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If x and y are different prime numbers, each greater than 2, which of

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

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New post 17 Sep 2018, 23:46
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If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x + y ≠ 91
II. x - y is an even integer
III. x/y is not an integer


(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III

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

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New post 17 Sep 2018, 23:55
1
Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x + y ≠ 91
II. x - y is an even integer
III. x/y is not an integer


(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


I. x + y ≠ 91

Prime numbers say p > 2 are always odd
odd + odd = even
since 91 is odd
This statament will always be true

II. x - y is an even integer
odd - odd = even
This statement will be always true

III. x/y is not an integer
since x and y both are prime numbers , y will never evenly divide x
This statement will be always true

E
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Re: If x and y are different prime numbers, each greater than 2, which of  [#permalink]

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New post 17 Sep 2018, 23:57
Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x + y ≠ 91
II. x - y is an even integer
III. x/y is not an integer


(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Prime number greater than 2 are all odd integers. Hence, we need to apply even-odd property here. Not to miss the statement given, both are different prime numbers.

I. Odd+Odd is always even - True
II. Odd - Odd is always even - True
III. Prime/Prime can never be an integer as factors of a prime are 1 and itself - True

+1 for E
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Re: If x and y are different prime numbers, each greater than 2, which of  [#permalink]

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New post 18 Sep 2018, 02:58
1
Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x + y ≠ 91
II. x - y is an even integer
III. x/y is not an integer


(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III



1. prime numbers other than 2 are all odd,
then odd+odd is always=even number, so x+y can never be =91.

2.prime numbers are odd always(other than 2) odd-odd=even always

3.prime numbers are divisible by itself or by 1, so x/y is never an integer.

All are always true. option E
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Re: If x and y are different prime numbers, each greater than 2, which of  [#permalink]

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New post 18 Sep 2018, 03:49

Solution


Given:
    • x and y are two different prime numbers, each greater than 2

To find:
    • Which of the given statements is/are always true?

Approach and Working:
Any prime number, which is greater than 2, is odd
    • Thus, x and y both are odd, which implies, x + y = even
      o Thus, Statement 1, “x + y ≠ 91”, is true
    • x and y both are odd, which implies, x - y = even
      o Thus, Statement 2, “x - y is an even integer”, is true
    • Since, x and y are distinct prime numbers, they do not have any common factor except 1.
      o Thus, Statement 3, “x/y is not an integer”, is true

Hence, the correct answer is option E.

Answer: E

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

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New post 19 Sep 2018, 18:08
Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x + y ≠ 91
II. x - y is an even integer
III. x/y is not an integer


(A) II only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III


Since x and y must be odd if each is greater than 2, so both x + y and x - y must be even. We see that I and II are true.

Since x and are different prime numbers, neither can be a multiple of the other, so x/y can’t be an integer. III is true also.

Answer: E
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Re: If x and y are different prime numbers, each greater than 2, which of  [#permalink]

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New post 19 Sep 2018, 20:06
2
Given
X and Y are prime number greater than 2, resulting both these numbers are Old Integer

Concept :- Odd +/- Odd = Even

St1 x + y ≠ 91.

By rephrasing, this statement becomes :- Odd + Odd is not equal to Odd. Based on the provided information, this statement is true

St2. x - y is an even integer
odd - odd = even. Based on the provided information, this statement is true

St3. x/y is not an integer
Since A prime number is a whole number greater than 1 ( in our case 2) whose only factors are 1 and itself, and x and y both are prime numbers, y is not the factor of X. Hence, this statement is true.
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Re: If x and y are different prime numbers, each greater than 2, which of &nbs [#permalink] 19 Sep 2018, 20:06
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