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17 Dec 2017, 05:54
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65% (hard)

Question Stats:

52% (01:29) correct 48% (01:53) wrong based on 47 sessions

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If Jack buys 5 pieces of three different items priced $20,$80 and $100, does he buy at least one piece of each item? (1) Three of 5 pieces are priced at$100 each.
(2) Average cost of 5 pieces is greater than $80. self made _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Director Joined: 06 Jan 2015 Posts: 605 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: If Jack buys 5 pieces of three different items priced$20, $80 and$10  [#permalink]

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17 Dec 2017, 06:11
chetan2u wrote:
If Jack buys 5 pieces of three different items priced $20,$80 and $100, does he buy at least one piece of each item? (1) Three of 5 pieces are priced at$100 each.
(2) Average cost of 5 pieces is greater than $85. self made (1) Three of 5 pieces are priced at$100 each.

It can be 3 $100 and 2 items of$20 & $800 Gives Yes It can be all 5$100 Gives No

(2) Average cost of 5 pieces is greater than $85. It says total cost is more than 425 It can be 3$100 and 2 items of $20 &$800 Gives Yes

It can be all 5 $100 Gives No Combining both doesn't give any info Hence E _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution Retired Moderator Joined: 25 Feb 2013 Posts: 1216 Location: India GPA: 3.82 If Jack buys 5 pieces of three different items priced$20, $80 and$10  [#permalink]

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17 Dec 2017, 06:11
chetan2u wrote:
If Jack buys 5 pieces of three different items priced $20,$80 and $100, does he buy at least one piece of each item? (1) Three of 5 pieces are priced at$100 each.
(2) Average cost of 5 pieces is greater than $80. self made Statement 1: other two items can be priced at$80 each or one can be of $20 & the other of$80. Insufficient

Statement 2: $$Average >80 =>$$ total price$$>400$$

Now if all three items are bought then cost of 3 items will be $$=20+80+100=200$$

so the total cost of remaining two items has to be at least 201. But maximum cost of any item is 100, hence we can reach only upto 200, resulting in total cost of 400. But we know total price >400

Hence all three items were not bought. Sufficient

Option B
Math Expert
Joined: 02 Aug 2009
Posts: 7415
Re: If Jack buys 5 pieces of three different items priced $20,$80 and $10 [#permalink] ### Show Tags 17 Dec 2017, 06:20 niks18 wrote: chetan2u wrote: If Jack buys 5 pieces of three different items priced$20, $80 and$100, does he buy at least one piece of each item?

(1) Three of 5 pieces are priced at $100 each. (2) Average cost of 5 pieces is greater than$80.

Statement 1: other two items can be priced at $80 each or one can be of$20 & the other of $80. Insufficient Statement 2: $$Average >80 =>$$ total price$$>400$$ Now all the 5 pieces could be of$100 amounting to $500 or 3 can be of$100, one of $80 & the other of$20. Insufficient

Combining 1 & 2 Total price of three items $$=100*3=300$$

so price or remaining two items $$>400-300$$

or price of remaining two items$$>100$$.

Now if one item is of 20 and other of 80 then total price of two items will be $$80+20=100$$, which is not possible.

Hence we can conclude that the remaining two items are of $80. Sufficient Option C Hi niks18, most of the time you are right there, but here you have missed a point in statement II (1) Three of 5 pieces are priced at$100 each.
other 2 could be 20 and 80 ..yes
other two can be both same type... No
insuff

(2) Average cost of 5 pieces is greater than $80. TRICK lies here.. Max average when all three items are there : one each of 20 and 80 and remaining three of 100 , so $$\frac{20+80+3*100}{5}=80$$ BUT the average is >80 so there is no item of$20.. ans is always NO
sufficient
B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Retired Moderator
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
Re: If Jack buys 5 pieces of three different items priced $20,$80 and $10 [#permalink] ### Show Tags 17 Dec 2017, 06:25 chetan2u wrote: niks18 wrote: chetan2u wrote: If Jack buys 5 pieces of three different items priced$20, $80 and$100, does he buy at least one piece of each item?

(1) Three of 5 pieces are priced at $100 each. (2) Average cost of 5 pieces is greater than$80.

Statement 1: other two items can be priced at $80 each or one can be of$20 & the other of $80. Insufficient Statement 2: $$Average >80 =>$$ total price$$>400$$ Now all the 5 pieces could be of$100 amounting to $500 or 3 can be of$100, one of $80 & the other of$20. Insufficient

Combining 1 & 2 Total price of three items $$=100*3=300$$

so price or remaining two items $$>400-300$$

or price of remaining two items$$>100$$.

Now if one item is of 20 and other of 80 then total price of two items will be $$80+20=100$$, which is not possible.

Hence we can conclude that the remaining two items are of $80. Sufficient Option C Hi niks18, most of the time you are right there, but here you have missed a point in statement II (1) Three of 5 pieces are priced at$100 each.
other 2 could be 20 and 80 ..yes
other two can be both same type... No
insuff

(2) Average cost of 5 pieces is greater than $80. TRICK lies here.. Max average when all three items are there : one each of 20 and 80 and remaining three of 100 , so $$\frac{20+80+3*100}{5}=80$$ BUT the average is >80 so there is no item of$20.. ans is always NO
sufficient
B

Yup agreed. I actually got confused between the earlier average posted 85 & the edited one 80. I changed the value but did not check the approach
Math Expert
Joined: 02 Aug 2009
Posts: 7415
Re: If Jack buys 5 pieces of three different items priced $20,$80 and $10 [#permalink] ### Show Tags 17 Dec 2017, 06:42 niks18 wrote: chetan2u wrote: niks18 wrote: Statement 1: other two items can be priced at$80 each or one can be of $20 & the other of$80. Insufficient

Statement 2: $$Average >80 =>$$ total price$$>400$$

Now all the 5 pieces could be of $100 amounting to$500 or 3 can be of $100, one of$80 & the other of $20. Insufficient Combining 1 & 2 Total price of three items $$=100*3=300$$ so price or remaining two items $$>400-300$$ or price of remaining two items$$>100$$. Now if one item is of 20 and other of 80 then total price of two items will be $$80+20=100$$, which is not possible. Hence we can conclude that the remaining two items are of$80. Sufficient

Option C

Hi niks18,

most of the time you are right there, but here you have missed a point in statement II

(1) Three of 5 pieces are priced at $100 each. other 2 could be 20 and 80 ..yes other two can be both same type... No insuff (2) Average cost of 5 pieces is greater than$80.
TRICK lies here..
Max average when all three items are there : one each of 20 and 80 and remaining three of 100
, so $$\frac{20+80+3*100}{5}=80$$
BUT the average is >80
so there is no item of $20.. ans is always NO sufficient B Yup agreed. I actually got confused between the earlier average posted 85 & the edited one 80. I changed the value but did not check the approach actually, irrespective of 80 or 85 it is going to be B. changed it to 80 to make it a bit more tricky for those getting at 80, otherwise 85 is straight B. _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Re: If Jack buys 5 pieces of three different items priced$20, $80 and$10   [#permalink] 17 Dec 2017, 06:42
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