Quantitative Practice Questions - 3 | Practice Questions for GMAT PDF Download

A Fibonacci-style sequence starts with two numbers, with each successive number being the sum of the previous two. The second term is therefore the difference of the fourth and third terms, and the first term is the difference of the third and second.
Second term:  30 − 16 = 14 
First term:  16 − 14 = 2

The multiples of 3 between 29 and 50 are 30, 33, 36, 39, 42, 45, and 48 - therefore,  A  has seven elements total. 

The number of subsets in a set can be calculated by raising 2 to the power of the number of elements. Therefore, the answer to our question is  2⁷ = 128 .

Simplify both sides of the equation as much as possible, and solve for  x  in the equation in terms of  N :

x  has exactly one solution unless the denominator is 0 - that is,  N = 2 . We make sure that this value renders no solution by substituting:

The equation has no solution, and  N = 2  is the correct answer.

Solve for  x  in the first equation:

Substitute into the second equation:

Solve for  x .
2x + 3(4) = 26 
2x + 12 = 26 
2x = 14 
x = 7

This can be seen, without loss of generality, as choosing each officer in turn.
There are 30 ways of choosing the president; there are then 29 ways of choosing the vice-president, and 28 ways of choosing the secretary-treasurer. Then 3 Student Senate representatives are chosen from the remaining 27 students; this is a combination of 3 elements from 27 - that is,  C₃²⁷ . By the multiplication principle, the number of possible selections of the officers is:

N = 71,253,000

The average is found by calculating the total payroll and then dividing by the total number of employees.

= 

= 

= $ 55,000

Think of this as a rate problem, with rate being measured in "tanks per minute".
Work = rate × time 
The pipes can fill the tank up at rates of 1/60 ,1/80 , and 1/50  tanks per minute, respectively. 
In the time  t  it takes to fill the tank, the three pipes fill up  1/60t  of the tank,  1/80t  of the tank, and  1/50t  of the tank, respectively. Add the amounts of work done by the three tanks to get the total amount of work - one job.

Let money Jack has be X.
Twice the money = 2X
Total money for 3 hamburgers = 3 x 0.96 = $2.88
Total money for 2 milk shakes = 2 x 1.28 = $2.56
2X = 2.88 + 2.56 = $5.44
X = 5.44/2 = $2.72

Answer C...

(90 -8(20:4))/(1/2)
= (90-8(5))*2
= (90- 40)*2
= 50*2
= 100

The distance in yards between points O and P is 10

The child creates a trapezoid with her walking pattern. The trapezoid can be divided into a rectangle and a right triangle

1) Find shape created by walking pattern. It will contain right angles (with compass points, "due [any direction]" = 90 degrees)

She walks 10 yards due north from point O to point A: OA = 10

Then 6 yards due east from A to B, which means a right angle at A. AB = 6

Then 2 yards due south from B to P. Another right angle. BP = 2

Connect P to O. She has created a trapezoid with her travel

2) Divide the shape into other shapes where distance between start and finish is easy to calculate

Draw a line from P, PX on diagram, that is perpendicular to OA
The new line divides trapezoid into two new shapes. Upper region is a rectangle. Lower region is right triangle

Rectangle has length = 6, width = 2

The rectangle's width, BP = AX = 2, divides original OA = 10 into two lengths AX and OX:
(OA - AX) = OX
(10 - 2) = 8 = OX

Looking at leg lengths PX and OX: the bottom portion is a 3-4-5 right triangle

3) Find distance between begin and end point

Find length of hypotenuse OP
Rule: If a right triangle has two legs in ratio 3x:4x, it is a 3x-4x-5x triangle and the hypotenuse = 5x

Leg PX = 6
Leg OX = (10 - 2) = 8

(3x: 4x: 5x) = (6: 8: 10)*

Distance between points O and P, in yards: 10

Answer (E)

We find the original rate, which is m meters per every s seconds, or m/s meters per second.

Since the number of seconds in a minute is 60, while we don't know how many seconds s is, we do know that to convert the rate in seconds to the rate in minutes we multiply by 60.
So, the rate per minute is 60m/s.
So, in x minutes, the cyclist will travel x * 60m/s = 60xm/s
The correct answer is E.

Alternative Method:
The greater m is, the further the cyclist will travel in a second or in x minutes. So m goes on top of the fraction.
We have m/ .
The greater s is, the slower the cyclist goes and the fewer meters traveled, because the greater s is the fewer meters the cyclist goes in 1 second. So, we put s on the bottom of the fraction.

We have m/s.
Since minutes have 60 seconds, to convert from rate per second to rate per minute, multiply by 60.

We have 60m/s.
The greater x is, the greater the number of meters traveled. So, put x on top of the fraction.
Final answer 60xm/s.

The correct answer is E.

Let's use the complement: P(Event A happening) = 1 - P(Event A not happening)

Given: P(person wins) =15/3000
So, P(person does NOT win)
Simplify to get: P(person does NOT win)
Rewrite with common denominator to get: P(person does NOT win)

Answer: D

The sales representative has two options: 1) A-E-C-F-A and 2) A-E-F-C-A. Now let’s compare the costs of these two options:

Option 1: A-E-C-F-A

From A to E the cost is 7 dollars. From E to C it’s 2 dollars. From C to F it’s 4 dollars. From F to A it’s 3 dollars. The total spent is 16 dollars.

Option 2: A-E-F-C-A

From A to E the cost is 7 dollars. From E to F it’s 6 dollars. From F to C it’s 4 dollars. From C to A it’s 3 dollars. The total spend is 20 dollars.

We see that option 1 is cheaper, and the cost is 16 dollars.

As n is odd, 2020n needs to divide without any remainders and will give us the median number. The only answer choices which divide 2020 without a remainder are B. 5 & D. 101.

Choice D. will not work. The median will be 2020/101=20 with 50 integers on either side. This means that the sequence will include zero and negative numbers, while we are told that the sum of n consecutive positive integers = 2020. Therefore, the answer has to be B.

To double check: 2020/5=404. With two numbers on either side, the sequence will be 402,403,404,405,406
Adding those numbers will give 2020.

Distance travelled before 1st rebound = 36
Distance travelled by ball from 1st rebound to 2nd rebound 

Distance travelled by ball from 2nd rebound to 3rd rebound
Distance travelled by ball from 3rd rebound to 4th rebound
and so on [ Distance travelled between 2 subsequent rebounds are in GP after the 1st rebound]
Sum of infinite GP = a/1-r. where a is first term and r is common ratio
a=24 and r=1/3
Total distance travelled

From 12 flavours, one flavour can be selected in = 12 ways
From 10 candies, one candy can be selected in = 10 ways
From 8 toppings, one topping can be selected in = 8 ways
From 5 nuts, one nut can be selected in = 5 ways
Total ways to order with/without cream = 2 ways
Total Possible combinations = 12*10*8*5*2 = 120*40*2 = 9600
Answer: Option A

The x = 3 and x = 4 are the critical values to consider when we evaluate the absolute value expressions. According to the critical values, we have the following cases.

Case 1: x < 3
|x – 3| + |x – 4| < 2
(-x + 3) + (-x + 4) < 2
-2x + 7 < 2
5 < 2x
2.5 < x => 2.5 < x < 3 [We have to combine the solution with the constraint x < 3.]

Case 2: 3 ≤ x < 4
|x – 3| + |x – 4| < 2
(x – 3) + (-x + 4) < 2
1 < 2 => 3 ≤ x < 4 [Although the inequality 1 < 2 is true for all x, we have to consider the constraint 3 ≤ x < 4 as well.]

Case 3: 4 ≤ x
|x – 3| + |x – 4| < 2
(x – 3) + (x – 4) < 2
2x – 7 < 2
2x < 9
x < 4.5 => 4 ≤ x < 4.5 [We have to combine the solution with the constraint 4 ≤ x.]

Now, we have to join the three intervals we found in the three cases:
2.5 < x < 3
3 ≤ x < 4
4 ≤ x < 4.5

So, we have:
2.5 < x < 4.5

Let positive number be 6x.
Wrong = x
Right = 36x
Error = 35x
Error% = (Error/Right)*100 = (35x/36x)*100 = 97% (B)

Total Calculators = x
Cost per calculator = 300/x
Calculators sold =  x - 2
Selling price per calculator 
Total amount received  
Solving,
x² − 26x − 120 = 0
x = 30

To find the number of movies that are action-drama-comedies, we use the principle of inclusion-exclusion.

Given:

• Total movies (T) = 38
• Action (A) = 10
• Drama (D) = 20
• Comedy (C) = 18
• Action and Drama (A ∩ D) = 5
• Action and Comedy (A ∩ C) = 3
• Drama and Comedy (D ∩ C) = 4

We need to find the number of movies that are in all three categories (A ∩ D ∩ C).
Using the principle of inclusion-exclusion:
∣A ∪ D ∪ C∣ = ∣A∣ + ∣D∣ + ∣C∣ − ∣A ∩  D∣ − ∣A ∩  C ∣ − ∣D ∩ C∣ + ∣A ∩ D ∩ C∣
Substitute the given values:
∣38 = 10 + 20 + 18 − 5 − 3 − 4 + ∣A ∩ D ∩ C∣
Simplify:
∣38 = 36 + ∣A ∩ D ∩ C∣
Solve for 
∣A ∩ D ∩ C∣:
∣A ∩ D ∩ C∣ = 38 − 36
∣A ∩ D ∩ C∣ = 2
Thus, the number of action-drama-comedies is: 2

We'll break our complex calculation (x99) into small, easy bits (x100 - x1)
This is a Precise approach.
100*X would be 81.818181818181 with infinite 81 after the decimal point.
That is, 100*X = 81.(81)
So 99*X 100*X - X = 81.(81) - 0.(81) = 81
(C) is our answer.