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If x and y are distinct prime numbers, each greater than 2,

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If x and y are distinct prime numbers, each greater than 2, [#permalink]

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If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II) x*y has even number of factors
(III) x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD
[Reveal] Spoiler: OA

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If x and y are distinct prime numbers, each greater than 2, [#permalink]

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New post 13 Nov 2010, 10:48
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nades09 wrote:
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD


First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.
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Re: Must be true - number properties [#permalink]

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New post 13 Nov 2010, 11:51
Yes, Thank you very much. You rock!

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Re: Must be true - number properties [#permalink]

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New post 13 Nov 2010, 12:10
Bunuel,

Does that mean that me never count 1 as a factor?

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Re: Must be true - number properties [#permalink]

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Re: If x and y are distinct prime numbers, each greater than 2, [#permalink]

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New post 29 Jan 2015, 12:38
Hi All,

Roman Numeral questions on the GMAT often come with a "design shortcut", meaning that you probably WON'T have to think about all 3 Roman Numerals (IF you pay attention to how the answer choices are designed).

Here, we're told that X and Y are DISTINCT (meaning "different") PRIME numbers that are each greater than 2. We're asked which of the following Roman Numerals MUST be true (which really means "which of these is ALWAYS TRUE no matter how many different examples you can come up with). It's often easier to try to prove that something is NOT true, so that should be our goal here - try to come up with a way to disprove a Roman Numeral so that we can ELIMINATE it.

TESTing VALUES will work perfectly here.

I. (X+Y) is divisible by 4

3+5 = 8 which is divisible by 4
3+7 = 10 which is NOT divisible by 4
Roman Numeral 1 is NOT always true, so we can ELIMINATE IT.

**NOTE: Look at the answers. Since Roman Numeral 1 has been eliminated, we can....
1) Eliminate answers A, C and E.
2) Notice that the two remaining answers both have Roman Numeral II in them, so that Roman Numeral MUST be TRUE. As such, we don't even have to deal with it!!!!!

III. (X+Y) has an even number of factors

3+5 = 8 which has 4 factors
3+7 = 10 which has 4 factors
3+11 = 14 which has 4 factors
3+13 = 16 which has 5 factors
Roman Numeral 3 is NOT always true, so we can ELIMINATE IT.
Eliminate Answer D.

Final Answer:
[Reveal] Spoiler:
B


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If x and y are distinct prime numbers, each greater than 2, [#permalink]

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New post 14 Mar 2016, 04:42
Bunuel wrote:
nades09 wrote:
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD


First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.


Are there any other primes so that there sum yields a perfect square ?
what about x-y being a perfect square ?
is it possible too?
just curious as i got this question wrong ..
Did not think of 13 and 3
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Re: If x and y are distinct prime numbers, each greater than 2, [#permalink]

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New post 14 Mar 2016, 06:06
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Chiragjordan wrote:
Bunuel wrote:
nades09 wrote:
Source: 4Gmat
Q. If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II)x * y has even number of factors
(III)x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only

I plugged in numbers for each option, but it took me more than 2 mins to get to the right answer -OA is B.

I had to consider x=13 and y=23 for ruling out (III), since x+y in this case =36 which has odd no. of factors.

PLease explain if there is any other method for solving this under 2 mins

Thanks
NAD


First of all we are asked "which of the following MUST be true" not COULD be true.

"MUST BE TRUE" questions:
These questions ask which of the following MUST be true, or which of the following is ALWAYS true no matter what set of numbers you choose. Generally for such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

As for "COULD BE TRUE" questions:
The questions asking which of the following COULD be true are different: if you can prove that a statement is true for one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.

I. x+y is divisible by 4 --> if \(x=3\) and \(y=7\) then \(x+y=10\), which is not divisible by 4. So this statement is not always true;

II. xy has even number of factors --> only perfect squares have an odd number of factors (check this: a-perfect-square-79108.html?hilit=perfect%20square%20reverse#p791479), as \(x\) and \(y\) are distinct prime numbers then \(xy\) cannot be a perfect square and thus cannot have an odd number of factors, so \(xy\) must have an even number of factors. This statement is always true;

III. x+y has an even number of factors --> now, \(x+y\) can be a perfect square, for example if \(x=3\) and \(y=13\) then \(x+y=16=perfect \ square\), so \(x+y\) can have an odd number of factors. So this statement is not always true;

Answer: B (II only).

Hope it's clear.


Are there any other primes so that there sum yields a perfect square ?
what about x-y being a perfect square ?
is it possible too?
just curious as i got this question wrong ..
Did not think of 13 and 3


2 + 7 = 9 = 3^2
3 + 13 = 16 = 4^2
2 + 23 = 25 = 5^2
5 + 31 = 36 = 6^2
2 + 47 = 49 = 7^2
3 + 61 = 64 = 8^2
...

3 - 2 = 1 = 1^2
7 - 3 = 4 = 2^2
11 - 2 = 9 = 3^2
19 - 3 = 16 = 4^2
...
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x and y are distinct prime numbers, each greater than 2, [#permalink]

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New post 02 Nov 2017, 15:57
nades09 wrote:
If x and y are distinct prime numbers, each greater than 2, which of the following must be true?

(I) x+y is divisible by 4
(II) x*y has even number of factors
(III) x+y has an even number of factors

A. I only
B. II only
C. I and III only
D. II and III only
E. I and II only


Since x and y are prime numbers greater than two, they are both odd prime numbers. Let’s analyze each answer choice:

I. x+y is divisible by 4

This is not true. If x = 11 and y = 7, then x + y = 18, which is not divisible by 4.

II. x*y has an even number of factors

The only numbers that have an odd number of factors are perfect squares. Since x and y are distinct primes, x*y can’t be a perfect square, and thus it must have an even number of factors. This statement is true.

III. x+y has an even number of factors

This is not true. If x = 3 and y = 13, then x + y = 16, which is a perfect square. Recall that in Roman numeral II, we’ve mentioned that a perfect square has an odd number of factors.

Answer: B
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Re: If x and y are distinct prime numbers, each greater than 2,   [#permalink] 02 Nov 2017, 15:57
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