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# Back in 1930, Tillie had to memorize her multiplication facts from 0*0

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Math Expert
Joined: 02 Sep 2009
Posts: 55277
Back in 1930, Tillie had to memorize her multiplication facts from 0*0  [#permalink]

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25 Apr 2019, 03:03
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Difficulty:

95% (hard)

Question Stats:

29% (02:18) correct 71% (02:10) wrong based on 45 sessions

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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

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Re: Back in 1930, Tillie had to memorize her multiplication facts from 0*0  [#permalink]

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25 Apr 2019, 10:40
1
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.
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Re: Back in 1930, Tillie had to memorize her multiplication facts from 0*0  [#permalink]

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25 Apr 2019, 17:04
I used visualization.

1 2 3 4 5 6 7 8 9 10 11 12
2
3
4
5
6
7
8
9
10
11
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
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Re: Back in 1930, Tillie had to memorize her multiplication facts from 0*0  [#permalink]

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29 Apr 2019, 09:41
Bunuel wrote:
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

Since there are 13 (0 to 12, inclusive) rows and 13 columns, there are 169 products (necessarily distinct). The product of two numbers is odd if both numbers are odd. There are 6 (i.e., 1, 3, 5, 7, 9, 11) odd numbers from 0 to 12, so there are 6 rows and 6 columns of odd numbers, creating 6 x 6 = 36 odd products. Therefore, the fraction of the products that are odd is 36/169 ≈ 0.21.

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Back in 1930, Tillie had to memorize her multiplication facts from 0*0  [#permalink]

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01 May 2019, 02:37
Rows: 0-12= 13
Columns: 0-12= 13
Total integers in table body= 169

Odd integers in rows: 1-3-5-7-9= 6
Odd integers in Column= 6
Total odd integers in table body= 36

Fraction= 36/169= 0.21 (approx)

(40/160= 0.25, so Ans must be less than 0.21)

Ans A
Back in 1930, Tillie had to memorize her multiplication facts from 0*0   [#permalink] 01 May 2019, 02:37
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