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12 Jul 2019, 04:34
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C
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Difficulty:
95%
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Question Stats:
43% (02:22) correct
57%
(02:38)
wrong
based on 189
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A group of more than 2 people share an amount of money equally between them. Does each person receive a whole number of dollars?
(1) If $45 was split evenly between the group they would each receive a whole number of dollars.
(2) If one fewer person were in the group, then each person remaining would receive $11 when the money was split equally.
(1) If $45 was split evenly between the group they would each receive a whole number of dollars.
(2) If one fewer person were in the group, then each person remaining would receive $11 when the money was split equally.
12 Jul 2019, 08:55
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If we have n people, Statement 1 just tells us n is a factor of 45, so is not sufficient, since we have no idea how much money we're dividing up.
Statement 2 is not sufficient, since we might have 3 people and $22 total, and 22 is not divisible by 3, or we might have 11 people and $110 total, and 110 is divisible by 11.
Using both Statements, if we have n people, Statement 2 tells us we have 11(n-1) = 11n - 11 dollars in total. We want to know if this is divisible by n, so we want to know if (11n-11)/n = 11 - (11/n) is an integer. For that to be an integer, 11/n will need to be an integer, and n will need to be a factor of 11. Since n is not allowed to be 1, then n would need to equal 11. But we know from Statement 1 that n must be a factor of 45, so n cannot be 11, and the money thus cannot be divided up so everyone gets a whole number of dollars. So the answer must be "no" using both Statements, and the answer is C.
Statement 2 is not sufficient, since we might have 3 people and $22 total, and 22 is not divisible by 3, or we might have 11 people and $110 total, and 110 is divisible by 11.
Using both Statements, if we have n people, Statement 2 tells us we have 11(n-1) = 11n - 11 dollars in total. We want to know if this is divisible by n, so we want to know if (11n-11)/n = 11 - (11/n) is an integer. For that to be an integer, 11/n will need to be an integer, and n will need to be a factor of 11. Since n is not allowed to be 1, then n would need to equal 11. But we know from Statement 1 that n must be a factor of 45, so n cannot be 11, and the money thus cannot be divided up so everyone gets a whole number of dollars. So the answer must be "no" using both Statements, and the answer is C.
22 Oct 2019, 00:45
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shridhar786
from first option, we can't determine how much money was distributed,so, it's not possible to tell whether whole numbers were distributed.
from option 2,although after testing some numbers it is assumed that whole numbers were not distributed(8*11=88(not divisible by 9; 5*11=55(not divisible by 6)), if u test this with the number 10 (10*11=110,which is divisible by 11), both yes and no are possible in option A
Combining both options tell us that there are 45 people and an amount of$45 was distributed; according to option 2, 45-1=44, which is divisible by 11,so, option 2 can be proved.
The answer will be C.
