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Karl and Nell made donations to the same charity last year. Did Karl d

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Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 22:02
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Karl and Nell made donations to the same charity last year. Did Karl donate more money to the charity than Nell did?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
(2) Karl donated more than $250 to the charity.

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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 22:03
1
Official Explanation

Answer: C


The question is: Is k > n ?

Statement (1) is insufficient. It tells us n = 2k - 200. If k is greater than 200, then n is greater. For instance, if k = 300, then n = 2(300) - 200 = 400. However, if k is smaller than 200, the opposite is true. If k = 150, then n = 2(150) - 200 = 100. We don't know the range of values for either k or n, so we can't answer the question.

Statement (2) is also insufficient. This doesn't tell us anything about the relationship between the donations, or about Nell's amount.

Taken together, the statements are sufficient. Since we know k is greater than 250, it must be greater than 200, meaning that Nell's contribution was greater, according to the equation in (1). Choice (C) is correct.
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 22:23
1
Quote:
Karl and Nell made donations to the same charity last year. Did Karl donate more money to the charity than Nell did?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
(2) Karl donated more than $250 to the charity.


Let Karl be K and Nell be N.
donation by K>donation by N? => K>N?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
N = 2K-200
since donations cannot be a negative amount, K>100 and K ≠ 0 since it is said that both made donations.
If K=101, N=2 => K>N? YES
If K= 200, N=200 => K>N? NO

INSUFFICIENT!

(2) Karl donated more than $250 to the charity.
K>250
However, we don't know anything about donations made by Nell, so can't say anything for sure. INSUFFICIENT!

(1) + (2)
N = 2K-200, where K>100 and K>250

If K=260, N=320 => K>N? NO
If K=300, N=400 => K>N? NO
Always NO.

IMO answer is option C.
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post Updated on: 24 Sep 2019, 23:04
1
Q. Did Karl donate more money to the charity than Nell did? (K > N)?

(1) N = 2K - 200
K > N --> K > 2K - 200 --> K < 200
This statement indicates if Karl donated less than $200,we are certain that Karl donated more money than Nell. HOWEVER, we don't know how much money Karl donated.
NOT SUFFICIENT

(2) Karl donated more than $250 to the charity.
We don't know how much money Nell donated.
Clearly NOT SUFFICIENT.

(1)+(2)
We are certain now that Karl donated more than $200 and consequently, Karl must donate less money than Nell.
SUFFICIENT.

Answer is (C)

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Originally posted by chondro48 on 24 Sep 2019, 22:29.
Last edited by chondro48 on 24 Sep 2019, 23:04, edited 1 time in total.
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 22:39
1
We are to determine if Karl’s donation, k, is more than Nell’s donation, n.

Statement 1 is insufficient. This is because we can only deduce that n=2k-200
When k=150, n=100, implying Karl donated less than Nell.
But when k=250, then n=300, and Nell now donates more than Karl.

Statement 2 is clearly insufficient because we only know that k>250. No information is provided about how much Nell donates so we can’t determine who donates more than the other.

1+2 however is sufficient. We can confidently say that Nell donates more than Karl. Hence the answer to the question posed is No, Karl did not donate more than Nell.

The answer is therefore C.

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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 22:55
1
Let ‘N’ be the amount donated by Neil and ‘K’ by Karl. K > N ?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
Now, N = 2*K -200
Since N > 0
2K - 200 > 0
K > 100

For K = 150 → N = 100 K > N (YES)
For K = 300 → N = 400 K < N (NO)

INSUFFICIENT.

(2) Karl donated more than $250 to the charity.
Nothing about Neil given. Hence

INSUFFICENT.

Together 1) and 2)
Clearly, using both statements if K > 200, K < N always. Thus, a clear NO answer.

K > 250 → N > 300 K > N (NO)
From Statement 1) K = 300 → N = 400 K < N (NO)

SUFFICIENT.

Answer (C).
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 24 Sep 2019, 23:36
(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
N = 2K - 200

If K=100, N =0 and if K=200, N = 200. Not sufficient

(2) Karl donated more than $250 to the charity. Not sufficient

(1)+(2) If Karl donated atleast 250$ then N must have donated 300$. The more we increase value of K, N will keep on increasing. Sufficient.

C is correct
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 25 Sep 2019, 01:14
find k>n
#1
The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
n=2k-200
value of n & k not know insufficient
#2
k=250
n not know insufficient
from 1 & 2
k=250 and n= 300
sufficient
IMO C

Karl and Nell made donations to the same charity last year. Did Karl donate more money to the charity than Nell did?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
(2) Karl donated more than $250 to the charity.
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 25 Sep 2019, 04:03
Quote:
Karl and Nell made donations to the same charity last year. Did Karl donate more money to the charity than Nell did?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated.
(2) Karl donated more than $250 to the charity.


Is K>N?

(1) The amount of money that Nell donated is $200 less than twice the amount that Karl donated: insufic.
Is K>N? N=2K-200…Is K>(2K-200)?…Is K<200?

(2) Karl donated more than $250 to the charity: insufic.

(1&2) Is K<200? K>250, sufic.

Answer (C)
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Re: Karl and Nell made donations to the same charity last year. Did Karl d  [#permalink]

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New post 25 Sep 2019, 10:41
K >? N

1) N= 2K -200 Insufficient.
2) K > 250 Insufficient

plugging the minimum (integer) amount for K in equation 1
N = 2 x 251 - 200 = 302
So, since 200 is constant and K can only get bigger, N will continue to get larger than 302.

Karl has definitely donated more than Nell. So we can solve the question. Answer C.
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Re: Karl and Nell made donations to the same charity last year. Did Karl d   [#permalink] 25 Sep 2019, 10:41
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