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17 Oct 2009, 05:44
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E
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Difficulty:
55%
(hard)
Question Stats:
62% (02:18) correct
38%
(01:38)
wrong
based on 53
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For a lottery ticket, Emily chose six numbers that average to 10. Did more than half the numbers have 2 digits?
(1) One of the numbers was 10.
(2) Three of the numbers added up to 40.
(1) One of the numbers was 10.
(2) Three of the numbers added up to 40.
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17 Oct 2009, 08:44
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Hmm I don't know a mathematical formula way to figure it out but you can solve it relatively quickly by picking good numbers.
Question stem says (N1+N2....+N6)/6 = 10 => N1+N2....+N6 = 60
Statement 1)
One of the numbers was 10.
This just means N1+N2+N3+N4+N5+10 = 60
N1+N2+N3+N4+N5= 50
Each of the numbers could be 10 or we could have 4 numbers as 1 and the last one as 46.
Insuff.
Statement 2)
Three numbers add to 40. The number of ways to do this could be:
- 1 double digit (eg. 38,1,1)
- 2 double digit (eg. 10,25,5)
- 3 double digit (eg 13,13,14)
The three remaining numbers add to 20. Only two ways to do this:
- 0 double digits (eg. 6,6,8)
- 1 double digit (eg. 10,5,5,)
In short from these combinations you can have more than half in double digits or just 1 double digit (or in fact anything in between). NOT sufficient.
Statements together)
Still not sufficient because the above examples could include a single 10.
ANS = E
Question stem says (N1+N2....+N6)/6 = 10 => N1+N2....+N6 = 60
Statement 1)
One of the numbers was 10.
This just means N1+N2+N3+N4+N5+10 = 60
N1+N2+N3+N4+N5= 50
Each of the numbers could be 10 or we could have 4 numbers as 1 and the last one as 46.
Insuff.
Statement 2)
Three numbers add to 40. The number of ways to do this could be:
- 1 double digit (eg. 38,1,1)
- 2 double digit (eg. 10,25,5)
- 3 double digit (eg 13,13,14)
The three remaining numbers add to 20. Only two ways to do this:
- 0 double digits (eg. 6,6,8)
- 1 double digit (eg. 10,5,5,)
In short from these combinations you can have more than half in double digits or just 1 double digit (or in fact anything in between). NOT sufficient.
Statements together)
Still not sufficient because the above examples could include a single 10.
ANS = E
