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Roger bought some pencils and erasers at the stationery store. If he b
[#permalink]
20 Jan 2023, 11:11

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Question Stats:

Roger bought some pencils and erasers at the stationery store. If he bought more pencils than erasers, and the total number of the pencils and erasers he bought is between 12 and 20 (inclusive), which of the following statements must be true?

Indicate all that apply

A. Roger bought no fewer than 7 pencils.

B. Roger bought no more than 12 pencils.

C. Roger bought no fewer than 6 erasers.

D. Roger bought no more than 9 erasers.

_________________

Indicate all that apply

A. Roger bought no fewer than 7 pencils.

B. Roger bought no more than 12 pencils.

C. Roger bought no fewer than 6 erasers.

D. Roger bought no more than 9 erasers.

_________________

Re: Roger bought some pencils and erasers at the stationery store. If he b
[#permalink]
23 Jan 2023, 23:21

Expert Reply

OE

Choice (A) is true because Roger would have bought at least 7 pencils (to go with 5 erasers) if he bought the minimum possible total number of items. (6 of each is impossible, as the number of pencils is greater than the number of erasers. Likewise, choice (C) is disproved, as the number of erasers would have been fewer than 6 in this case.) If he bought more than 12 items, the number of pencils could not be any less than 7 and still be greater than the number of erasers.

On the other hand, choice (B) need not be true, because Roger could have bought as many as 19 pencils, even if you assume that he has to buy at least one of each item.

Finally, choice (D) must be true, because even if Roger bought the maximum possible number of items (20), less than half of those would have to be erasers. Thus, 9 erasers is the most he could have purchased; io of each is impossible.

_________________

Choice (A) is true because Roger would have bought at least 7 pencils (to go with 5 erasers) if he bought the minimum possible total number of items. (6 of each is impossible, as the number of pencils is greater than the number of erasers. Likewise, choice (C) is disproved, as the number of erasers would have been fewer than 6 in this case.) If he bought more than 12 items, the number of pencils could not be any less than 7 and still be greater than the number of erasers.

On the other hand, choice (B) need not be true, because Roger could have bought as many as 19 pencils, even if you assume that he has to buy at least one of each item.

Finally, choice (D) must be true, because even if Roger bought the maximum possible number of items (20), less than half of those would have to be erasers. Thus, 9 erasers is the most he could have purchased; io of each is impossible.

_________________

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