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13 Jan 2022, 02:30
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E
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Difficulty:
45%
(medium)
Question Stats:
58% (01:44) correct
42%
(01:56)
wrong
based on 74
sessions
History
Date
Time
Result
Not Attempted Yet
What is the value of positive integer x?
(1) x is a factor of the product of all integers from 1 to 5, inclusive
(2) x has 6 factors
(1) x is a factor of the product of all integers from 1 to 5, inclusive
(2) x has 6 factors
13 Jan 2022, 02:47
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Can we identify the exact value of a positive integer x?
(1) Only. x can be 1 or 2. Not Sufficient.
(2) Only. Evidently insufficient.
(1) and (2) Together.
12 = 4*3 = 2^2 * 3. It contains 3*2=6 factors and is a factor of the product.
20 = 4*5 = 2^2 * 3. It contains 3*2=6 factors and is a factor of the product.
Not Sufficient.
Answer is (E).
How to come up with the number of 12 and 20?
We can find the number of factors of a given number using the following steps. (Read more from https://www.cuemath.com/numbers/factors/)
Step 1: Find its prime factorization, i.e. express it as the product of primes.
Step 3: Write the prime factorization in the exponent form.
Step 3: Add 1 to each of the exponents.
Step 4: Multiply all the resultant numbers. This product would give the number of factors of the given number.
The product = 1 * 2 * 3 * 4 * 5 = 2^3 * 4 * 5
Condition (2) stipulates that x have 6 = 3 * 2 factors = (2+1)*(1+1) factors.
We have to pick 2^2 to supply (2+1)
then, we can pick either 3 or 5 to supply (1+1)
(1) Only. x can be 1 or 2. Not Sufficient.
(2) Only. Evidently insufficient.
(1) and (2) Together.
12 = 4*3 = 2^2 * 3. It contains 3*2=6 factors and is a factor of the product.
20 = 4*5 = 2^2 * 3. It contains 3*2=6 factors and is a factor of the product.
Not Sufficient.
Answer is (E).
How to come up with the number of 12 and 20?
We can find the number of factors of a given number using the following steps. (Read more from https://www.cuemath.com/numbers/factors/)
Step 1: Find its prime factorization, i.e. express it as the product of primes.
Step 3: Write the prime factorization in the exponent form.
Step 3: Add 1 to each of the exponents.
Step 4: Multiply all the resultant numbers. This product would give the number of factors of the given number.
The product = 1 * 2 * 3 * 4 * 5 = 2^3 * 4 * 5
Condition (2) stipulates that x have 6 = 3 * 2 factors = (2+1)*(1+1) factors.
We have to pick 2^2 to supply (2+1)
then, we can pick either 3 or 5 to supply (1+1)
13 Jan 2022, 11:28
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What is the value of positive integer x?
Stat1: x is a factor of the product of all integers from 1 to 5, inclusive
Product = 120, we have no idea of x. Not sufficient.
Stat2: x has 6 factors; x = 2^5 or 3^5 or, 2^1 *3^2...Not sufficient.
Combining both, Product = 120 = 2^8 *3*5; to reach factor of 6, we need 2^2 and 3^1 or 5^1.
X can be 12= 2^2*3 or 20 = 2^2*5. Not Sufficient.
So, I think E.
Stat1: x is a factor of the product of all integers from 1 to 5, inclusive
Product = 120, we have no idea of x. Not sufficient.
Stat2: x has 6 factors; x = 2^5 or 3^5 or, 2^1 *3^2...Not sufficient.
Combining both, Product = 120 = 2^8 *3*5; to reach factor of 6, we need 2^2 and 3^1 or 5^1.
X can be 12= 2^2*3 or 20 = 2^2*5. Not Sufficient.
So, I think E.
