sanju09 wrote:Edburg bought some apples, mangoes, and bananas. He bought 42 fruits in all. The number of bananas he bought is less than half the number of apples he bought; the number of mangoes he bought is more than one-third the number of apples he bought but less than three-fourths the number of bananas he bought. How many bananas did he buy?
(A) 5
(B) 6
(C) 8
(D) 11
(E) 12
A + M + B = 42
Because we are dealing with objects, all values must be positive integers.
Translating the second sentence into a series of inequalities, we have:
B < A/2, which, because we are dealing only with positive integers, can be safely rewritten as: A > 2B;
M > A/3, which can be rewritten as: 3M > A; and
M < 3B/4
Thus:
3M > A > 2B
we can see that 3M > 2B or
M > 2B/3...and we also know that
M < 3B/4
(ie, 2B/3 < M < 3B/4)
Now, we have to test the answer choices against the last two inequalities that I wrote (ie, the ones I've emboldened). When backsolving, in general, we should start from B or D. (although for this particular question, it wouldn't really matter).
Looking at B: if the number of Bananas is 6, then M > (2*6)/3 and M < (3*6)/4,
or 4 < M < 4.5, which makes the number of mangoes a non-integer, and therefore this choice is incorrect.
Looking at D: If B = 11, then M > (2*11)/3 and M < (3*11)/4 or 7.3333 < M < 8.25. Then, the number of mangoes is 8. If there are 8 mangoes, 11 bananas, and 42 fruit in total, then there are 23 apples. These numbers satisfy all of the inequalities. As there can only be one answer choice that satisfies all the conditions (ie, the correct answer), the correct answer is choice D.
Last edited by
Testluv on Thu Jan 14, 2010 12:17 am, edited 1 time in total.
Kaplan Teacher in Toronto
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