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26 Mar 2024, 09:07
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C
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Difficulty:
95%
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Question Stats:
51% (02:58) correct
49%
(03:10)
wrong
based on 99
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If x ≠ 1 and x is a common factor of integer y and odd integer z, is x a prime number?
(1) –85 < 10 – y < –80
(2) 140 < z < 145
(1) –85 < 10 – y < –80
(2) 140 < z < 145
26 Mar 2024, 09:30
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If x ≠ 1 and x is a common factor of integer y and odd integer z, is x a prime number?
(1) –85 < 10 – y < –80
Multiply bu -1 and flip the signs:
80 < y - 10 < 85
Add 10 to each part:
90 < y < 95
y can be 91, 92, 93, or 94. Not sufficient.
(2) 140 < z < 145
Given that z is odd, it can be 141 or 143. Not sufficient.
(1) + (2) Factoring possible values of z gives: z = 141 = 3 * 47, and z = 143 = 11 * 13. Now, x cannot be either 141 or 143 because those numbers are not factors of any possible value of y. Thus, x is 3, 47, 11, or 13, all of which are primes. Sufficient.
Answer: C.
(1) –85 < 10 – y < –80
Multiply bu -1 and flip the signs:
80 < y - 10 < 85
90 < y < 95
(2) 140 < z < 145
Given that z is odd, it can be 141 or 143. Not sufficient.
(1) + (2) Factoring possible values of z gives: z = 141 = 3 * 47, and z = 143 = 11 * 13. Now, x cannot be either 141 or 143 because those numbers are not factors of any possible value of y. Thus, x is 3, 47, 11, or 13, all of which are primes. Sufficient.
Answer: C.
26 Mar 2024, 19:12
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We definitely need the value of y,z to find the common factor of them.
So range of y is {91,92,93,94} we can get this from the statement 1.
{13*7, 23*2*2, 3*31,47*2}
We know that z is not a even hence 2 or 2 multiples cannot be common factors.
From the above set common factors can be 7, 13 , 91, 23, 3,31,93,47.
Hence we cannot conclude whether x is prime or not.
Had the question been slightly tricky by stating x<y in given argument. Then we don't need another statement to conclude about x.
Now we need statement 2 as well.
Hence IMO C
So range of y is {91,92,93,94} we can get this from the statement 1.
{13*7, 23*2*2, 3*31,47*2}
We know that z is not a even hence 2 or 2 multiples cannot be common factors.
From the above set common factors can be 7, 13 , 91, 23, 3,31,93,47.
Hence we cannot conclude whether x is prime or not.
Had the question been slightly tricky by stating x<y in given argument. Then we don't need another statement to conclude about x.
Now we need statement 2 as well.
Hence IMO C
