GMAT Math : GMAT Quantitative Reasoning
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Example Questions
Example Question #1 : Dsq: Calculating Discrete Probability
Data sufficiency question
What is the probability of choosing a red marble at random from a bag filled with marbles?
1. There are only red and black marbles in the bag
2. 
each statement alone is sufficient
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
From statement 1, we learn that there are only two different colored marbles in the bag. From statement 2, we learn that 
Example Question #3 : Discrete Probability
Assume that we are the immortal gods of statistics and we know the following population statistics:
1) average driving speed for women=50 mph with a standard deviation of 12
2) average driving speed for men=45 mph with a standard deviation of 11
We look down from our statistical Mount Olympus and notice that the Earth mortals have randomly sampled 60 women and 65 men in an attempt to detect a significant difference in the average driving speed.
What is the probability that the Earth mortals will properly reject the assumption (i.e. the null hypothesis) that there is no significant difference between the average driving speeds. The Earth mortals have decided to use a 2-tailed 95% confidence test.
standard deviation of the difference between the sample means =
the sample difference must be 4 or greater
(note: the probability of the sample difference being -4 or less is so small (4.5 standard deviations) that it will be ignored and we will only consider the probability that the difference is 4 or more.)
the probablity of the sample difference being 4 or greater (knowing that the population difference is 5) =
the table shows that .3156 lies below -.48, so, .6844 lies above -.48
In English - there is a .6844 probability that the 2 sample means will yield a sample difference that is 1.96 or more standard deviations above 0.
Example Question #4 : Discrete Probability
In a popular state lottery game, a player selects 5 numbers (on 1 ticket) out of a possible 39 numbers. There are 575,757 possible 5 number combinations.
So, the odds are 575,757 to 1 against winning.
What are the odds of getting 4 of the 5 numbers correct on 1 ticket?
575,757 must be divided by -
Example Question #5 : Dsq: Calculating Discrete Probability
Your friend at work submits a bold hypothesis. He suggests that the number of sales per day follow the pattern - Monday-10%, Tuesday-10%, Wednesday-10%, Thursday 35% and Friday 35%.
You and he then record the number of sales for the following week: Monday-120, Tuesday-85, Wednesday-105, Thursday-325 and Friday-365.
After viewing the observed data, your friend expresses serious concern regarding his hypothesis.
You can help; you can tell him the probability of the observed data occuring if the hypothesis is true. Hint - Excel ChiTest.
Use Excel ChiTest to get the .063 probability. If you are old-fashioned, you can also obtain the Chi-Squared number (8.928) by using ChiInv; but, it is not needed
Example Question #3151 : Gmat Quantitative Reasoning
A certain tutor boasts that his 2 week training program will increase a student's score on a 2400 point exam by at least 100 points (4.167%). A 10 student 'before-and-after' study was conducted to validate the claim. The following results were obtained - the 3 columns represent the before, afer and increase numbers for each of the 10 students:
1300 1340 40
1670 1790 120
1500 1710 210
1360 1660 300
1580 1730 150
1160 1320 160
1910 2100 190
1410 1490 80
1710 1880 170
1990 2060 70
Assume the null Hypothesis:
'The average increase is less than 100 points'
What is the highest level of significance (p-value) at which the null hypothesis will be rejected?
Using Excel, the average increase (column 3) is 149 and Standard Deviation of the increases is 76.37
Using Excel - a t value of 2.03 for 9 degrees of freedom = .036
Example Question #51 : Arithmetic
A test for a new drug was conducted. In the control or placebo group, 7 of 210 participants experienced positive results. The group that took the drug experienced 27 out of 374 positive resluts.
The placebo group had a sucess rate of .0333 and the drug group had a success rate of .0722. The difference is .0389 and the overall percentage (for both groups combined) is .0582
At what level is the difference of .0389 significant? Asked another way - what is the p-value for .0389?
The standard error of the difference (.0389) =
test statistic -
from the table (or excel NormsDist) - Z=1.9245 translates to .9729
Example Question #3151 : Gmat Quantitative Reasoning
Jerry is a Cardinal fan and he and his family live on a street with 9 other families that are all Cardinal fans. One block to the north, there are 11 families and they are all Cub fans. These 21 households all buy their lawn fertilizer from Ben's Lawn and Garden Shop. Jerry suspects that Ben (who is originally from Chicago) is a Cub fan and that he provides better fertilizer to the Cub fans than to the Cardinal fans, while charging the same price for all.
Last Saturday everyone in town mowed their lawn. At 2:00 AM Sunday morning, Jerry snuck around town and weighed all of the grass clippings for the 21 households in question.
The weights (in lbs) of the grass clippings for the 10 Cardinal homes were:
82, 85, 90, 74, 80, 89, 75, 81, 93, 75
The weights (in lbs) of the grass clippings for the 11 Cub homes were:
90, 87, 93, 75, 88, 96, 90, 82, 95, 97, 78
The Cardinal average was 82.4; the Cub average was 88.27.
At what level is the 5.87 lb difference significant? - Asked another way - what is the p value for the 5.87 lb difference.
Cub variance = 53.218; Cardinal variance = 45.378.
The standard deviation of the difference (5.87) is:
TDIST of 1.918 with 19 Degrees of Freedom = .035
So, we would reject the null hypothesis (the hypothesis that claims that the means are equal) at 95% confidence (p=.05) and not reject at 99% (p=.01)
Example Question #3152 : Gmat Quantitative Reasoning
A pair of dice - one fair, one loaded, but each with the usual numbers 1-6 on their faces - are rolled. What is the probability that one die will show a 5 and the other will show a 6?
Statement 1: The probability of rolling a 5 on the loaded die is 
Statement 2: The probability of rolling a 6 on the loaded die is 
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The probability of rolling a 5 and the probability of rolling a 6 on the fair die are both 
Let the probabilities of rolling a 5 and a 6 on the loaded die be 
The probability of rolling a 6 on the fair die and a 5 on the loaded die is 
The probability of rolling a 5 on the fair die and a 6 on the loaded die is 
Therefore, the probability of rolling a 5-6 one way or the other is their sum:
which is dependent on both probabilites given in the two statements.
Example Question #61 : Arithmetic
Four cards are removed from a standard deck of fifty-two cards. Did the probability that a randomly drawn card will be a heart increase, decrease, or stay the same?
Statement 1: At least three of the cards are spades.
Statement 2: At least one of the cards is a club.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
One-fourth of the cards in a standard deck are hearts; in order to know whether the probability of drawing a heart increased, decreased, or stayed the same, we need to know whether fewer than, exactly, or more than one-fourth of the cards remaining are hearts. Therefore, we need to know whether no hearts, one heart, or more than one heart was removed.
Neither statement alone allows this question to be answered definitively, as we know nothing about the suit(s) of the other card(s). But both statements together tell us that no hearts were removed, so thirteen of the forty-eight cards remaining are hearts. This raises the probability from 
Example Question #62 : Arithmetic
Four cards are removed from a standard deck of fifty-two cards. Did the probability that a randomly drawn card will be a club increase, decrease, or stay the same?
Statement 1: The four cards that were removed were all kings.
Statement 2: One card of each suit was removed.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Thirteen of the fifty-two cards in a standard deck - one-fourth - are clubs, so the probability of drawing a club is 
Either statement tells us that one card of each suit was removed (there is one king of each suit), leaving twelve clubs out of forty-eight cards - one fourth of them. This keeps the probability of drawing a club at 
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