foryearss wrote:
shuvodip04 wrote:
EgmatQuantExpert wrote:
e-GMAT Question of the Week #40The set S is defined as {1, -2, -3, 8, 21, 30, -22, -5, 6, -11}. The chi of set is defined as the product of any 3 elements of the given set S. How many values of chi are possible such that chi is at least 7?
A. 50
B. 59
C. 60
D. 61
E. 120
Product of three elements in the set S is defined as chi
We have to find the cases where chi>=7
Total negative elements = 5
Total positive elements = 5
Following are the only possibilities when product of three elements >= 7
1) 2 negative and 1 positive - 2 negative out of 5 can be selected in 5C2 ways and 1 positive in 5 ways
Number of possible values of chi = 5C2 * 5 - 1 [subtracting for the case when -2,-3 and 1 will be selected]
=50 -1 = 49
2) three positive terms
Out of 5 three positive can be chosen in 5C3 ways
Number of possible values = 5C3 = 10
For every other combination such as , (3 Negative , 2 Positive + 1 negative)value of chi will be negative.
Hence possible values of chi = 49 + 10 =59
IMO (B)
yes , but when choosing (-2 , -3 , positive number other 1 ) isn't this the same when we choose (6 , 1 , other positive number ) let's say we choose the following
-2 , -3 , 30
6 , 1 , 30
both have the same result and we counted them twice , same for -2 , -3 , 8 and 6 , 1 , 8
also : -22 , 3 , negative other than -22 or -11
and 6 , -11 , negative other than -22 or -11
I'm not gonna count all possible double entrees since the only answer below 59 is is A
please correct me
I think you are right.But I could count only 3 values for which it holds true (-2,-3,8);(-2,-3,21);(-2,-3,30) with (6,1,8);(6,1,21);(6,1,30)
So number of values: (59-3) = 56
Quote:
also : -22 , 3 , negative other than -22 or -11
3 is not in the set.
other combinations will not be possible :- (-22,-3) with (1,8,21,30,6) and (6,-11) with (-2,-3,-22,-5) no values overlap.
I could not find other overlaps. Could not count it down to 50. Can you please list if you find other 6 numbers?