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If x is a two-digit prime number whose digits are the reverse of the

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If x is a two-digit prime number whose digits are the reverse of the [#permalink]

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New post 21 Dec 2014, 13:17
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If x is a two-digit prime number whose digits are the reverse of the two-digit prime number y, what is the value of x?

(1) x –y = 54

(2) x + y = 88

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Re: If x is a two-digit prime number whose digits are the reverse of the [#permalink]

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New post 21 Dec 2014, 13:45
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GMAT888 wrote:
If x is a two-digit prime number whose digits are the reverse of the two-digit prime number y, what is the value of x?

(1) x –y = 54

(2) x + y = 88


let x= 10a +b
and y= 10b+y

st.1) x-y = 54

now since difference between x and y is positive therefore, x is greater than y. also, by substituting the values of x and y we have:

=10a+b-10b-a=54
= 9(a-b)=54
or a-b=6
thus possible values of a and b are (7,1),(8,2),(9,3). hence values of x can be 71,82,93 and corresponding value of y can be 17,28,39. now since y is prime only for 71. hence value of x is 71.

2) x+y=88
by substituting the value of x and y we have,
10a+b+10b+a =88
or 11(a+b)=88
a+b=8
thus value of a and b are (1,7),(7,1),(2,6),(6,2),(3,5),(5,3)
now out of these values a and b, x and y will be prime for (1,7) and (7,1). but since we don't know which of x and y is greater than the other. thus possible value of x can be either 17 or 71. hence st.2 alone is not sufficient.
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Re: If x is a two-digit prime number whose digits are the reverse of the [#permalink]

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New post 21 Dec 2014, 20:29
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Hi GMAT888,

This DS question has a few Number Property shortcuts that you can take advantage of (that will significantly limit the possibilities and the amount of work that you'll have to do).

We're told that X is a 2-digit PRIME number and Y is the REVERSE of X and ALSO a PRIME number.

For example....
X = 13
Y = 31

Since we know that they're BOTH primes with the digits reversed, we know that NONE of the digits can be 0, 2, 4, 6, or 8 (because those even numbers would not be prime) NOR can any of them be 5 (since any of those 2-digit multiples of 5 would not be prime either).

This means that the digits can ONLY be 1, 3, 7 or 9. There can't be that many 2-digit numbers AND their reverses that would fit this description and would both be prime. Some numbers in THIS group aren't even prime (e.g. 39 and 93). Making this deduction up front will make dealing with the two Facts a lot easier.

We're asked for the value of X.

Fact 1: X - Y = 54

Here, we know that X > Y and that the two digits have to be relatively far apart. There are only a few options to check:

71 - 17 = 54 This MATCHES
91 - 19 = 72 Does NOT fit
93 - 39 = Irrelevent. Neither are prime.

From this, X MUST be 71.
Fact 1 is SUFFICIENT

Fact 2: X + Y = 88

Here, we don't have to check anything. Because of the way that DS questions are written, there MUST be AT LEAST one solution, but we won't know if X is the bigger number or the smaller number. You might realize relatively quickly that 71 and 17 fit this Fact, but we don't know which one is X.
Fact 2 is INSUFFICIENT.

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Re: If x is a two-digit prime number whose digits are the reverse of the [#permalink]

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New post 15 Jun 2018, 23:06
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Re: If x is a two-digit prime number whose digits are the reverse of the   [#permalink] 15 Jun 2018, 23:06
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