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# For any integers x and y, min(x, y) and max(x, y) denote the minimum

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For any integers x and y, min(x, y) and max(x, y) denote the minimum  [#permalink]

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22 Mar 2018, 19:33
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45% (medium)

Question Stats:

63% (01:36) correct 37% (00:59) wrong based on 41 sessions

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For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?

(1) b, c and d are factors of a
(2) a – 2d = b + c

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Re: For any integers x and y, min(x, y) and max(x, y) denote the minimum  [#permalink]

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22 Mar 2018, 20:29
saswata4s wrote:
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?

(1) b, c and d are factors of a
(2) a – 2d = b + c

max(a, max(b, min(c, d))) ... You will get MAX value out of the 4 only if a or b are max....
max(d, max(a, min(b, c))) .... You will get the max value out of the four only if a and d are max..

So we can say max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?
In two conditions..
1) if A is the max
2) if C is the max as it will get discarded in MIN and we will get the second largest from the remaining 3

Let's see the statements..
(1) b, c and d are factors of a.
Since all are different, we can say a is largest.
Meets our first criterion, is Ans will be a from both sides
Suff
(2) a-2d=b+C
a=b+c+2d
So a is largest..
Suff

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: For any integers x and y, min(x, y) and max(x, y) denote the minimum  [#permalink]

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22 Mar 2018, 21:14
saswata4s wrote:
For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(2, 1) = 1 and max(2,1) = 2. If a, b, c and d are distinct positive integers, is max(a, max(b, min(c, d))) = max(d, max(a, min(b, c))) ?

(1) b, c and d are factors of a
(2) a – 2d = b + c

Statement I:

a is the maximum of b,c,d. So, $$max(a, max(b, min(c, d)))$$ & $$max(d, max(a, min(b, c)))$$ will always be a.

Statement II:

$$a = b + c + 2d.$$ As, $$a, b, c & d$$ are distinct POSITIVE Integers, a will always be maximum.

$$max(a, max(b, min(c, d)))$$ & $$max(d, max(a, min(b, c)))$$ will always be a.

Hence, D.
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Re: For any integers x and y, min(x, y) and max(x, y) denote the minimum &nbs [#permalink] 22 Mar 2018, 21:14
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