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Syumbel1
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If y is an integer, is y a prime number of the form 4k-1, where k is a 28 Nov 2023, 07:39
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95% (hard)

Question Stats:

36% (02:26) correct 64% (02:40) wrong based on 39 sessions

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If y is an integer, is y a prime number of the form 4k-1, where k is a positive integer

1) (7y^9+6)^2/4 is an integer
2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient
d) EACH statement ALONE is sufficient
e) Statement 1) and 2) TOGETHER aren't sufficient
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D
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stne
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If y is an integer, is y a prime number of the form 4k-1, where k is a 28 Nov 2023, 14:54
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Syumbel1
If y is an integer, is y a prime number of the form 4k-1, where k is a positive integer

1) (7y^9+6)^2/4 is an integer
2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient
d) EACH statement ALONE is sufficient
e) Statement 1) and 2) TOGETHER aren't sufficient
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1) (7y^9+6)^2/4 is an integer

\(\frac{49y^{18} +36 +84y^9}{4} =\) Integer

Hence \(y\) must be divisible by \(4\)

If \(y\) is divisble by \(4\) then \(y \) is not a prime

SUFF.

2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite

\(1\) is neither prime nor composite

Hence (7y^5-222)^2/8 =1

We can solve for \(y.\)

SUFF.

Ans D

Hope it helped.
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If y is an integer, is y a prime number of the form 4k-1, where k is a 21 Dec 2023, 21:02
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stne
Syumbel1
If y is an integer, is y a prime number of the form 4k-1, where k is a positive integer

1) (7y^9+6)^2/4 is an integer
2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient
d) EACH statement ALONE is sufficient
e) Statement 1) and 2) TOGETHER aren't sufficient

1) (7y^9+6)^2/4 is an integer

\(\frac{49y^{18} +36 +84y^9}{4} =\) Integer

Hence \(y\) must be divisible by \(4\)

If \(y\) is divisble by \(4\) then \(y \) is not a prime

SUFF.

2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite

\(1\) is neither prime nor composite

Hence (7y^5-222)^2/8 =1

We can solve for \(y.\)

SUFF.

Ans D

Hope it helped.
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Plz explain statement 1 again as i fail to understand what we consider here.
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If y is an integer, is y a prime number of the form 4k-1, where k is a 21 Dec 2023, 21:31
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If y is an integer, is y a prime number of the form 4k-1, where k is a positive integer

1) (7y^9+6)^2/4 is an integer
\(\frac{ (7y^9+6)^2}{4}=x\)
\( (7y^9+6)^2=4k\)
Only possible when \( (7y^9+6)^2\) is a multiple of at least 4.
That is \( 7y^9+6\) is even or y is even.
If y is even, it cannot be of the form 4k-1.
Sufficient

2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite
Knowing \(\frac{ (7y^5-222)^2}{8}\) is an integer is sufficient as shown in statement 1.
Again y has to be even, otherwise [m] (7y^5-222)^2[m] is odd and cannot be divided by 8.
Sufficient


D
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If y is an integer, is y a prime number of the form 4k-1, where k is a 22 Dec 2023, 23:32
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Syumbel1
If y is an integer, is y a prime number of the form 4k-1, where k is a positive integer
1) (7y^9+6)^2/4 is an integer
2) (7y^5-222)^2/8 is a positive integer, which is neither prime nor composite
Show more

Sol: Option-D

Is y a prime number of the form 4k-1 : 3, 7, 11, ...
Stat-1:
\((7y^9+6)^2\)/4 is an integer , Therefore, \((7y^9+6)^2\) is divisible by 4 or

\((7y^9+6)^2\) = 4*p

4*p is an even number , therefore, \((7y^9+6)^2\) is even and square for a number is even only if the number is even.
This implies, \((7y^9+6)\) is even.

Odd*x + Even = Even and thus, y^9 is even. and y is even and can't be a prime of the form 4k-1
This statement is Sufficient.

Stat-2:
\((7y^5-222)^2\)/8 is a positive integer ; With same reasoning as in stat-1
\((7y^5-222)^2\) = 8*p

Odd*x-Even = Even , and thus, y^5 is even. and y is even and can't be a prime of the form 4k-1
This statement is also Sufficient.
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