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x*y is a prime number greater than 2 where x and y are positive intege

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x*y is a prime number greater than 2 where x and y are positive intege  [#permalink]

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26 Aug 2017, 06:27
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Difficulty:

85% (hard)

Question Stats:

43% (01:47) correct 57% (01:39) wrong based on 59 sessions

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x*y is a prime number greater than 2 where x and y are positive integers.
What is the unit digit of 4^x + 3^y

1) x > 39
2) y=1

Source: www.GMATinsight.com

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x*y is a prime number greater than 2 where x and y are positive intege  [#permalink]

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26 Aug 2017, 07:35
1
GMATinsight wrote:
x*y is a prime number greater than 2 where x and y are positive integers.
What is the unit digit of 4^x + 3^y

1) x > 39
2) y=1

Source: http://www.GMATinsight.com

Hi...

Quote:
x*y is a prime number greater than 2 where x and y are positive integers.

MEANS
One of x or y is surely 1 and other some ODD number..
$$4^x+3^y$$

lets see the statements

1) x>39
this means y =1 ...
so $$4^x+3^y=4^x+3^1=4^x+3$$
now x can take various values but ONLY ODD and each of this value will be of type 4a+1 or 4a+3..
$$4^{odd.. number}$$ will always have 4 as units digit.. example $$4^1=4..4^3=64$$
so units digit will be 4+3=7
sufficient

2) y=1..
same as above
suff

D
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Re: x*y is a prime number greater than 2 where x and y are positive intege  [#permalink]

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26 Aug 2017, 09:53
x*y is a prime number greater than 2 where x and y are positive integers.
What is the unit digit of 4^x + 3^y

1) x > 39
2) y=1

x*y = prime > 2;
Few things to be kept in mind:
1. All primes greater than 2 are odd
2. A prime has only 2 factors: 1 and itself

Statement 1:
X>odd # greater than 39; so, y must be 1.
4^odd will have 4 as units digit; 3^1 = 3; Thus units digit will always be 7 --> SUFFICIENT

Statement 2:
y=1; then, x=odd number.
4^odd will have 4 as units digit; 3^1 = 3; Thus units digit will always be 7 --> SUFFICIENT

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Re: x*y is a prime number greater than 2 where x and y are positive intege   [#permalink] 26 Aug 2017, 09:53
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