GMAT Math : GMAT Quantitative Reasoning
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Example Questions
Example Question #62 : Data Sufficiency Questions
The table below gives the population of the city of Renfrow for each of six census years.
Did Renfrow have a larger population in 1945 or 1955?
Statement 1: The population rose every year from 1940 to 1950.
Statement 2: The population rose every year from 1950 to 1960.
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.
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.
Statement 1 alone tells us that the population of Renfrow in 1945 was between 13,251 and 15,049, but says nothing about the population in 1955.
Similarly, Statement 2 alone tells us that the population in 1955 was between 15,049 and 19,415, but says nothing about the population in 1945.
The two statements together, however, tell us that the population rose every year from 1940 to 1960, so the population in 1955 had to have been greater than the population in 1945.
Example Question #63 : Data Sufficiency Questions
The table below gives the population of the city of Renfrow for each of six census years.
Did Renfrow have a greater population in 1965 or 1975?
Statement 1: The population of Renfrow decreased every year from 1960 to 1970.
Statement 2: The population of Renfrow increased every year from 1970 to 1980.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
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.
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 insufficient to answer the question.
From the two statements together, it can only be surmised that the population in both 1965 and 1975 exceeded the 1970 population. No conclusions can be drawn about the size of the 1965 population relative to the size of the 1975 population.
Example Question #64 : Data Sufficiency Questions
The above is the menu at Monorail Sandwich Shop.
Julie and Janice are each ordering four sandwiches from the above menu. Julie works at Monorail and is entitled to a 25% employee discount; Janice does not work at Monorail.
Who will pay more for her sandwiches, ignoring tax?
Statement 1: Janice is ordering four veggie sandwiches.
Statement 2: Julie is ordering four beef sandwiches.
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.
DO NOT calculate how much Janice and Julie will pay! It's extra work that will slow you down on test day. We don't actually need to determine which of the two women will pay more - we only need to decide if it is possible to figure out who will pay more. Obviously neither statement alone tells us enough. Together, however, the two statements tell us exactly what Janice and Julie ordered. Therefore, using both statements, we have enough information to answer the question.
Example Question #1 : Dsq: Understanding Diagrams
Four candidates - two boys named Patrick and Quincy, and two girls named Rhonda and Sally - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
As can be seen in the figure above, which reflects the share of the vote each candidate won, there will be a runoff. Which two candidates will face each other?
Statement 1: Candidates A and B are both girls.
Statement 2: Candidate B and C are Rhonda and Patrick, respectively.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.
Statement 1 does just that by identifying them as Rhonda and Sally. It does not identify which one is which, but it is not necessary to know that.
Statement 2 identifies Rhonda as Candidate B, but only Patrick can be eliminated as Candidate A.
Example Question #71 : Data Sufficiency Questions
Four candidates - two boys named Mickey and Oswald, and two girls named Nora and Phyllis - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
As can be seen in the figure above, which reflects the share of the vote each candidate won, there will be a runoff. Which two candidates will face each other?
Statement 1: Nora is candidate B and Oswald is Candidate C.
Statement 2: Candidates A and C are boys.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.
Statement 1 alone establishes that Nora is Candidate B, making her one of the top two vote-getters. Oswald is not one of the top two, since he is Candidate C, but neither Mickey nor Phyllis can be eliminated as Candidate A.
Statement 2 alone established that one boy is Candidate A, one of the top two vote-getters. Since the other boy is Candidate C, then the other one of the top two, Candidate B, is a girl. However, it does not establish the identity of any of them.
Now, assume both statements to be true. By Statement 2, the top two are a boy and a girl. Statement 1 establishes that the girl is Nora. Since Statement 1 also establishes that Oswald is not the boy, the boy is Mickey, and it follows that Mickey and Nora will face each other in the runoff.
Example Question #73 : Data Sufficiency Questions
Four candidates - Anya, Barry, Carla, and David - ran for student body president. By the rules, the candidate who wins more than half the ballots cast wins the election outright; if no candidate wins more than half, there must be a runoff between the two top vote-getters. You may assume that no other names were written in.
As can be seen in the figure above, which reflects the share of the vote each candidate won, there will be a runoff. Which two candidates will face each other?
Statement 1: Neither Barry nor Carla is Candidate D.
Statement 2: Anya is candidate C.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.
Neither statement alone is sufficient to answer the question.
Assume Statement 1 alone. Barry and Carla could be Candidates A and B, respectively, in which case they would be the runoff candidates; also they could be Candidates B and C, respectively, in which case, Barry and one of the other two would be the runoff candidates.
Statement 2 alone only knocks Anya out of the runoff election; it leaves the other three as possible candidates.
Assume both statements to be true. Anya is Candidate C. Candidate D, being neither Barry nor Carla, is David. Therefore, Candidates A and B are Barry and Carla; it is unclear which is which, but it is irrelevant; either way, they are the top two vote-getters, and they will participate in the runoff.
Example Question #1 : Mixture Problems
Two hydrochloric acid solutions, one of concentration 40% and one of concentration 25%, are mixed together to make a solution of 35% concentration.
How much solution is made?
1) 200 ml of 40% solution is used
2) 100 ml of 25% solution is used
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
BOTH statements TOGETHER are 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.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.
Suppose we only know that 200 ml of the 40% solution is used. Then we can call 
So 100 ml of the 25% solution is used.
Similarly, if we only know that 100 ml of the 25% solution is used, then we can call 
So 200 ml of the 10% solution is used.
Either way, we get that
and 300 ml of solution is created.
The answer is that either statement is sufficient to answer the question.
Example Question #2 : Mixture Problems
A delivery truck is carrying two types of packages, green boxes and brown boxes. Green boxes weigh 10 lbs each, while brown boxes are 30 lbs each. At the weigh station, the driver notes that his load weighs exactly 400 lbs. How many green boxes does he have in his truck?
1. He is carrying exactly 20 boxes.
2. The driver never loads more brown boxes than green boxes.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
EACH statement ALONE is sufficient to answer the question asked
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Using statement 1, we can find that he has 10 green boxes and 10 brown. We solve mixture problems using 2 equations. If we let 
1) 
2)
Solving equation 1) for 
Subsituting for 
Simplifying we get 
Therefore, this answer would be 10 green boxes and 10 brown.
The second statement is irrelevant in finding our answer.
Example Question #2181 : Gmat Quantitative Reasoning
Mark, the barista at Moose Jaw Coffee, has to mix together two kinds of coffee beans, Chocolate Explosion and Cherry Cherry Delight, to produce a blend that costs $12 per pound.
How much of each coffee goes into the mixture?
Statement 1: The Chocolate Explosion coffee costs $10 per pound.
Statement 2: The Cherry Cherry Delight coffee costs $16 per pound.
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 insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements are true.
Let 
However, there is no further information we can use to set up a second equation, so there is insufficient information to answer the question.
Example Question #2182 : Gmat Quantitative Reasoning
Carl, the barista at Moose Jaw Coffee, has to mix together two kinds of coffee beans - Vanilla Heaven, which costs $10 a pound, and Mountain Goodness, which costs $15 a pound - to produce a blend that costs $12 a pound.
How many pounds of Vanilla Heaven coffee beans go into the mixture?
Statement 1: The mixture will include 30 pounds of Mountain Goodness beans.
Statement 2: The finished blend will weigh 75 pounds.
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 insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Let 
If we assume Statement 1 alone, then the total price of the Vanilla Dream coffee beans is $10 per pound times 
If we assume Statement 2 alone, the price of the Vanilla Dream beans is again 
From either equation we can solve for 
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