In the multiplication above, each symbol represents a different unknown digit, a

Question

In the multiplication above, each symbol represents a different unknown digit, and . What is the three-digit integer ? 263 236 194 491 452 A professional gambler has won 40% of his 25 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of his games for the week? A feed store sells two varieties of birdseed: Brand A, which is 40% millet and 60% sunflower, and Brand B, which is 65% millet and 35% sunflower. If a customer purchases a mix of the two types of the birdseed that is 50% millet, what percent of the mix is Brand A?

Explanation / Answer

(7) Let the number required be abc, where a,b and c represent the individual digits

Given product of digits = 36

a * b * c = 36

According to the options, the digits can be (2,3,6) or (1,4,9). The numbers can be the premutations of these numbers. We can eliminate possibililties using the 1st relation.

Its clear that the product of the last digit along with itself is the same number i.e. the square of the number is itself. From the possibilities, the only 2 digits are 1 and 6.

But its also clear that the product of the 2 digits numbers is a 3 digit number, which would not be possible in case of 1,4,9. Therefore the 2 digits are 2,3,6 where the diammond stands for 6, the square stands for 3 and the circle stands for 2.

The reqd number is : 236 , Ans (B)

(8) Games played till now = 25

Games won = 40% of 25 = 10 games

Now, let the gambler play x more games

No of games won among x games = 80% of x = 0.8x

Total number of games = x + 25

Given that overall win% is 60%

Total number of games won overall = 60% of (x + 25)

= 0.6(x + 25)

Equating the number of games won,

No of games won till now at 40% + No of games won at 80% = Overall number of games won at 60%

10 + 0.8x = 0.6(x + 25)

10 + 0.8x = 0.6x + 15

0.2x = 5

x = 25

The gambler has to play 25 more games to ensure that he secures an overall win% of 60%

(9) Let the fraction of brand A used by x

Fraction of brand B used = (1 - x)

Total millet content = sum of individual contributions from samples A and B

50% = x (40%) + (1 - x)(60%)

=> 0.5 = 0.4x + 0.6 - 0.6x

=> 0.2x = 0.1

=> x = 0.5

Therefore, Brand A constitutes 50% of the mixture

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