Archive for June, 2008
Yesterday, we posted a 700+ level GMAT question. Below is the answer and explanation. How’d you do?
Answer: E
This is a tough remainder question. First off, we can see right away that the answer cannot be A, B, or D, since each statement refers to only part of the question. Now we simply need to figure out if they can work together to secure a consistent answer.
The key is to realize that if we divide p by 3, the only remainders that are possible or 1 or 2. If we divided p by 4, the only options are 1, 2, or 3. So the options are limited. We just need to see what p could be, and figure out if the remainders always work in one way or another.
Do a quick little chart on your paper. This won’t take long, and you’ll have the answer right away.
p 1 2 3 4 5 6 7
q 1 2 0 1 2 0 1
r 1 2 3 0 1 2 3
Since q and r must be positive integers, we can eliminate all instances where they are 0. But we can still see that q can be either larger, smaller, or equal to r, so there is no way to answer this question.
June 25th, 2008
Every Tuesday we post a 700+ level GMAT question here on our blog, and post the answer and explanation the following day. Do you have what it takes?
p, q, and r are all positive integers. Is q > r?
1. p divided by 3 yields a remainder of q.
2. p divided by 4 yields a remainder of r.
June 24th, 2008
Yesterday, we posted a 700+ level GMAT question. Below is the answer and explanation. How’d you do?
Answer: A
To solve this question quickly, we need to know how to sum consecutive numbers quickly.
The process, as we teach all our students, is the following:
1. Find the middle number by averaging the endpoints:
(37 + 5)/2 = 21
2. Find the number of numbers. When we are including both the first and last number, subtract the endpoints and add 1:
(37 – 5) + 1 = 33
3. Multiply:
21×33 = 693
Now find the prime factors of 693. You will see that they are 3, 3, 7, 11.
Thus, the lowest prime factor is 3.
June 18th, 2008
Every Tuesday we post a 700+ level GMAT question here on our blog, and post the answer and explanation the following day. Do you have what it takes?
What is the lowest prime factor of the sum of all the numbers from 5 to 37, inclusive?
A) 3
B) 5
C) 7
D) 11
E) 37
June 17th, 2008
Yesterday, we posted a 700+ level GMAT question. Below is the answer and explanation. How’d you do?
Answer: D
Since each employee typically produces 60 units per day, in a month of 20 days the total units produced would have been 48,000. In February, though, 5 employees were sick for four days each, so they combined did not produce 1200 units while they were sick (4 x 5 x 60). Because of that, Company X produced only 46,800 units in February. Divide by 40 employees and 20 days, and we arrive at an average of 58.5 units per employee per day.
June 11th, 2008
Every Tuesday we post a 700+ level GMAT question here on our blog, and post the answer and explanation the following day. Do you have what it takes?
Each of the 40 employees at Company X produces 60 units of Product Y per workday. However, in February, 5 employees were sick for an average (arithmetic mean) of four days each. If February had 20 workdays, what was the average number of units produced per employee per day in February?
a) 65
b) 62.5
c) 60
d) 58.5
e) 55
June 10th, 2008
Yesterday, we posted a 700+ level GMAT question. Below is the answer and explanation. How’d you do?
Answer: C
This is a dependent probability problem. If you want to find the probability of choosing 2 black marbles, you will need to figure out the probability that the first marble will be black and that the second marble will be black. In this case, the question wants to know if that probability is larger than 1/3.
Statement 1 tells us that less than half the marbles are white, which means that more than half the marbles are black. The best way to approach this is to systematically (but quickly) figure out what the probability of two black marbles is for each scenario. We can do it easily by drawing a chart:
As you can see, when less than half the marbles are white, the probability of choosing 2 black marbles can be higher or lower than 1/3, depending on how many black marbles there are. This is not sufficient.
Statement 2 tells us that the probability of choosing one black marble and one white marble is 7/15. This is a trap. Since the probability given is exact, it may seem that only one scenario of black marbles and white marbles will work. If you work through all the scenarios, you will see that when there are 7 black marbles and 3 white marbles, the probability of choosing one of each is 7/15. However, it would also be true in reverse: If there were 7 white marbles and 3 black marbles, the probability would also be 7/15. Therefore, this is not enough information.
Combining them does give us enough information. From statement 2 we know that there must be 7 of one color and 3 of the other, and from statement 1 we know that there must be more black than white, so we know there must be 7 black marbles and 3 white marbles.
June 4th, 2008
Every Tuesday we post a 700+ level GMAT question here on our blog, and post the answer and explanation the following day. Do you have what it takes?
A jar has 10 marbles, either black or white. 2 marbles are randomly chosen simultaneously from the jar. If q is the probability that both will be black , is q > 1/3?
- Less than ½ of the marbles in the jar are white.
- The probability that 1 white marble and 1 black marble will be chosen together is 7/15.
June 3rd, 2008