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Can the positive integer n be written as the sum of two diff

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Can the positive integer n be written as the sum of two diff [#permalink] New post 12 Feb 2014, 01:14
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Data Sufficiency
Question: 90
Category: Arithmetic Properties of numbers
Page: 158
Difficulty: 650


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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 12 Feb 2014, 01:14
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SOLUTION

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NONE of the odd integers greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd getdefinite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:

If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;

If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 12 Feb 2014, 02:02
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From 1: n>3 => put n=4 (Cannot be written), n=5 (can be written), Insufficient, A,D ruled out
From 2: n= odd => put n=1(Cannot be written), n=5 (can be written), Insufficient, B ruled out
Combining 1 &2 :
n>3 and n is odd => sum of the primes is odd => one of the primes =2
Now, to rephrase this: the question asks "odd no. - 2 = prime ?" => maybe and may not be : C ruled out

Answer is E
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 12 Feb 2014, 04:21
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St1: n is greater than 3.

If n = 5 -> 2 + 3 - yes
If n = 4 -> 1 + 4 - no

Not sufficient.

Down to B, C or E.

St2: n is odd.

If n = 5 -> 2 + 3 - yes
If n = 1 -> 1 + 0 - no

St1 + St2:

If n = 5 -> 2 + 3 - yes
If n = 11 -> 2 + 9 - no

Answer (E).
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 17 Feb 2014, 01:27
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SOLUTION

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NONE of the odd integers greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd getdefinite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:

If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;

If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 27 May 2014, 06:13
Bunuel wrote:
SOLUTION

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NONE of the odd integers greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd getdefinite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:

If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;

If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.


Bunuel , is there any way to solve this question without putting values ?
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 04 Jun 2014, 05:37
I really don't like the word 'Can' in this question as it is not precise. Is there a chance that this would be a real GMAT question?
I mean, I understand your explanation Bunuel, but you can actually answer the question with either statements. "Can it be?" - Sure it can, but also cannot, it depends on what the value of 'n' is.

Is that the way to approach this question? Ask yourself: "What is the value of n?" and if this is not given in the statements, then choose E?
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 04 Jun 2014, 07:50
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I really don't like the word 'Can' in this question as it is not precise. Is there a chance that this would be a real GMAT question?
I mean, I understand your explanation Bunuel, but you can actually answer the question with either statements. "Can it be?" - Sure it can, but also cannot, it depends on what the value of 'n' is.

Is that the way to approach this question? Ask yourself: "What is the value of n?" and if this is not given in the statements, then choose E?


This is OG question, so it's quite "real".
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 16 Jun 2014, 06:49
2 different prime numbers : We are ruling out option 'C' with an eg 11= 2+9 (9 is not prime)

However 11 = 2 +3 +3 = Sum of 2 different prime nos (2 and 3).based on this can we select C ...???
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 16 Jun 2014, 07:03
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sinhautkarsh wrote:
2 different prime numbers : We are ruling out option 'C' with an eg 11= 2+9 (9 is not prime)

However 11 = 2 +3 +3 = Sum of 2 different prime nos (2 and 3).based on this can we select C ...???


The question asks whether n can be written as the sum of two different prime numbers, so whether n = prime 1 + prime 2. If n = 11, then it cannot be written as the sum of two different primes. 2 + 3 + 3 + 3 cannot be said to be the sum of two primes, it's the sum of 4 numbers not 2.
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 03 Nov 2015, 01:43
Bunuel wrote:
SOLUTION

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NONE of the odd integers greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd getdefinite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:

If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;

If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.


Hi Bunuel, I've 1 question regarding picking numbers for combined statement (1) + (2)
Could we also pick following numbers here: ??
n=5 -> 3+2 Yes
n=5 -> 4+1 No
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 03 Nov 2015, 05:18
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Bunuel wrote:
SOLUTION

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NONE of the odd integers greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd getdefinite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:

If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;

If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Answer: E.


Hi Bunuel, I've 1 question regarding picking numbers for combined statement (1) + (2)
Could we also pick following numbers here: ??
n=5 -> 3+2 Yes
n=5 -> 4+1 No


n=5 gives an YES answer to the question. 5 CAN be written as the sum of two difference prime numbers: 5 = 2 + 3.

While if n=11 or n=17 the answer would be NO. Neither 11 nor 17 can be written as the sum of two different prime numbers.
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 03 Nov 2015, 20:46
I selected B because I took examples like 5 = 3+2, 9 = 7+2......19 = 17+2,
Hence I thought that , it is possible to write using two prime numbers and data is sufficient.
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Re: Can the positive integer n be written as the sum of two diff [#permalink] New post 08 Nov 2015, 04:43
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

There is one variable (n) and 2 equations are given from the 2 conditions, so there is high chance (D) will be our answer.
For condition 1, the answer is 'yes' for n=5=2+3, but 'no' for 23=2+21
For condition 2, the answer is 'yes' for n=5=2+3, but 'no' for 23=2+21
Looking at the conditions together, answer is 'yes' for n=5=2+3, but 'no' for 23=2+21.
The answer is not unique; the answer becomes (E).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Can the positive integer n be written as the sum of two diff   [#permalink] 08 Nov 2015, 04:43
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