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As a summer school assignment history teacher asked Four of her studen
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19 Mar 2025, 00:38
19 Mar 2025, 00:38
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As a summer school assignment history teacher asked Four of her students (Tom, John, Harry and David) to collect antique coins. The number of coins they collected were in the ratio 2 to 3 to 5 to 4 , respectively. If one of them collected 60 coins which of the following CANNOT be the total number of coins collected by all the four students?
(A) 168
(B) 210
(C) 280
(D) 420
(E) 500
(A) 168
(B) 210
(C) 280
(D) 420
(E) 500
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Re: As a summer school assignment history teacher asked Four of her studen
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23 Mar 2025, 04:45
23 Mar 2025, 04:45
Expert Reply
OFFICIAL EXPLANATION
We know that the number of coins collected by Tom, John, Harry \& David were in the respective ratio of $\(2: 3: 4: 5\)$, so let the number of their coins be $\(2 \mathrm{k}, 3 \mathrm{k}, 4 \mathrm{k}\)$ and 5 k respectively, where k is any positive integer.
So, the total number of coins with all 4 friends is $\(2 k+3 k+4 k+5 k=14 k\)$
As one of them has a total of 60 coins, that person can be any one of the 4 persons. Considering all possibilities we get
gre TABLE.png [ 39.74 KiB | Viewed 413 times ]
Hence out of the given only 500 cannot be the total number of coins, so the answer is (E).
We know that the number of coins collected by Tom, John, Harry \& David were in the respective ratio of $\(2: 3: 4: 5\)$, so let the number of their coins be $\(2 \mathrm{k}, 3 \mathrm{k}, 4 \mathrm{k}\)$ and 5 k respectively, where k is any positive integer.
So, the total number of coins with all 4 friends is $\(2 k+3 k+4 k+5 k=14 k\)$
As one of them has a total of 60 coins, that person can be any one of the 4 persons. Considering all possibilities we get
Attachment:
gre TABLE.png [ 39.74 KiB | Viewed 413 times ]
Hence out of the given only 500 cannot be the total number of coins, so the answer is (E).
gmatclubot
Re: As a summer school assignment history teacher asked Four of her studen [#permalink]
23 Mar 2025, 04:45
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