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25 Apr 2019, 03:03
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A
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:
33% (02:22) correct
67%
(02:17)
wrong
based on 136
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Back in 1930, Tillie had to memorize her multiplication facts from 0*0 to 12*12. The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of the numbers in the body of the table are odd?
(A) 0.21
(B) 0.25
(C) 0.46
(D) 0.5
(E) 0.75
(A) 0.21
(B) 0.25
(C) 0.46
(D) 0.5
(E) 0.75
25 Apr 2019, 10:40
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Total number of rows = 12-0+1 = 13
Total number of columns = 12-0+1 = 13
Body will contain 169 elements.
Only Odd*Odd = Odd.
So the total number of odd products in each row = 6 (6 even and 6 odd products)
And we need to reject the even columns, as the products will all be even.
Hence the numbers of columns with odd products = 6
Total odd products in body = 6*6 = 36
Fraction of odd in the body = 36/169
36*4 = 144
144+18 = 162 = almost equal to 4.5 times 36
36/169 = 1/4.5 = 1/(9/2) = 2/9 = 0.22 (1/9 = 0.1111)
Hence A is the closest answer.
Total number of columns = 12-0+1 = 13
Body will contain 169 elements.
Only Odd*Odd = Odd.
So the total number of odd products in each row = 6 (6 even and 6 odd products)
And we need to reject the even columns, as the products will all be even.
Hence the numbers of columns with odd products = 6
Total odd products in body = 6*6 = 36
Fraction of odd in the body = 36/169
36*4 = 144
144+18 = 162 = almost equal to 4.5 times 36
36/169 = 1/4.5 = 1/(9/2) = 2/9 = 0.22 (1/9 = 0.1111)
Hence A is the closest answer.
25 Apr 2019, 17:04
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I used visualization.
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Any time an odd number crosses with an even, the product is even. So we can only include odd * odd numbers in this set.
There are 6 rows of odd numbers * 6 columns of odd numbers.
36 /144 = 1/4
Let us not forget that the table includes factors of 0, an even number so the answer must be less than .25
1 2 3 4 5 6 7 8 9 10 11 12
2
3
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5
6
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12
Any time an odd number crosses with an even, the product is even. So we can only include odd * odd numbers in this set.
There are 6 rows of odd numbers * 6 columns of odd numbers.
36 /144 = 1/4
Let us not forget that the table includes factors of 0, an even number so the answer must be less than .25
