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Manager  Joined: 01 Jul 2009
Posts: 149
If x is a two-digit prime number whose digits are the reverse of the  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 42% (02:25) correct 58% (02:15) wrong based on 155 sessions

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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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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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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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This is a Value question. We need to be able to determine exactly one and only one value for x to have sufficiency. We are told that x and y are two-digit prime numbers and that if we reverse the digits of x, we’d get y. We’ll jot down a list of the two-digit primes and see which are the reverse of the other. Those primes are: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, and 97.

Whittling this list down to pairs whose digits are reversed, we get the possibilities for x and y: 11 and 11, 13 and 31, 17 and 71, 37 and 73, and 79 and 97.

We need to figure out which pair we are looking at and which number is x.

Evaluate the Statements:

Statement (1): We are given that the difference of x and y is 54. From our list of possible combinations, only 17 and 71 give us a difference of 54. x must be the larger of the pair (if x were the smaller value, then x – y would be negative), so x = 71.

Statement (1) is Sufficient to answer the question. Eliminate choices (B), (C), and (E).

Statement (2): Again, looking at our possibilities, only 17 and 71 add to 88. But we do not know from Statement (2) whether x is the larger or the smaller value. Therefore, Statement 2 is Insufficient. Eliminate choice (D).

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_________________ Re: If x is a two-digit prime number whose digits are the reverse of the   [#permalink] 06 Jul 2020, 01:58

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