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Esther is giving Christmas presents to her family members. Each family

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Bunuel
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Esther is giving Christmas presents to her family members. Each family [#permalink] New post   22 Jun 2022, 06:30
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Esther is giving Christmas presents to her family members. Each family member gets the same number of presents and no presents were leftover. If each family member gets at least one present, did each family member receive more than one present?

(1) Esther has forty Christmas presents to give out.
(2) If the number of family members were doubled, it would not be possible for each family member to get at least one present



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Ivy17
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   29 Jun 2022, 18:01
Bunuel zhanbo, can you help me understand how statement 2 is sufficient?
Say there are 20 gifts and 20 members initially, so each member gets 1 gift, but now when we double the number of members of the family to 40 then not all will get atleast 1 gift. In this case the answer to out stimulus will each family member initially does not receive more than 1 gift, however if we take the number of gifts to be 6 and the number of members to be 2, then initially each gets 3 gifts each but when we double it to 4, then not all will get atleast 1 gift. In this case we can see that each family member initially receives more than 1 gift.
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   29 Jun 2022, 19:28
Esther is giving Christmas presents to her family members. Each family member gets the same number of presents and no presents were leftover. If each family member gets at least one present, did each family member receive more than one present?

(1) Esther has forty Christmas presents to give out. - Statement 1 is clearly insufficient, for we don't know the number of members.


(2) If the number of family members were doubled, it would not be possible for each family member to get at least one present -

Ok, let's consider a case.

Let the number of family members be 10 and the number of gifts be 15. The statement says that if the number of faimly member is doubled (So, the number of family member becomes 20), Everyone won't receive a give. Some would be left out. And the case that we took fits very well. 20 members won't be able to share the 15 gifts while ensuring that each member gets a gift. Hence when considering with 10 people and dividing 15 gifts among then, not all the members gets more than one. There will always be individuals limited to just one gift. - Hence, this one is sufficient.

Therefore B.

Correct me if I am wrong. :)
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   29 Jun 2022, 20:13
itskAKku wrote:
Esther is giving Christmas presents to her family members. Each family member gets the same number of presents and no presents were leftover. If each family member gets at least one present, did each family member receive more than one present?

(1) Esther has forty Christmas presents to give out. - Statement 1 is clearly insufficient, for we don't know the number of members.


(2) If the number of family members were doubled, it would not be possible for each family member to get at least one present -

Ok, let's consider a case.

Let the number of family members be 10 and the number of gifts be 15. The statement says that if the number of faimly member is doubled (So, the number of family member becomes 20), Everyone won't receive a give. Some would be left out. And the case that we took fits very well. 20 members won't be able to share the 15 gifts while ensuring that each member gets a gift. Hence when considering with 10 people and dividing 15 gifts among then, not all the members gets more than one. There will always be individuals limited to just one gift. - Hence, this one is sufficient.
Therefore B.

Correct me if I am wrong. :)


Hi itskAKku
We cannot take family members to be 10 since the stimulus states that each member must receive the same number of gifts with no gifts left out. In your case, 15 gifts cannot be divided equally among 10 members, so the starting condition cannot taken as that to begin with
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   29 Jun 2022, 20:54
Ivy17 wrote:

Hi itskAKku
We cannot take family members to be 10 since the stimulus states that each member must receive the same number of gifts with no gifts left out. In your case, 15 gifts cannot be divided equally among 10 members, so the starting condition cannot taken as that to begin with


Yeah you have a point. I completely agree with you. Thank you for pointing that out :)
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   29 Jun 2022, 20:59
itskAKku wrote:
Ivy17 wrote:

Hi itskAKku
We cannot take family members to be 10 since the stimulus states that each member must receive the same number of gifts with no gifts left out. In your case, 15 gifts cannot be divided equally among 10 members, so the starting condition cannot taken as that to begin with


Yeah you have a point. I completely agree with you. Thank you for pointing that out :)


No worries! However the correct answer mentioned is B,but I've posted my query above in the very first post. Could you take a look at the query and help me understand how statement 2 is sufficient?

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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   30 Jun 2022, 00:38
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Ivy17 wrote:
Bunuel zhanbo, can you help me understand how statement 2 is sufficient?
Say there are 20 gifts and 20 members initially, so each member gets 1 gift, but now when we double the number of members of the family to 40 then not all will get atleast 1 gift. In this case the answer to out stimulus will each family member initially does not receive more than 1 gift, however if we take the number of gifts to be 6 and the number of members to be 2, then initially each gets 3 gifts each but when we double it to 4, then not all will get atleast 1 gift. In this case we can see that each family member initially receives more than 1 gift.


if we take the number of gifts to be 6 and the number of members to be 2, then initially each gets 3 gifts each.
Now, if we double the family number to be 4.
With 6 gifts to give out, each of the family number can still get at least 1 gift.
(Not all of them will get 2 gifts, though.)
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Re: Esther is giving Christmas presents to her family members. Each family [#permalink] New post   30 Jun 2022, 00:53
zhanbo wrote:
Ivy17 wrote:
Bunuel zhanbo, can you help me understand how statement 2 is sufficient?
Say there are 20 gifts and 20 members initially, so each member gets 1 gift, but now when we double the number of members of the family to 40 then not all will get atleast 1 gift. In this case the answer to out stimulus will each family member initially does not receive more than 1 gift, however if we take the number of gifts to be 6 and the number of members to be 2, then initially each gets 3 gifts each but when we double it to 4, then not all will get atleast 1 gift. In this case we can see that each family member initially receives more than 1 gift.


if we take the number of gifts to be 6 and the number of members to be 2, then initially each gets 3 gifts each.
Now, if we double the family number to be 4.
With 6 gifts to give out, each of the family number can still get at least 1 gift.
(Not all of them will get 2 gifts, though.)


Ah understood, thanks a lot zhanbo! :)

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Re: Esther is giving Christmas presents to her family members. Each family [#permalink]
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