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# Mike bought 10 pens, all having distinct prices in integer number of

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1435
Location: India
Mike bought 10 pens, all having distinct prices in integer number of  [#permalink]

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06 Aug 2018, 11:20
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Difficulty:

65% (hard)

Question Stats:

37% (02:17) correct 63% (01:36) wrong based on 34 sessions

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Mike bought 10 pens, all having distinct prices in integer number of cents. If the cheapest pen costs 10 cents, what is the price of the costliest pen?

(1) Out of these 10 pens, difference between prices of any two pens is less than 11 cents.

(2) Median price of these 10 pens is 15 cents.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Mike bought 10 pens, all having distinct prices in integer number of  [#permalink]

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Updated on: 06 Aug 2018, 13:42
2
amanvermagmat wrote:
Mike bought 10 pens, all having distinct prices in integer number of cents. If the cheapest pen costs 10 cents, what is the price of the costliest pen?

(1) Out of these 10 pens, difference between prices of any two pens is less than 11 cents.

(2) Median price of these 10 pens is 15 cents.

Note:-
a) All pens have distinct prices.
b) Price of pens are in integer form ,obviously price can't be a negative or a free purchase.
c) Price of cheapest pen is 10 cents. Price of remaining 9 pens is not known.

Question stem:- what is the price of the costliest pen?

St1:- Out of these 10 pens, difference between prices of any two pens is less than 11 cents. (Or, range of price <11)
If x is the price of any of the remaining pen, then (x-10)<11 or, $$(x-10)\leq{10}$$ or, $$x\leq{20}$$. ($${10\leq{x}\leq{20}}$$)
So the price of the costliest pen could be 19 or 20 cents.
Insufficient.

St2:- Median price of these 10 pens is 15 cents.
There can be more than one set of prices with 15 as median.
So, the highest price is not unique.
Insufficient.

Combined, the only set of prices that satisfies st1 and 2:-

10,11,12,13,14,16,17,18,19,20

Ans. (C)

Edit: Filled the missing information as corrected by @Hero8888

_________________
Regards,

PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 06 Aug 2018, 12:52.
Last edited by PKN on 06 Aug 2018, 13:42, edited 1 time in total.
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Joined: 29 Dec 2017
Posts: 383
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Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
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WE: Marketing (Telecommunications)
Mike bought 10 pens, all having distinct prices in integer number of  [#permalink]

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06 Aug 2018, 13:17
1
Hi PKN

What if I tell you:

1. 10,11,12,13,14,15,16,17,18,19 OR 10,11,12,13,14,15,16,17,18,20
In both cases range is (9 and 10) less than 11. Not suff

2. 10,11,12,13,15,16,17,18,19,20 OR 10,11,12,13,15,16,22,31,44,50 . We are not told that we are given arithmetic progression. Not suff

1+2 Sufficient, the costest pen = 20 cents. Answer C.
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: Mike bought 10 pens, all having distinct prices in integer number of  [#permalink]

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06 Aug 2018, 13:34
1
Hero8888 wrote:
Hi PKN

What if I tell you:

1. 10,11,12,13,14,15,16,17,18,19 OR 10,11,12,13,14,15,16,17,18,20
In both cases range is (9 and 10) less than 11. Not suff

2. 10,11,12,13,14,16,17,18,19,20 OR 10,11,12,13,14,16,22,31,44,50 . We are not told that we are given arithmetic progression. Not suff

1+2 Sufficient, the costliest pen = 20 cents. Answer C.

You are absolutely correct. I missed it. Thanks.

However, I did a little correction in your explanation in order to maintain 15 as median.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Re: Mike bought 10 pens, all having distinct prices in integer number of   [#permalink] 06 Aug 2018, 13:34
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