Bunuel
What is the value of the integer p ?
(1) Each of the integers 2, 3, and 5 is a factor of p.
(2) Each of the integers 2, 5, and 7 is a factor of p.
Diagnostic Test
Question: 26
Page: 25
Difficulty: 550
ASIDE:
For questions involving factors (aka "divisors"), we can say:
If k is a divisor of N, then k is "hiding" within the prime factorization of NConsider these examples:
3 is a divisor of 24 because 24 = (2)(2)(2)
(3), and we can clearly see the
3 hiding in the prime factorization.
Likewise,
5 is a divisor of 70 because 70 = (2)
(5)(7)
And
8 is a divisor of 112 because 112 = (2)
(2)(2)(2)(7)
And
15 is a divisor of 630 because 630 = (2)(3)
(3)(5)(7)
Conversely, we can say that, if
k is "hiding" within the prime factorization of N, then N is a multiple of kExamples:
24 = (2)(2)(2)
(3) <--> 24 is a multiple of
3(2)
(5)(7) <--> 70 is a multiple of
5330 =
(2)(3)(5)(11) <--> 330 is a multiple of
6----NOW ONTO THE QUESTION-------------
Target question: What is the value of the integer p ? Statement 1: Each of the integers 2, 3, and 5 is a factor of p. So, p = (
2)(
3)(
5)(possibly other primes)
This tells us that p is a multiple of
30.
There are infinitely many values of p that satisfy statement 1.
For example,
p could equal 30 or
p could equal 60 (etc)
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Each of the integers 2, 5, and 7 is a factor of p. So, p = (
2)(
5)(
7)(possibly other primes)
This tells us that p is a multiple of
70.
There are infinitely many values of p that satisfy statement 2.
For example,
p could equal 70 or
p could equal 140 (etc)
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that p = (
2)(
3)(
5)(possibly other primes)
Statement 2 tells us that p = (
2)(
5)(
7)(possibly other primes)
When we COMBINE the statements, we can conclude that p = (
2)(
3)(
5)(
7)(possibly other primes)
In other words, p is a multiple of
210.
There are infinitely many values of p that satisfy this condition.
For example,
p could equal 210 or
p could equal 420 (etc)
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
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