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06 Aug 2018, 11:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:15) correct
53%
(01:48)
wrong
based on 178
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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.
(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.
amanvermagmat
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)
Moderator Note: Filled the missing information as corrected by @Hero8888
06 Aug 2018, 13:17
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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.
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.
