Roger bought some pencils and erasers at the stationery store. If he b

Question

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?

I. Roger bought no fewer than 7 pencils.
II. Roger bought no more than 12 pencils.
III. Roger bought no more than 9 erasers.

A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III

CareerGeek · Answer

Given p > e

Case 1: Assume least total = 12
—> p + e = 12
—> Possible values are (7, 5), (8, 4), (9, 3), (10, 2), (11, 1)

Case 2: Assume highest total = 20
—> p + e = 20
—> Possible Values are (11, 9), (12, 8), . . . . (19, 1)

I. Roger bought no fewer than 7 pencils. —> True

II. Roger bought no more than 12 pencils —> False

III. Roger bought no more than 9 erasers —> True

IMO Option C

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IanStewart · Answer

"If he bought more pencils than erasers" means more than half of the things he bought were pencils, and less than half were erasers. So if he bought at least 12 things, he bought at least 7 pencils, and if he bought no more than 20 things, he bought no more than 9 erasers. So I and III are true. He might have bought 18 pencils and 2 erasers, say, so II does not need to be true.

farharajeev · Answer

let pencils be p and erasers be e , the 12<p+e<20 and given p>e

I. Roger bought no fewer than 7 pencils

12 < 7 + e < 20. thus e must be minimum 6 as total needs to be > 12. however, p>e , thus p must be greater than 6 . Statement I true

II. Roger bought no more than 12 pencils

12< p + e< 20. here no. of pencils can be 13 and no of erasers can be 1, thus this statement must not be true.

III. Roger bought no more than 9 erasers

12< p+ 9< 20. if p>e condition must be held then p= 10. p cannot be greater than 10, as the 12<p+e<20 inequality will be violated. thus the statement is true.

I and III only (C)

saad166 · Answer

i didnt understand the explanation for "Roger bought no more than 12 pencils" please explain it once more. No more means atmost right so the number of pencils he should get should be <=12 now if he gets 12 pencils and 11 erasers then it violates the inequality but suppose he get 12 pencils and 7 erasers (pencils > erasers) then he will get 18 in total which does satisfy the inequality as its in between 12 and 20 so why wont we consider this option as well

Roger bought some pencils and erasers at the stationery store. If he b

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Roger bought some pencils and erasers at the stationery store. If he b

Prep Toolkit

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My Rewards