pranav6082 wrote:
dabral wrote:
I will give you my take on how to jump from Q50 to Q51. First if you are consistently scoring Q50, then that means you have all the basics and the advanced ideas in place. It is also possible that there may be some subtopics where you are not as strong as others. Clearly beefing up on those would be a good strategy.
As for the specific problem types, there are two category of questions that can hold you back from a Q51. The first ones are the medium level ones where one could misinterpret a statement and fall for a trap. These are problems that you know everything about but still trip on something small and make a mistake. These are really hard to correct, other than having extreme focus and double checking your work. This can happen to anyone on any day. I personally double check the easier problems, because I know I am more likely to miss an easier problem than a hard one. The reason is that the harder ones rely on testing an advanced concept and rely less on how the questions are phrased or need to be interpreted.
The second category of questions that mostly rely on a new idea require you to be fairly flexible in your approach. These questions often rest on testing an idea that you may not have seen before. Of course, they are not entirely new, but are significantly different than what you may have seen in practice tests. To be able to deal with these problems, I generally recommend going one step beyond GMAT, this where others may disagree with me. I will illustrate with an example. Let's say I want to push my understanding of Counting and Number Theory. I would give the following question to a student(Source American Mathematics Competition AMC 12 2003 Problem#23):
How many perfect squares are divisors of the product (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)?
(A) 504 (B) 672 (C) 864 (D) 936 (E) 1008
This problem is beyond what you would encounter on GMAT, however it has the elements of the concepts necessary for the GMAT, and it does an excellent job of forcing you to think and come up with an approach to solve this problem. This struggle that is inherent in solving this problem is extremely valuable for those few hard problems on the GMAT that determine the difference between Q50 and Q51.
Cheers,
Dabral
Hi @Darbal
Could you please post answer to the above question.
Thanks!
Hi Pranav,
Step 1: Find the prime factorization of given expression.
\begin{tabular}{ | c | c | c | c | c | }
\hline
Factorial & No. of 2 & No. of 3 & No. of 5 & No. of 7 \\ \hline
2! & 1 & 0 & 0 &0 \\ \hline
3! & 1 & 1 & 0 & 0\\
4! & 3 & 1 & 0 & 0\\ \hline
5! & 3 & 1 & 1 & 0 \\ \hline
6! & 4 & 2 & 1 & 0 \\ \hline
7! & 4 & 2 & 1 & 1 \\ \hline
8! & 7 & 2 & 1 & 1 \\ \hline
9! & 7 & 4 & 1 & 1 \\ \hline
Total & 30 & 13 & 5 & 3 \\
\hline
\end{tabular}
(1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!) = \(2^{30} \times 3^{13} \times 5^{5} \times 7^{3}\)
Step 2: Since we have to find perfect squares as divisors, so each prime number should be in a pair.
=> \(2^{15} \times 3^{6} \times 5^{2} \times 7^{1}\)
Step 3: Total no. of divisors = (15+1)*(6+1)*(2+1)*(1+1) = 672
Answer option (b).
Thanks.