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manimani
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Ten different items are for sale in a store, and each is Updated on: 26 Jun 2012, 07:36
Originally posted by manimani on 26 Jun 2012, 07:32.
Last edited by Bunuel on 26 Jun 2012, 07:36, edited 1 time in total.
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59% (01:33) correct 41% (01:33) wrong based on 350 sessions

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Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

(1) The five most expensive items each increased in price by 10%.
(2) The five least expensive items each decreased in price by 10%.
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Bunuel
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Ten different items are for sale in a store, and each is 26 Jun 2012, 08:01
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Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

The question basically asks whether there will be an increase in total price of those 10 items after the price change.

(1) The five most expensive items each increased in price by 10%. Not sufficient since we know nothing about the other items.
(2) The five least expensive items each decreased in price by 10%. Not sufficient since we know nothing about the other items.

(1)+(2) 10% of the total price of 5 most expensive items is clearly more than 10% of the total price of 5 least expensive items, so overall there will be an increase in total price. Sufficient.

Answer: C.

Hope it's clear.
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Ten different items are for sale in a store, and each is 26 Jun 2012, 09:28
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WOW !!! i cant believe it was that simple... explanation given in there was pretty crappy one.. Thanks Bunuel
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Ten different items are for sale in a store, and each is 15 Jun 2023, 08:18
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Bunuel
Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

The question basically asks whether there will be an increase in total price of those 10 items after the price change.

(1) The five most expensive items each increased in price by 10%. Not sufficient since we know nothing about the other items.
(2) The five least expensive items each decreased in price by 10%. Not sufficient since we know nothing about the other items.

(1)+(2) 10% of the total price of 5 most expensive items is clearly more than 10% of the total price of 5 least expensive items, so overall there will be an increase in total price. Sufficient.

Answer: C.

Hope it's clear.
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Hi Bunuel, i think the option should be D as both options individually can tell the answer

Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

(1) The five most expensive items each increased in price by 10%.
(2) The five least expensive items each decreased in price by 10%.

We can assume the ten items with their prices in increasing order as below

x1, x2, x3, x4, x5, x6, x7, x8, x9 & x10 with x1 least priced item and x10 highest.
Now with option (1), x6, x7,x8,x9 & x10 each increased by 10%, i.e x1 is now 1.1x1 and so on.

Now avg formula= (x1+x2+x3+x4+x5+x6+x7+x8+x9+x10)/10= (x1+x2+x3+x4+x5+1.1x6+1.1x7+1.1x8+1.1x9+1.1x10)/10=
(x1+x2+...x10)+0.1 (x6+x7+x8+x9+x10)/10=1650+0.1(x6+x7+x8+x9+x10)/10=165+ something positive, hence obviously with option 1, the average would be more than 165.

Similarly with option (2) we will come up with (x1+x2+x3+....x10)-0.1(x1+x2+x3+x4+x5)/10=165-something positive which obviously gives us average change.

Hence both options individually can tell us that whether avg price would increase or not. In option 1 yes, while in option 2, No. So shouldn't the answer be option D.
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Ten different items are for sale in a store, and each is 25 Apr 2024, 00:59
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Deep32470

Bunuel
Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

The question basically asks whether there will be an increase in total price of those 10 items after the price change.

(1) The five most expensive items each increased in price by 10%. Not sufficient since we know nothing about the other items.
(2) The five least expensive items each decreased in price by 10%. Not sufficient since we know nothing about the other items.

(1)+(2) 10% of the total price of 5 most expensive items is clearly more than 10% of the total price of 5 least expensive items, so overall there will be an increase in total price. Sufficient.

Answer: C.

Hope it's clear.


Hi Bunuel, i think the option should be D as both options individually can tell the answer

Ten different items are for sale in a store, and each is sold at a different price. The average (arithmetic mean) price of these 10 items is $165. If the prices of all the items are changed, will the average price increase?

(1) The five most expensive items each increased in price by 10%.
(2) The five least expensive items each decreased in price by 10%.

We can assume the ten items with their prices in increasing order as below

x1, x2, x3, x4, x5, x6, x7, x8, x9 & x10 with x1 least priced item and x10 highest.
Now with option (1), x6, x7,x8,x9 & x10 each increased by 10%, i.e x1 is now 1.1x1 and so on.

Now avg formula= (x1+x2+x3+x4+x5+x6+x7+x8+x9+x10)/10= (x1+x2+x3+x4+x5+1.1x6+1.1x7+1.1x8+1.1x9+1.1x10)/10=
(x1+x2+...x10)+0.1 (x6+x7+x8+x9+x10)/10=1650+0.1(x6+x7+x8+x9+x10)/10=165+ something positive, hence obviously with option 1, the average would be more than 165.

Similarly with option (2) we will come up with (x1+x2+x3+....x10)-0.1(x1+x2+x3+x4+x5)/10=165-something positive which obviously gives us average change.

Hence both options individually can tell us that whether avg price would increase or not. In option 1 yes, while in option 2, No. So shouldn't the answer be option D.
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­why are you assuming that x1+x2+x3+x4+x5 is not going to change? The questions says "If the prices of all the items are changed".
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