Is there a point of intersection between the circle (X^{2} + Y^{2} = 4)and the Line ( Y = aX + b) ?
(1) a = b^{2}.
(2) The line intersects the Xaxis at (40, 0).
The best answer is C.
From statement (1) we learn that the equation of the line can be written as Y = b^{2}X + b.
From statement (2) we learn that the line goes threw the point (40, 0), from that we can find the equation of the line by posting the coordinate in the equation: 0 = b^{2}40 + b.
There is no need to solve it, both statements are sufficient to solve the problem.
Zigfield bought his car using M% of his bank savings. He also bought a house that costs 4 times the price of the car. What is the price of the house?
(1) M = 12.
(2) The price of the car and the house was $140,000.
Price of car, c = (M/100)*bank savings
Price of house, h= 4c
(1) M=12,Bank savings not given . Hence insufficient.
(2) c+ h= 140000
c+ 4c = 140000, which gives the value of c and hence, price of house could be found. Sufficient.
Eddy gave Q% of the money he earned last year to his first wife Sandra, W% of the money he earned last year went to his second wife Tawana. How much money did Eddy earn this year?
(1) Q = 20, W = 2Q.
(2) All the money Eddy earned last year went to his two wives
The best answer is E.
From statement (1) and (2) taken together we know how much Eddy earned last year but we know
Nothing about this year, we have no connections between them. Therefore, both statements are not sufficient to answer the question.
Of the 10,000 people that went to the statefair, how many men ate at the fair?
(1) The percentage of men who ate at the statefair was twice as those who didn’t eat.
(2) 3,500 women ate at the statefair.
The best answer is E.
From statement (1) we know the ratio between the men who ate to those who didn’t, but we don’t know how many men were at the fair. Statement (2) doesn’t reveal the number of woman that went to the fair, only the number of woman that ate there.
Therefore, more data is needed to answer the question.
Out of the 100 kids that went to the party, how many girls danced there?
(1) 25 girls don’t like to dance and so they didn’t.
(2) The number of boys that danced is twice the number that didn’t dance.
The best answer is E.
From statement (1) we know that 25 out of X girls didn’t dance. We need to know how many girls in total were in the party. Statement (2) doesn’t tell us anything about the number of boys or girls that went to the party but only the ratio between those who danced to those who didn’t.
Therefore, more sufficient data is needed to solve the problem.
990 people went to the GMAT exam, how many boys didn’t pass the test?
(1) 321 girls didn’t pass the test, which is the number of boys that did.
(2) One fifth of the people that went to the GMAT exam were boys who eventually didn’tpass the test.
The best answer is B.
Statement (1) gives us information about the number of boys that passed the test but no useful information about the other part of the boys.
Statement (2) by itself gives us the answer to the question (1/5 x 990).
Therefore, the answer is B.
What is the area of the rectangle with the following coordinates: (x, y), (10, y), (10, 5), (x, 5)?
The best answer is E.
First of all, draw the rectangle with the given coordinates.
You can see that only one side of the rectangle is given and not the second, therefore there isn’t enough data to answer the question.
What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
The best answer is D.
First of all, draw the square with the given coordinates.
We know only one of the square’s sides but it’s enough because it is a square and both sides are equal. The area, therefore, is (15 x 15 = 225).
Is the largest of 7 consecutive numbers odd?
(1) The product of the seven numbers is zero.
(2) The sum of the seven numbers is zero.
The best answer is B.
From statement (1) we learn that there is a 0 among the seven numbers, yet the largest number can be odd or even. (0, 1, 2, 3, 4, 5, 6 or 1, 0, 1, 2, 3, 4, 5).
From statement (2) we know that the numbers are located symmetrically around the zero, therefore the largest number is even.
Is the sum of X consecutive numbers zero?
(1) The largest number is 5.
(2) The median number is zero.
The best answer is B.
Statement (1) is not sufficient because the series of numbers is not blocked from the smaller numbers.
Statement (2) is sufficient by itself because we know that if the median number is 0, then the sum of the numbers must be even.
If X and Y are positive integers, what is the ratio between Y and X?
(1) XY = 150.
(2) Y is 22% of X.
The best answer is B.
The question actually asks what is Y/X or X/Y.
Statement (1) is not sufficient because from the product of the two variables we can’t make out the ratio. Statement (2) is sufficient by itself, Y = 22X/100 à Y/X = 11/50.
Therefore the answer is B
if x and y are positive integers (x>y), what is the units’ digit of (10^{x} – 9^{y})^{2} ?
The best answer is E.
Try some numbers, x=2, y=1.
(10^{6} – 9^{2})^{2} = 81. And it will work with any given number under the conditions given.
What is the value of A + B ?
(1) A = 8 – B.
(2) (A + B)^{2} – 64 = 0.
The best answer is A.
From statement (1) we know right away that A + B = 8.
From statement (2) we don’t know if A + B = 8 or –8.
Therefore only statement one is sufficient to answer the question.
What is the value of (A – B)?
(1) A = 8 – B.
(2) A^{2} – B^{2} – 64 = 0.
The best answer is C.
From statement (1) we know the value of A + B.
From statement (2) we know the value of A^{2} – B^{2} = (A – B)(A + B) à (A – B)8 = 64
→ the answer is equal to 8, therefore both statements are needed on order to answer the question.
What is the value of (A + B) ?
(1) B = 12 – 3B.
(2) A^{2} + 4A – 16 = 0.
The best answer is E.
From statement (1) we can find the exact value of B.
From statement (2), we can find two answers for variable A, therefore the answer is not unequivocally and both statements taken together are not enough, more sufficient data is needed.
What is the value of (X^{2} + Y^{2})?
(1) (X – Y)^{2} = 36.
(2) (X + Y)^{2} = 48.
The best answer is C.
Statement (1) can be written as X^{2} – 2XY +Y^{2} = 36.
Statement (2) can be written as X^{2} + 2XY +Y^{2} = 48.
Adding both equations will give: 2X^{2} + 2Y^{2} = 84 à X^{2} + Y^{2} = 42.
Therefore, both statements are needed in order to solve the question.
There are X dogs in the dog hound, each dog eats Y Kg of food every day. What percent of the total food weight does each dog eat?
(1) If there were 3 dogs less then each dog could eat 1.2 Kg more than he is does now.
(2) If there were half the dogs, each dog could eat 3 Kg more than he is does now.
The best answer is C.
In order to know the answer we need two equations:
From statement (1) we can write: XY = (X – 3)(Y + 1.2).
From statement (2) we can write: XY = (X/2)(Y + 3).
You don’t need to solve the equations, the answer is C, both equations are needed to solve the question
If (R, R^{2} + 1) is the (x, y) coordinate of a point located on the line: Y = 2X + 4, what Can be the value of the parameter R?
The best answer is D.
If the point is on the line then you can plug the coordinate into the equation.
Y = 2X + 4 → R^{2}+1 = 2R + 4 → R= 3 or R= 1.
A(5, w^{3}) is the (x, y) coordinate of point located on the parabola Y = X^{2} + 2.
What is the value of w?
The best answer is A.
Plug into the equation the coordinate to get: w^{3} = 5^{2} + 2 = 27 → w = 3
If x and y are positive integers, is 5^{x}(1/4)^{y} < 1 ?
(1) y = 3x.
(2) x = 2.
The best answer is A.
Use statement (1) to write: 5^{x}(1/4)^{3x }= (5/64)^{x}. Because x is a positive integer only, the expression will always be smaller than 1. This statement alone provides us the answer.
Use statement (2) to write: 5^{2}(1/4)^{y} à the answer here is dependent on y, a different combinations of the variable y will give different results.
Therefore the answer is A.
If x and y are integers, is 3^{x}(0.5)^{y} < 1 ?
(1) y = 2x.
(2) x = 8.
The best answer is C.
Use statement (1) to write the expression: 3^{x}(0.5)^{2x} = (0.75)^{x} à the value of this expression can be either smaller or larger than 1, if x was only a positive integer the answer would be distinct.
Use statement (2) alone to write the expression: 3^{8}(0.5)^{y} à this expression is either bigger or smaller than 1.
Use both statements together: (0.75)^{8} < 1. Therefore both statements are needed to answer the question
A and B are integers, is (0.5)^{AB} > 1 ?
(1) A is positive integer and B is negative integer.
(2) A and B are two consecutive numbers.
The best answer is D.
From statement (1) we know that one is positive and the other is negative, therefore their product is negative. (0.5)^{negative} = a number bigger than 1. This statement is sufficient to answer the question.
From statement (2) we know the answer also. This is a tricky part.
Try all the options: (2 and –1), (1 and 0), (0 and 1), (1 and 2).
All of these options give out AB that is positive or equal to zero, in both cases (0.5)^{AB} will be either smaller than 1 or equal to 1 but never bigger. Therefore each statement by itself is sufficient
A jar of 264 marbles is divided equally among a group of marbleplayers. If 2 people join the group, each one would receive 1 marble less. How many people are there in the group today?
The best answer is C.
You can backsolve it. 264 marbles divided by 22 (answer C) is 12 marbles per person.
If two people join, there will be 24 people, 264/24 is 11, which is 1 marble less.
A basket of 1430 apples is divided equally among a group of apple lovers. If 45 people join the group, each apple lover would receive 9 apples less. How many apples did each person get before 45 people joined the feast?
The best answer is C.
Try to backsolve the problem. (1430/22 = 65) people, if 45 came then there are 110 people.
(1430/110 = 13) apples, which is 9 apples less per person
A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 28 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?
The best answer is A.
You can use the answers to backsolve the question or you could write the equations.
Take 392 pastry goods and divide them by 28 customers, each one will receive 14 products.
If there were 49 customers, each one would receive (392/49 = 8), which is 6 less.
In the equation 4Y 3kX = 18, k is a constant and Y equals 42 when X equals 12. What is the approximate value of X when Y equals 36?
The best answer is B.
First, find the constant k. Plug in the numbers for X and Y, to receive 4 x 42 – 3k x 12 = 18 → k = (18 – 168)/36 = 25/6.
Now, plug in the value of Y to receive: 4 x 36 – 3kX = 18 → after a little math, X is equal to 10.08, therefore the approximate answer is 10.
In the equation (X + Y = k), k is a constant and X equals 13 when Y equals 23.5. What can be the value of X^{2} when Y^{2 }is equal to 36?
The best answer is E.
First, find the constant k. Plug in the numbers to get k = 13 + 23.5 = 36.5.
Now, Y^{2} = 36 → Y = 6 or (6). Plug both numbers to get X = 30.5 or X = 42.5.
The best answer is E, (30.5)^{2} = 930.25.
Did the owner of the garage sale made more than $130 last Saturday?
(1) There were 15 products at the garage sale, each one cost $25.
(2) All the products were sold.
The best answer is C.
Statement (1) tells us how many products were in the sale and how much did each cost.
Statement (2) tells us that all the products were sold, therefore the owner made 15 x $25 = $375.
Both statements are required to answer the question
What is the total amount of Jellybeans that Benjamin ate last week?
(1) This week Benjamin ate 20% more Jellybeans than two weeks ago.
(2) Two weeks ago Benjamin ate 65 Jellybeans.
The best answer is E.
Statement (1) gives us information about this week and two weeks ago, statement (2) also doesn’t give us any sufficient data on last week, but on two weeks ago.
Therefore, more sufficient data is required.
How many hamburgers did “Wacdonalds” sell last year?
(1) Two years ago “Wacdonalds” sold 422,000,000 hamburgers.
(2) The average amount of hamburgers sold by “Wacdonalds” each year is 5 million.
The best answer is E.
Statement (1) gives us data on the sales of two years ago.
Statement (2) gives us data on the average amount of sales each year.
We can’t assume that the sales two years ago + last years sales divided by two is the average amount of sales, therefore more sufficient data is needed to answer the question.
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