Quantitative Practice Questions - 5 | Mock Test series for GMAT Classic Edition PDF Download

It can already be ascertained from the figure that  y = 8  , since the left portion is a rectangle, so Statement 2 is redundant.
We can already calculate the area of the rectangular portion of the arrow:
16 x 8 = 128 
All this is left is to calculate the area of the triangular portion. If we know Statement 1, we can take half the product of the height, which is 13, and the base, which is
3 + 8 + 3 = 14 :
1/2 x 13 x 14 = 91 
Add these numbers to get the area of the arrow:   128 + 91 = 219

The proportions of corresponding sides of similar triangles must be equal.
Therefore,  8/12 = 10/x .  8x = 120; x = 15 .

The longest side is opposite the largest angle for all triangles.
(1) Substituting 3 for  k  means that  AB = 3  and  BC = 5 . But the value of  m  given for side  AC  is still unknown  →   NOT sufficient.
(2) Since  k + 3 > k , the longest side must be either  k + 3  or  m . So, knowing whether  m > k + 3  is sufficient.
If  m = k + 4 , knowing that   k + 4> k + 3  , 
then  m > k + 3  →  SUFFICIENT.

First, we need to solve for x from the first equation in order to calculate the second quadratic function. To solve for x, we need to subtract four on each side of the equation, then we will get
5x = 15
The answer for x would be 15/5, which is 3.
So now we can calculate the function by plugging in x = 3.
3² = 9, and 9  x  4 = 36.
36 - 5 = 31

Let x = length of the short plank and x + 30 = length of the long plank.
x + x + 30 = 70 is the length of the pre-cut board, or combined length of both planks
2x + 30 = 70
2x = 40
x = 20

Then,

Let's look at  f,g,and h  and see if any of them are functions.
1.  f  = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of  X  because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2.  g  = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of  X  because it contains no ordered pair with first coordinate 2.  Because the set  X  = {1, 2, 3, 4}, we need an ordered pair of the form (2,  ) .
3.  h  = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function.  Even though two of the ordered pairs have the same number (2) as the first coordinate,  h  is still a function of  X  because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.

−14 + 6b + 7 − 2b = 1 + 5b 
−7 + 4b = 1 + 5b
4b − 5b = 1 + 7
−b = 8
b = −8

Solve the first equation to get  y = 27−4x 
Substitute that into the second equation and get
2x − 3 x (27 − 4x) =  −11 
Solve the equation to get  x = 5 , then substitute that into the first equation to get
y = 7.
Plugging those two values into  x² − y , gives
5² − 7 = 18

Let's combine like terms.
2x + 3y − 3 = 2x + 3y 
−3 = 0 , so the equation has no solution.

From the first statement, we can calculate the number of cupcakes Cassie can decorate in 150 minutes. From there, we can calculate the rate at which Derek decorates. Therefore, Statement 1 alone is sufficient to answer the question.
The second statement gives the rate at which Derek decorates cupcakes. Therefore, Statement 2 alone is also sufficient to answer the question.

Statement 1 alone does not tell us enough about the speed of train B to answer the question. Statement 2 alone does not tell us about the rates of either individual train, so it is also not sufficient by itself to answer the question.
But can we figure out the answer using both pieces of information? Yes, we can! If we know that the trains meet at 6:40, then their combined rate of travel is 60 total miles in 40 minutes. Statement 1 says that Train A travels twice as fast as Train B, so we can determine the distances covered by the two trains in those 40 minutes. From there, we can find rates for both trains and then answer the question. Thus, both statements together are sufficient to answer the question, but neither statement alone is sufficient.
Note: We didn't actually answer the question of Train B's arrival time. For data sufficiency questions, don't waste time trying to find the specific answer. All that is necessary is determining whether or not it is POSSIBLE to answer the question with the information given.

124 + 87 + 87 + 98 + 75 = 471  students voted, so 236 votes were necessary to win a simple majority. 
From Statement 1 alone it can be determined that Crane won at least  124 + 87 = 211  votes (his own initial votes plus all of the votes that previously went to Jones), and Trask won at least 98 (his own initial votes).
From Statement 2 alone, it can be determined that Crane won at least 124 + 1/3 × 75 = 124 + 25 = 149  (his own initial votes plus one-third of the votes that previously went to Wells), and Trask won at least  98 + 2/3 × 75 = 98 + 50 = 148  votes (his own initial votes plus two-thirds of the votes that previously went to Wells). 
Neither statement alone will prove a majority vote. From Statement 1 and 2 together, however, it is known that Crane won at least his own initial votes, all of Jones' votes, and one-third of Wells' votes - a minimum of 
124 + 87 + 1/3 × 75 = 124 + 87 + 25 = 236  votes. Therefore Crane is the winner, and both statements are needed to prove this.

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.

Assume both statements are true.
Let  A  be the amount of Chocolate Explosion and  B  be the amount of Cherry Cherry Delight. Then the price of the Chocolate and Cherry coffees will be  10A  dollars and 16B  dollars, respectively. The total price of the beans is  12(A + B) , so we can set up the equation:
10A + 16B = 12(A + B) 
However, there is no further information we can use to set up a second equation, so there is insufficient information to answer the question.

Let  V  be the number of pounds of Vanilla Heaven coffee beans in the mixture.
If we assume Statement 1 alone, then the total price of the Vanilla Dream coffee beans is $10 per pound times  V  pounds, or  $10V . Similarly, the total price of the Mountain Goodness beans is  $15 × 30 = $450 , and the overall price of the beans in the mixture is  $12(V + 30) . Add these together to get the equatios
10V + 450 = 12(V + 30)
If we assume Statement 2 alone, the price of the Vanilla Dream beans is again  $10V . However, the price of the Mountain Goodness beans is  $15(75 − V)  and the overall price of the beans is  $12 × 75=900 , so we can set up this equation
10V + 15(75 − V) = 900 
From either equation we can solve for  V  and get the answer to the question. 

A  20%  discount implies that the discounted price is  80%  of the original price; a  5%  tax means that  105%  of the price will have to be paid. Let  N  be the original price.
We can now write an equation and solve for  N :
1.05⋅0.80⋅N = $444.36 
0.84⋅N = $444.36 
0.84⋅N ÷ 0.84 = $444.36 ÷ 0.84 
N = $529.00

Even with both statements,  AE  cannot be determined because the length of  BD  is missing.
For example, we can have  AB = DE = 8  and  BD = 16 , making  AE = 32 ; or,
we can have   AB = DE = 10  and  BD = 14 , making  AE = 34 . Neither scenario violates the conditions given.

By definition, if  ∠1  and  ∠2  are supplementary angles, then  m ∠1 + m∠2=180 .
If Statement 1 is assumed and  m ∠1 < 100 , then  m ∠2 > 80 . This does not answer our question, since, for example, it is possible that  m ∠1 = 91  and  m ∠2 = 89 , or vice versa.
If Statement 2 is assumed, then  m∠2>90 , and subsequently,  m ∠1 <90 ; by transitivity,  m ∠2 > m ∠ 1 .

Complementary angles have degree measures that total  90^∘ , so the measure of an angle complementary to a  48^∘  angle would have measure  (90−48)^∘ = 42^∘ . If Statement 1 is assumed, then  m∠1 = 42^∘ .
Statement 2 gives no useful information. Adjacent angles do not have any numerical relationship; they simply share a ray and a vertex.

Any two consecutive angles of a parallelogram are supplementary, so if one angle has measure  90^∘ , all angles can be proven to have measure  90^∘ . This is the definition of a rectangle. Statement 1 therefore proves the parallelogram to be a rectangle.
Also, a parallelogram is a rectangle if and only if its diagonals are congruent, which is what Statement 2 asserts. 
From either statement, it follows that parallelogram  ABCD  is a rectangle.

To prove that Parallelogram  ABCD  is also a rectangle, we need to prove that any one of its angles is a right angle.
If we assume Statement 1 alone, that  m∠1 = 90^∘ , then, since  ∠1  and  ∠BCD  form a linear pair,  ∠BCD  is right. 

If we assume Statement 2 alone, that  (AB)² +( BC)² = (AC)² , it follows from the converse of the Pythagorean Theorem that  ΔABC  is a right triangle with right angle ∠B .
Either way, we have proved that the parallelogram is a rectangle.

In order to find the median, the set needs to be written in numerical order:
6,7,13,29,41,67 
Since  13  and  29  are both the middle numbers, taking their average will give the median of the set.

V = l x w x h 
New V = 2l x 2w x 2h
New V = 8 x l x w x h
Then, the new volume is 8 times the old volume.

The Celsius-to-Fahrenheit conversion formula is:

Substitute 45 for  C :

The answer is  113^∘ F .

Remember the simple interest formula, where I is interest, p is principle, r is rate, and t is time:

I = p x r x t

t = 10years

Break even profit is  0 . Plug this value into the equation to solve for the number of units:
P(x) = 500x − 10,000 
0 = 500x − 10,000 
10,000 = 500x
x = 20

There are 12 marbles total. The probability of picking a blue marble first is  8/12 = 2/3 .
The probability of then picking a red marble out of the 11 remaining marbles is  4/11 .
Therefore, the probability is  2/3 × 4/11 = 8 / 33 .

The boss orders seven sandwiches, so two of the sodas will be free. Therefore, she will pay for three beef sandwiches, two turkey sandwiches, two ham sandwiches, and five large sodas. Their total price:
$5.89 × 3 + $5.49 × 2 + $5.19 × 2 + $1.99 × 5 
= $17.67 + $10.98 + $10.38 + $9.95 
= $48.98 
The change from a $100 bill is
$100.00 − $48.98 = $51.02 .

Jim arrived at the common destination in 70 minutes, or  7 / 6  hours. His average speed was 54 miles per hour, so their workplace is 
7 / 6 x 54 = 63  miles away from Jim and Julia's home.
Julia traveled those 63 miles in 80 minutes, or  4 / 3  hours, so her average speed was

or, rounded, 47 miles per hour.

Multiply the diameter of the smaller circle by 12 to convert it to inches - this will be  12k , which is also the radius of the larger circle. The radius of the smaller circle will be half this, or  6k .
Using the area formula for a circle  A = πr² , we can substitute these quantities for  r  and subtract the area of the smaller circle from that of the larger:
A₁ = πr² = π(12k)² = 144πk2  square inches
A₂ = πr²= π(6k)² = 36πk²  square inches
A = A₁ − A₂ = 144πk² − 36πk² = 108πk²  square inches

4x + 3y = 19 
5x + 4y = 23 
Subtract the first equation from the second:
x + y = 4 ⇒ y = 4 − x 
Now we can substitute this into either equation. We'll plug it into the first equation here:
4x + 3(4 − x) = 19 ⇒ 4x + 12 − 3x = 19 ⇒ x + 12 = 19 
Thus we get  x = 7  and  y = 4 − (7) = −3 .
Therefore  x  is positive and  y  is negative.

We can use the fact that  (xa)b = x^{a ∗ b}  to see that  (x²)³ = x⁶.  
Since  x2 = 5 , we have
(x²)³ = (x²)(x²)(x²) = (5)(5)(5) = 125 .

Since 0.375 is not in the range  [1,10) , we adjust the answer as follows:

= 3.75 × 10⁷

(f∘g)(4) = f(g(4))  = f(4⋅4 + 7) = f(23) = 3⋅23 − 1 = 68  
(g∘f)(−4) = g(f(−4)) = g(2⋅(−4) + 1) = g(−7) = 3(−7) − 1 = −22
(f∘g)(4) − (g∘f)(−4) = 68−(−22) = 90

First, evaluate  3 ‡ 2  by substituting  a = 3,b = 2 :
a ‡ b = 2ab − a − b 
3 ‡ 2 = 2 x 3 x 2 − 3 − 2 = 12 − 3 − 2 = 7 
Second, evaluate  4‡7  in the same way.
a ‡ b = 2ab − a − b 
4 ‡ 7 = 2⋅4⋅7 − 4 − 7 = 56 − 4 − 7 = 45

g(x) = ⌊x + 0.5⌋ − ⌈x − 0.5⌉ 
g(3.9) = ⌊3.9 + 0.5⌋ − ⌈3.9 − 0.5⌉
g(3.9) = ⌊4.4⌋ − ⌈3.4⌉
g(3.9) = 4 − 4 = 0

A function is odd if and only if  f(−x) = −f(x)  for each value of  x  in the domain; it is even if and only if  f(−x) = f(x)  for each value of  x  in the domain. To disprove a function is odd or even, we need only find one value of  x  for which the appropriate statement fails to hold. 
Consider  x = 1 :
f(x) = x³ − 2 
f(1) = 1³ − 2 = 1−2 = −1
f(x) = x³ − 2 
f(−1) = (−1)³ − 2 = −1 − 2 = −3 
f(−1) ≠ −f(1) , so  f  is not an odd function;  f(−1) ≠ f(1) , so  f  is not an even function.

(f∘g)(−4) = f(g(−4)) 
First we evaluate g(−4). Since the parameter is negative, we use the first half of the definition of g:
g(x) = 2x − 5
g(−4) = 2(−4) − 5 = −8 − 5 = −13
f(g(−4)) = f(−13); since the parameter here is again negative, we use the first half of the definition of f:
f(−13) = 1
Therefore, (f∘g)(−4) = 1.