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

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

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New post 10 Sep 2017, 07:57
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Difficulty:

  55% (hard)

Question Stats:

38% (01:16) correct 63% (02:26) wrong based on 27 sessions

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

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New post 10 Sep 2017, 11:42
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SajjadAhmad 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.
(2) If the number of family members were doubled, it would not be possible for each family member to get at least one present


The question can be logically interpreted to arrive at correct answer B. However mathematically we can proceed as -

Let the number of guests be \(x\) and number of gifts for each guest be \(y\) (here both \(x\) & \(y\) have to be integers). So total number of gifts \(= xy\)
We need to find the value of \(y\)

Statement 1: Total number of gifts \(= xy = 40\). As nothing is given about \(x\) so we cannot calculate the value of \(y\). hence insufficient

Statement 2: number of guests doubled but total gifts remained the same, so gifts to each guest must have changed. let gifts to each guest be \(y'\)
Therefore \(2xy' = xy\) or \(y' = \frac{y}{2}\). Now it is given that none of the guest received at least \(1\) present
so \(y'<1\) or \(\frac{y}{2}<1\)
therefore \(y<2\). Hence \(y = 1\). Sufficient

Option B
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Esther is giving Christmas presents to her family members. Each family   [#permalink] 10 Sep 2017, 11:42
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