=14 then Fri+Sat=90-14=76, so Store S could have sold less than 11 copies on Friday (for example if Fri+Sat=10+66=76) as well as more than 11 copies (for example if Fri+Sat=12+64=76). Not sufficient.

(2) Last week Store S sold 38 copies on Saturday --> Sun+Mon+Tue+Wed+Thu+Fri+38=90 --> Sun+Mon+Tue+Wed+Thu+Fri=52. Now, if Store S didn't sell more than 11 copies on Friday, then max possible copies sold before Saturday would be Sun+Mon+Tue+Wed+Thu+Fri=6+7+8+9+10+11=51<52 --> so, Store S must have been sold more than 11 copies on Friday. Sufficient.

Answer: B.

Hope it's clear.

Hello Bunnel, The explanation is very clear..Just would like to ask one Q.. It is mentioned: Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days and to explain this you have taken 0,1,2,3,4 to explain... But I am just wondering can we take 0 in this case because he has sold some copies and its different from that of the other days..I think we should start from 1,2,3,4,5. (The answer does not depend on this query but I am just asking out of curiousity)

I think the store could have sold zero copies on any day (except Friday and Saturday). Why not? Nothing in the stem indicates that the # of sold copies were more than zero.

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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16 Apr 2011, 05:54

Store S sold a total of 90 copies of a certain book during the seven days last week and it sold different numbers of copies on any 2 days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Firday, did Store S sell more than 11 copies on Friday?

1) Last week Store S sold 8 copies on Thursday 2) Last week Store S sold 38 copies on Saturday

Lets produce the contradiction.

1) The store sold 11 copies on Friday. The answer is NO 8 (Thursday) + 11 (Friday) + 71 copies on rest of the days (with highest copies on Sat)

The store sold 12 copies on Friday. The answer is YES 8 (Thursday) + 12 (Friday) + 70 copies on rest of the days (with highest copies on Sat)

Insufficient.

2) Lets assume the contradiction. The store 11 copies on Friday. Copies sold on Thursday = 38. hence the remaining copies are 90 - 38 = 52. Maximizing the number of copies sold - lets assume 11 (Friday) + 10 (Thu) + 9 (Wed) + 8 (Tue) + 7(Mon) + 6 (Sun) copies are sold on the rest of the six days. Total = 51 copies. Not high enough - we are short by 1 copy. The contradiction is wrong - the store indeed sold more than 11 copies on Friday. Proved.

Re: Did Store S sell more than 11 copies on Friday? [#permalink]

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16 Apr 2011, 10:57

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Hussain15 wrote:

Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?

1) Last week Store S sold 8 copies on Thursday. 2) Last week Store S sold 38 copies on Saturday

Thanks "jimmy86" to help us dig out this interesting question for others to take a look at. Kudos+1.

Sol: 1) Last week Store S sold 8 copies on Thursday.

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Copies Sold(Friday>11)

1

2

3

4

8

12

90-24=66

Copies Sold(Friday<=11)

1

2

3

4

8

11

90-23=67

We did not violate any condition mentioned in the stem: Every day the store sold different number of copies. Greatest number of copies were sold on Saturday. Second greatest number of copies were sold on Friday.

Order in which the rows were filled: Row1: Thursday(8), Friday(12), Sunday(1), Monday(2), Tuesday(3), Wednesday(4), Saturday(90-(Sum of rest)) Row2: Thursday(8), Friday(11), Sunday(1), Monday(2), Tuesday(3), Wednesday(4), Saturday(90-(Sum of rest))

We proved that with 8 copies sold on the Thursday, the store could have sold 11 or more on the Friday. Not Sufficient.

2) Last week Store S sold 38 copies on Saturday

Sunday

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Copies Sold(Friday>11)

1

2

3

4

5

90-53=37

38

Copies Sold(Friday<=11)

X

X

X

X

X

11

38

Row1: We showed one of the possible combinations of copies sold when the store sold more than 11 copies on Friday. Order: Saturday(38), Sunday(1), Monday(2), Tuesday(3), Wednesday(4), Thursday(5), Friday(90-Sum of rest)

Row2: Saturday=38 and Friday=11 The store must sell (90-38-11)=(90-49)=41 copies in order to satisfy the stem.

We cannot possibly assign a number bigger than 11 for the rest of the days because Friday needs to be second greatest. Saturday is standing greatest with 38 and Friday is the second greatest with 11. The maximum number of copies the store could sell on other days, given it sold 11 copies on Friday, would be 10+9+8+7+6=40, which is 1 short of the required number. This proves that there were indeed more than 11 copies that were sold on the Friday. In fact, the minimum number of copies that could be sold on Friday with these conditions would be "12".

Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?

(1) Last week Store S sold 8 copies of the book on Thursday (2) Last week Store S sold 38 copies of the book on Saturday.

(1) NS. This tells us we must sell atleast 9 books on Friday, but not necessarily 11, because the excess demand can all be taken by saturday since there is no restriction.

(2) Check the maximums

IF we set friday to 11 and everything else to the most we possibly can, we have to check if we can still get 90 of total volume

M 6 T 7 W 8 T 9 F 11 S 38 S 10 = total of 89, and we can't increase anything but friday, because if we increase another day, two days will have the same number of sales, or will have more sales that friday, which is not allowed. -> sufficient

This above configuration indicates the minimum possible value for each day given the constraint: 1) Different copies for each day 2) Saturday > Friday (# of copies) 3) Saturday = 38 copies 4) Friday = 11 copies?

When we add this possibility up we get 89. Since 89 < 90. We know that the value for Friday MUST be greater than 11.

1st attempt I got this wrong,, but eventually dod it rigt here's how.

I is insufficient II - sale from sunday to Fri is 52. now, since no to values are same, the value of friday is maximised when sale on the other days are consecutive integers so, let sale on sunday = x, monday = x+1 etc.. therefore , 5x+4 + friday = 52. friday = 48-5x. At x=7, the value on friday is 13, at x=8, the value is 8. but if x=8, friday cannot be the day with second largest sale.. therefore x>7 and friday sales is atleast 13.. hence suff.

Re: Store S sold a total of 90 copies of a certain book during [#permalink]

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