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# For any integers x and y, sum (x, y) and diff (x, y) denote the sum an

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For any integers x and y, sum (x, y) and diff (x, y) denote the sum an  [#permalink]

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13 Mar 2019, 23:50
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Difficulty:

25% (medium)

Question Stats:

85% (01:34) correct 15% (01:47) wrong based on 27 sessions

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For any integers x and y, sum (x, y) and diff (x, y) denote the sum and the difference of x and y, respectively. For example, sum (1, 2) = 3 and diff (1, 2) = -1. For the integer p, what is the value of sum (10, p)?

(1) diff (diff (10, p), sum (10, p)) = sum (diff (10, p), sum(10,p))
(2) sum(10, p) = diff (-10, p)

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D)EACH statement ALONE is sufficient to answer the question asked.

E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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Re: For any integers x and y, sum (x, y) and diff (x, y) denote the sum an  [#permalink]

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14 Mar 2019, 09:59
The question is just asking "what is 10+p", so if we can find p, we're done. The question then is just about decoding these sum(x,y) and diff(x,y) things correctly - it's important to use brackets when looking at Statement 1.

In Statement 1 we have:

diff (diff (10, p), sum (10, p)) = sum (diff (10, p), sum(10,p))

(10-p) - (10+p) = (10-p)+(10+p)
-2p = 20
p = -10

which is sufficient.

In Statement 2 we have

sum(10, p) = diff (-10, p)

10 + p = -10 - p
20 = -2p
10 = -p

which is also sufficient.
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Re: For any integers x and y, sum (x, y) and diff (x, y) denote the sum an  [#permalink]

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19 Mar 2019, 12:21
#1diff (diff (10, p), sum (10, p)) = sum (diff (10, p), sum(10,p))

10-p-10-p = 10-p+10+p
p= -10
so sum (10, p) = 0
sufficient
#2
sum(10, p) = diff (-10, p)
10+p=-10-p
p=-10
again sufficeint
IMO D

mangamma wrote:
For any integers x and y, sum (x, y) and diff (x, y) denote the sum and the difference of x and y, respectively. For example, sum (1, 2) = 3 and diff (1, 2) = -1. For the integer p, what is the value of sum (10, p)?

(1) diff (diff (10, p), sum (10, p)) = sum (diff (10, p), sum(10,p))
(2) sum(10, p) = diff (-10, p)

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

C)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

D)EACH statement ALONE is sufficient to answer the question asked.

E)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Re: For any integers x and y, sum (x, y) and diff (x, y) denote the sum an   [#permalink] 19 Mar 2019, 12:21
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# For any integers x and y, sum (x, y) and diff (x, y) denote the sum an

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