This question is based on the concept of factors and of course, the concept of HCF. Also, this is not a question you could classify as easy or medium. This is probably in the
medium-hard band of the difficulty spectrum. As such, you need to analyse the statements in depth and be on the lookout for trap answers.
From the question statement, we know that z is an integer. So, z can be a negative integer or ZERO or a positive integer. But, the question is asking us whether z is prime. Therefore, in a subtle way, it is hinting that we need to probably consider positive integral values of z only. Remember that factors and remainders are defined for positive integers only on the GMAT.
Using Statement I alone, we get that the GCD (or the HCF) of z and 140, is 7. You need to observe that
140 is an even multiple of 7. Therefore,
any other even multiple of 7, when taken in conjunction
with 140 will never have GCD as 7. Therefore, we can say that z cannot be 14 or 28 or 42 and so on.
Also, 140 = 2^2 * 7 * 5. Therefore,
any multiple of 35, along
with 140 will also
not have a GCD of 7.
Therefore, can we say that the only possible value of z that fits the bill in every possible way is 7 itself??
The answer would be NO. And if you miss this fact, you will end up thinking that the first statement alone is sufficient and mark A (or D, depending on your interpretation of the second statement) which is a TRAP answer
You need to observe that 140 does not have a 3 or an additional 7 or a 11 and so on. So, z can be 7 or 21 or 63 or 77 or 91 and so on. If
z = 7,
the answer to the main question will be a YES and if
z is equal to some of the other values, then the answer to the main question will be a NO.
Hence, statement I alone is insufficient.
Using statement II alone, we cannot figure out a unique value of z, let alone figuring out whether it is prime or not.
If z = 4, the sum of the distinct factors of 4 i.e. 1,2 and 4 is 7, which is less than 10. In this case, z is composite.
If z = 7, the sum of the distinct factors of 7 i.e. 1 and 7 is 8, which is less than 10. In this case, z is prime.
If z = 1, the sum of the factors will be 1, which is less than 10. In this case, z is neither prime nor composite.
Therefore, we can see that statement II alone is grossly insufficient.
When we combine the data given in both the statements, it can be seen clearly that
7 is the only value of z that satisfies the conditions given in the statements. Hence, we can definitely say that z is prime.
The
correct answer option is
C.
So, as mentioned earlier, it is very important
to not jump to conclusions when arriving at values after analyzing a statement. In fact, it is important to analyse the statement as much as possible,
so that most of the values which don’t satisfy the condition get eliminated, as we demonstrated in this question. Whatever values are left will be easy to handle.
Hope this helps!
Arvind,
CrackVerbal Prep Team