GMAT Data Sufficiency- What is The Value of (a!+b!)(c!+d!)?

Question: What is the value of (a!+b!)(c!+d!)?
(1) b!d!=4(a!d!)
(2) 60(b!c!)=(b!d!)

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are not sufficient.

“What is the value of (a!+b!)(c!+d!)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The question isn't as straight forward as many may believe. There is a trick which is the factorials and that n! can take only a limited set of values.
To get (a!+b!)(c!+d!), we need the values of all - a!, b!, c! and d!
Statement 1: b!d!=4(a!d!)
b! = 4*a!
Certainly, value of a can only be 3 and the value of b can only be 4. There is no other way that this relation will hold.
Let us think of it this way:
1*2*3*... = 4*(1*2*3*....)
4 has to be the last number multiplied on the left side.
Hence, b! = 4! and a! = 3!
We are unable to get any information about c and d so, the answer is not sufficient.
Statement 2: 60(b!c!)=(b!d!)
60*c! = d!
Now this is a little trickier. c! could be 59! and d! could be 60! but
60 = 3*4*5, which leads us to another value of c and d.
c! could be 2! and d! could be 5!
3*4*5 *2! = 5!
Hence we got two different values for c! and d!
We can say that this is also Not sufficient.
If we consider both statements together, we still do not know the exact value of c and d. Hence together also, they are not sufficient.

Correct Answer: E

Approach Solution 2:
In this problem statement, we need to find the value of (a!+b!)(c!+d!)
Let us consider the statement 1:
b!*d!=4*a!*d!
Dividing both sides by d! as it is +ve;
b!=4a!
Hence, the answer is Not Sufficient.
Let us consider the statement 2:
60*b!*c!=b!*d!
Dividing both sides by b! as it is +ve;
60*c!=d!
Hence, the answer is Not Sufficient.
(a!+b!)(c!+d!)
=5*a!*61*c!
=305*a!*c!
This also stands at Not Sufficient.
As we are unable to get the exact value using both the statements.

Correct Answer: E

Approach Solution 3:

To solve this problem, we must determine the value of (a!+b! (c!+d!
Take into consideration the formula 1:
Take into consideration the formula 1:
Given that both sides are divided by d!, b!=4a!
As a result, the response is Not Sufficient.
Let's think about the second statement:
60*b!*c!=b!*d!
The result of dividing both sides by b! is 60*c!=d!
As a result, the response is Not Sufficient.
(a!+b!)(c!+d!)
=5*a!*61*c!
=305*a!*c!
This is also rated as insufficient.
Since neither of the statements allows us to obtain the exact values.

Correct Answer: E

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GMAT Data Sufficiency- What is The Value of (a!+b!)(c!+d!)?

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