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One-third, one-quarter, one-fifth and one-seventh of the human populat

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Bunuel
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One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink] One-third, one-quarter, one-fifth and one-seventh of the human populat   28 Dec 2021, 08:00
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One-third, one-quarter, one-fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers & their sum is exactly the population of island Y. What is the population of Island Y?

(A) 4200
(B) 4279
(C) 4581
(D) 4800
(E) None of these


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Re: One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink] One-third, one-quarter, one-fifth and one-seventh of the human populat   06 Jan 2023, 11:32
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Bunuel wrote:
One-third, one-quarter, one-fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers & their sum is exactly the population of island Y. What is the population of Island Y?

(A) 4200
(B) 4279
(C) 4581
(D) 4800
(E) None of these


Are You Up For the Challenge: 700 Level Questions


The first point to observe in the question is One-third, one-quarter, one-fifth and one-seventh of the human population of Island X are all whole numbers.

If we assume the population of island X as 'P'

\(\frac{1}{3} * P\); \(\frac{1}{4}*P\); \(\frac{1}{5}*P\); \(\frac{1}{7}*P \) are all whole numbers, so P is a LCM of (3,4,5,7)

P = 420 * x

x is some factor

It's also given that population of island Y = Sum when the population of island X is divided by 1/3, 1/4, 1/5 & 1/7

So population of island Y = \(\frac{1}{3} * 420x + \frac{1}{4} * 420x + \frac{1}{5} * 420x + \frac{1}{7} * 420x = 389x \)

Hence we can infer that the population of island Y is a multiple of 389.

We can test out options and find which option is a multiple of 389.

(A) 4200

We can rule out A , as A is even while 389 is odd.

(B) 4279

389 * 11 = 4279

Option B
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Re: One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink] One-third, one-quarter, one-fifth and one-seventh of the human populat   08 Jan 2023, 04:28
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gmatophobia wrote:
Bunuel wrote:
One-third, one-quarter, one-fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers & their sum is exactly the population of island Y. What is the population of Island Y?

(A) 4200
(B) 4279
(C) 4581
(D) 4800
(E) None of these


Are You Up For the Challenge: 700 Level Questions


The first point to observe in the question is One-third, one-quarter, one-fifth and one-seventh of the human population of Island X are all whole numbers.

If we assume the population of island X as 'P'

\(\frac{1}{3} * P\); \(\frac{1}{4}*P\); \(\frac{1}{5}*P\); \(\frac{1}{7}*P \) are all whole numbers, so P is a LCM of (3,4,5,7)

P = 420 * x

x is some factor

It's also given that population of island Y = Sum when the population of island X is divided by 1/3, 1/4, 1/5 & 1/7

So population of island Y = \(\frac{1}{3} * 420x + \frac{1}{4} * 420x + \frac{1}{5} * 420x + \frac{1}{7} * 420x = 389x \)

Hence we can infer that the population of island Y is a multiple of 389.

We can test out options and find which option is a multiple of 389.

(A) 4200

We can rule out A , as A is even while 389 is odd.

(B) 4279

389 * 11 = 4279

Option B



When I was wondering how do I find multiples of 389..
So we know its a factor of 389.. 389*10 = 3890
We can just try the next 1 or 2 multiples.. i.e 389*11 = 4279 (our answer)
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Re: One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink] One-third, one-quarter, one-fifth and one-seventh of the human populat   20 Jan 2024, 09:51
One-third, one-quarter, one-fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers & their sum is exactly the population of island Y. What is the population of Island Y?

(A) 4200
(B) 4279
(C) 4581
(D) 4800
(E) None of these
Since LCM of 3,4,5,7 is 420, the population of X is a multiple of 420. As max population is less than 5000, the range of population is 420 to 4620.
Checking the options we see that A and D can't be the answer because 4800 is beyond the range and 4200 is already 100% of population of X which if is a population of X then population of Y has to be less than 4200{1-(1/3+1/4+1/5+1/7)}, and here we don't have any such choice available. Or we can say that factor for population of X is greater than factor for population of Y(the two can't be same) and this is because of {1-(1/3+1/4+1/5+1/7)}. Hope I'm able to communicate my thoughts.
E is already eliminated.

Among B and C, if C is the answer then 39 (4620-4581) must be equal to the left out{1-(1/3+1/4+1/5+1/7) = 31/420 of some value} part of 4620. But this is not possible since 39 is not a multiple of 31.

Now, we have our answer in B after POE but let's check.
4620 - 4279 = 341 and this is a multiple of 31(31*11 = 341)
Hence population of X was 4620 and population of Y is 4279.

Answer B.
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Re: One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink] One-third, one-quarter, one-fifth and one-seventh of the human populat   21 Jan 2024, 07:18
Bunuel wrote:
One-third, one-quarter, one-fifth and one-seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole numbers & their sum is exactly the population of island Y. What is the population of Island Y?

(A) 4200
(B) 4279
(C) 4581
(D) 4800
(E) None of these


Are You Up For the Challenge: 700 Level Questions


x/3 + x/4 + x/5 + x/7 = 389x/420. From option B, 4279=389*11 so (B).
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Re: One-third, one-quarter, one-fifth and one-seventh of the human populat [#permalink]
21 Jan 2024, 07:18
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