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# p and q are different two-digit prime numbers with the same

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Manager
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p and q are different two-digit prime numbers with the same  [#permalink]

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10 Aug 2010, 21:39
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p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p – q = 36
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Re: This is a hard one  [#permalink]

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10 Aug 2010, 22:09
It is always good to remember the first 25 prime numbers. These prime numbers are less than 100.
They are:
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

Taking a look at them, we note:
13,31 17,71, 37,73.

Notice that 37 and 73 are the only two-digit prime numbers with the same digits, but in reversed order that meet statements 1 and 2.
Are you sure the OA is C?
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Re: This is a hard one  [#permalink]

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10 Aug 2010, 22:16
Will the GMAT actually ask us to memorize the primes? That would seem harsh. On the other hand this question without the prime statement etc. could have just read what is p and q? and we could answer with both the conditions, it would not have mattered if they were primes
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Re: This is a hard one  [#permalink]

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10 Aug 2010, 22:56
I am not sure. But I am seeing a lot of prime number questions on GMAT. So I got myself familiar to the first 25.
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Re: This is a hard one  [#permalink]

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10 Aug 2010, 23:37
4
I got D too.

Here is how i approached it.

Let's assume xy and yx are the 2 prime numbers (x and y being the individual digits) xy is the bigger prime number

1) p+q =110.
xy
yx
--------------
10(x+y)+(y+x) = 110 => x+y =10
The only possible values for p and q are
19,91 28,82 37,73 46,64 55,55 Out of which only 37 and 73 pair has both prime numbers. Hence sufficient

2) p-q = 36
xy
yx
-------------
10(x-y)+(y-x)=36 => x-y = 4
The only possible values for p and q are
51,15 62,26 73,37 out of which only 73,37 pair has both prime numbers. Hence sufficient.
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Re: This is a hard one  [#permalink]

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10 Aug 2010, 23:56
mainhoon wrote:
Will the GMAT actually ask us to memorize the primes? That would seem harsh. On the other hand this question without the prime statement etc. could have just read what is p and q? and we could answer with both the conditions, it would not have mattered if they were primes

Offhand, I can't think of a single a real GMAT question (and I've seen thousands of the things ) where it would be helpful to know any prime numbers greater than 50. I often see prep books which recommend memorizing primes up to 100 (or more), and I'm not sure why they make that suggestion.

In any case, if a *two digit* number is not divisible by 2, 3, 5 or 7, it's prime, always. If you know that, you don't need to memorize any primes beyond the smallest ones. This test won't work reliably for numbers greater than 120, but you won't need to recognize primes that large on the GMAT anyway.
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Re: This is a hard one  [#permalink]

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11 Aug 2010, 02:05
the answer could not be D as we are asked to find WHICH IS THE LARGER!!!
so the answer could be only C
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Re: This is a hard one  [#permalink]

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11 Aug 2010, 21:11
Jinglander wrote:
p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p – q = 36

C is correct

My attempt:

p and q are different two-digit prime numbers with the same digits, but in reversed order.

My first thought was to find the possible digits.... since it is a 2 digit prime...it cannot be even...
Hence the possible numbers were 1,3 and 7.

Now the options for the two numbers could be (13, 31), (37, 73) and (17, 71).

Statement A: p+q = 110

(37, 73) satisfies the equation. However insufficient since the larger of the two cannot be determined.

p could be 37 or 73. Similarly q could be 37 or 73.

Statement B: p-q = 36

Again, (p, q) being (73, 37) satisfies the statement. Sufficient.

Hence option B should be the correct answer.
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Re: This is a hard one  [#permalink]

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11 Aug 2010, 22:50
The question is not asking whether p is larger than q. It's asking for the *value* of whichever letter is the larger of the two. If you can determine that the numbers are 37 and 73, then the larger of these two numbers is 73. Each statement is sufficient here, and the answer is D.
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Re: This is a hard one  [#permalink]

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11 Jan 2011, 02:29
Can someone please explain to me:

I think it is totally irrelevant here that two numbers are prime. In order to find the largest, we have to solve both equations to find p and q.

Am I right?
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p and q are different two-digit prime numbers with the same  [#permalink]

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11 Jan 2011, 02:54
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1
nonameee wrote:
Can someone please explain to me:

I think it is totally irrelevant here that two numbers are prime. In order to find the largest, we have to solve both equations to find p and q.

Am I right?

No, that' not right.

p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

Given: $$p=prime=10x+y$$ and $$q=prime=10y+x$$, for some non-zero digits $$x$$ and $$y$$ (any two digit number can be expressed as $$10x+y$$ but as both $$p$$ and $$q$$ are two-digit then $$x$$ and $$y$$ must both be non-zero digits).

(1) p + q = 110 --> $$(10x+y)+(10y+x)=110$$ --> $$x+y=10$$. Now, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 91 and 19, 82 and 28, 73 and 37, 64 and 46, ... Thus the larger number could be: 91, 82, 73, or 64. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

(2) p – q = 36 --> $$(10x+y)-(10y+x)=36$$ --> $$x-y=4$$. Again, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15. Thus the larger number could be: 95, 84, 73, 62, or 51. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

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Re: This is a hard one  [#permalink]

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11 Jan 2011, 03:09
Thanks a lot. I got it.
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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20 Sep 2015, 22:13
Bunuel

I approached it this way, please let me know whether it is correct
I used both the statements to get a hint on what could be the 2 primes.

p + q = 110
p – q = 36

Add both to get 2p = 146
p = 73, so q = 37

now we know what the 2 primes are...we can evaluate statement 1 and 2.

1. we know that the sum has to be 110, we already know the prime numbers which will give a sum of 110.
we can determine the larger of p and q. Sufficient

2. we know that the difference (larger - smaller) has to be 36, we already know the prime numbers which will give a difference of 36.
we can determine the larger of p and q. Sufficient
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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19 Feb 2016, 10:54
Using the approach 10x+y and 10y+x looks much more easy for me. Thanks
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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27 Jun 2017, 03:30
1
Bunuel wrote:
nonameee wrote:
Can someone please explain to me:

I think it is totally irrelevant here that two numbers are prime. In order to find the largest, we have to solve both equations to find p and q.

Am I right?

No, that' not right.

p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

Given: $$p=prime=10x+y$$ and $$q=prime=10y+x$$, for some non-zero digits $$x$$ and $$y$$ (any two digit number can be expressed as $$10x+y$$ but as both $$p$$ and $$q$$ are two-digit then $$x$$ and $$y$$ must both be non-zero digits).

(1) p + q = 110 --> $$(10x+y)+(10y+x)=110$$ --> $$x+y=10$$. Now, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 91 and 19, 82 and 28, 73 and 37, 64 and 46, ... Thus the larger number could be: 91, 82, 73, or 64. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

(2) p – q = 36 --> $$(10x+y)-(10y+x)=110$$ --> $$x-y=4$$. Again, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15. Thus the larger number could be: 95, 84, 73, 62, or 51. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

Cool and simple (after you see it set up) solution for approaching this. Bunuel, just one thing - your 2nd statement should read =36, not =110
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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27 Jun 2017, 04:05
laxpro2001 wrote:
Bunuel wrote:
nonameee wrote:
Can someone please explain to me:

I think it is totally irrelevant here that two numbers are prime. In order to find the largest, we have to solve both equations to find p and q.

Am I right?

No, that' not right.

p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

Given: $$p=prime=10x+y$$ and $$q=prime=10y+x$$, for some non-zero digits $$x$$ and $$y$$ (any two digit number can be expressed as $$10x+y$$ but as both $$p$$ and $$q$$ are two-digit then $$x$$ and $$y$$ must both be non-zero digits).

(1) p + q = 110 --> $$(10x+y)+(10y+x)=110$$ --> $$x+y=10$$. Now, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 91 and 19, 82 and 28, 73 and 37, 64 and 46, ... Thus the larger number could be: 91, 82, 73, or 64. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

(2) p – q = 36 --> $$(10x+y)-(10y+x)=110$$ --> $$x-y=4$$. Again, if we were not told that $$p$$ and $$q$$ are primes than they could take many values: 95 and 59, 84 and 48, 73 and 37, 62 and 26, 51 and 15. Thus the larger number could be: 95, 84, 73, 62, or 51. But as we are told that both $$p$$ and $$q$$ are primes then they can only be 73 and 37, thus the larger number equals to 73. Sufficient.

Cool and simple (after you see it set up) solution for approaching this. Bunuel, just one thing - your 2nd statement should read =36, not =110

Thank you. Edited the typo. +1.
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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27 Jun 2017, 04:39
Jinglander wrote:
p and q are different two-digit prime numbers with the same digits, but in reversed order. What is the value of the larger of p and q?

(1) p + q = 110
(2) p – q = 36

Given : p and q, two digit pprime numbers with same digits but in reversed order
Let the number be xy and yx

DS: what is the value of larger of p and q

So p = 10x + y, q = 10y + x

Option 1 : 10x + y + 10y + x = 11(x+y) = 110
-> x+y = 10.

so the nos pair can be(19,91), (28,82), (37,73),(46,64), (55,55)
So, only required no is 73.
SUFFICIENT

Option 2: 10x+y - 10y -x = 36
9(x-y) = 36
x-y = 4
(51,15), (62,26), (73,37), (84,48),(95,59)
So, only required no is 73.
SUFFICIENT

Its a very gud question and a very good learning concept... Even if people are asking that do we need to remember prime numbers upto and whether this question will be asked in GMAT, I m sure this is an easy but tricky question and can be easily asked in GMAT..

I learnt 2 concepts here..
1. How to solve this type of problem by taking 10x+y as value..
2. If a two digit number is not divisible by 2,3,5 & 7, it must not be a prime number... A very good concept which will help us to fidn the prime numbers without remembering prime numbers upto 100.
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Re: p and q are different two-digit prime numbers with the same  [#permalink]

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15 Mar 2018, 13:07
Hi All,

The prompt includes a LOT of information about the 2 variables that severely limits the possibilities. Since both numbers have to be PRIME and have the same digits (in reverse order), we know that the digits CANNOT be EVEN, nor can either be 5. With a little bit of work, you can figure out all of the possibilities before you even look at the two Facts. They are:

13 and 31
17 and 71
37 and 73
79 and 97.

The question asks for the LARGER of the two numbers.

Fact 1: P + Q = 110

With this new information and the limited options that are available, the two numbers MUST be 37 and 73, so the answer is 73.
Fact 1 is SUFFICIENT

Fact 2: P - Q = 36

With this new information and the limited options that are available, the two numbers MUST be 37 and 73, so the answer is 73.
Fact 2 is SUFFICIENT

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Re: p and q are different two-digit prime numbers with the same   [#permalink] 15 Mar 2018, 13:07
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