Data Sufficiency

Hi, there. I'm happy to help with these.

1) If d is a positive integer and f is the product of the first positive 30 integers, what is the value of d?
Statement #1: 10^d is a factor of f.

Well, we need to figure out how many power of 10 go into f = 30!. Among the numbers from 1-30, there are 6 six multiples of 5, and one multiple of 25, so that's seven factors of 5 total. There are many many more factors of two, so that means f has seven factors of 10.

This means it's divisible by 10, 100, 1000, 10000, 100000, 1000000, and 10000000. From Statement #1, d could be any of the integers from 1 to 7. Statement #1 by itself is not sufficient.

Statement #2: d > 6
We did a lot of work in Statement #1, and we have to forget all that and consider Statement #2 on its own merits. All we know is that f = 30!, and d is a positive integer greater than six. We have absolutely no idea what the relationship is between d and f. Statement #2 by itself is not sufficient.

Statements #1 & #2 combined:
From statement #1, we know d is can be from 1 to 7, and if, according to Statement #2, it's greater than 6, d must equal 7. Combined, the statements are sufficient.

Answer = C

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2) The mass of 1 cubic meter of a substance is 800kg. What is the volume in cubic centimeters of 1gram of this substance? (1kg = 1000g and 1 cum = 1,000,000 cc).

We set up a proportion. We begin with (1 cubic meter)/(800 kg) = (1000000 cc)/(800000 g)
Canceling five zeros, we get

= (10 cc)/(8 g) = (10/8)(cc/g) = 1.25 cc/g

That means 1 gram would have a volume of 1.25 cc.

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3) 1000 video cameras were manufactured in 1993. X% more in 1994 compared to 93. Y% more in 95 compared to 94. How many were manufactured in 94?
Note: basically, we need to find the value of x to answer this question.

Statement #1: xy = 20
This statement, by itself, does not allow us to solve for x. Statement #1, by itself, is insufficient.

Statement #2: x+y+(xy/100) = 9.2
This statement, by itself, does not allow us to solve for x. This statement, by itself, would allows us to solve for the number of video cameras sold in 1995.

Sold in 1993 = 1000
Sold in 1994 = 1000*(1 + x/100)
Sold in 1995 = 1000*(1 + x/100)*(1 + y/100) = 1000(1 + x/100 + y/100 + (xy/10000))
= 10*100*(1 + x/100 + y/100 + (xy/10000))
= 10*(100 + x + y + xy/100)
Since statement #2 gives us the value of the green expression, we can plug in 9.2 for that expression and solve for the total number of video cameras sold in 1995. Unfortunately, that's not what the question asked.

If the question asked for the video cameras sold in 1995, the answer would be B.

Instead, it asks for the video cameras sold in 1994. Neither statement is sufficient for that, but if combined the statements are sufficient, and the answer would be C. I will forbear going through all that math because I suspect that the prompt might have been miscopied. Does the prompt ask for 1995 instead of 1994?

Does all this make sense? Please let me know if you have any follow-up questions.

Mike

Question 1)
If d is a positive integer and f is the product of the first positive 30 integers, what is the value of d?
1) 10^d is a factor of f.
2)d > 6

Answer is given as C. I dont understand why C and why not A?

f is the product of the first positive 30 integers implies f = 30!

(1) 10^d is a factor of f implies for any integer k, 30! = k * (10^d)
10^1, 10^2 and 10^3 are all factors of f, which implies d could be either 1, 2 or 3.
No definite answer; NOT sufficient.

(2) d > 6 implies d can be any integer greater than 6; obviously NOT sufficient.

Combining (1) and (2), let us first find the power of 5 in 30!
So, 30/5 + 30/25 = 6 + 1 implies there are 7 zeroes in 30! Now d = 7 also is > 6; SUFFICIENT.

The correct answer is C.

Question 2)
The mass of 1 cubic meter of a substance is 800kg. What is the volume in cubic centimeters of 1gram of this substance? (1kg = 1000g and 1 cum = 1,000,000 cucm)
The answer is 1.25. My answer is 0.80

Volume of 800 kg substance = 1 cubic meter = 1,000,000 cubic cm
Volume of 1 kg, i.e. 1000 g substance = (1,000,000/800) cubic cm
Volume of 1 g substance = (1,000/800) = 1.250 cubic cm