At a certain fruit stand, oranges cost $0.35 each and grapefruits cost

Question

At a certain fruit stand, oranges cost $0.35 each and grapefruits cost $0.45 each. In a single transaction, Jean bought some oranges and some grapefruits. How many oranges did Jean buy in the transaction?

(1) Jean spent a total of $1.60 for the oranges and grapefruits at the stand.

This implies that

Since both "o" (oranges) and "g" (grapefruits) must be positive integers, this equation has only one set of values that satisfy it: o = 2 and g = 2. Sufficient.

(2) Jean bought an equal number of oranges and grapefruits.

This is clearly insufficient.

Answer: A.

Bunuel · Accepted Answer

At a certain fruit stand, oranges cost $0.35 each and grapefruits cost $0.45 each. In a single transaction, Jean bought some oranges and some grapefruits. How many oranges did Jean buy in the transaction?

(1) Jean spent a total of $1.60 for the oranges and grapefruits at the stand.

This implies that

35o + 45g = 160
7o + 9g = 32

Since both "o" (oranges) and "g" (grapefruits) must be positive integers, this equation has only one set of values that satisfy it: o = 2 and g = 2. Sufficient.

(2) Jean bought an equal number of oranges and grapefruits.

This is clearly insufficient.

Answer: A.

Kinshook · Answer

@najanapatGiven: At a certain fruit stand, oranges cost $0.35 each and grapefruits cost $0.45 each. In a single transaction, Jean bought some oranges and some grapefruits.
Asked: How many oranges did Jean buy in the transaction?
Let the number of oranges and grapefruits be o & g respectively

(1) Jean spent a total of $1.60 for the oranges and grapefruits at the stand.
.35o + .45g = 1.6
(o, g) = (2,2) since o & g are integers
SUFFICIENT

(2) Jean bought an equal number of oranges and grapefruits.
o=g
The information is not sufficient since absolute value of total purchase is not provided
NOT SUFFICIENT

IMO A

Vanshikakataruka · Answer

In such type of eqns how do we know that an eqn as in statement A will have only one answer? Is there a way to know cz trial and error might take up lots of time

Bunuel · Answer

Trial and error, combined with some number sense, is pretty much the only way. It's actually not that complex. You simply need to check if 32 minus a multiple of 9 results in a multiple of 7. We get 32 - 2*9 = 14 = 2*7.

Rokrrishi · Answer

Vanshikakataruka  you could just write the multiples of 35 and 45 and check if more than a pairs add to 160. If there are two or more pairs, the statement is insufficient, and if there is just one pair (as here, 70 + 90, which makes two oranges and two grapefruits), the statement is sufficient.

I have observed that many problems can very easily be solved just by listing out the possibilities (except for in probability and in combinations, in which this approach may be more cumbersome).

Posted from my mobile device

bumpbot · Answer

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At a certain fruit stand, oranges cost $0.35 each and grapefruits cost

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At a certain fruit stand, oranges cost $0.35 each and grapefruits cost

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