Free Quantitative Reasoning MCQs with Answers

411. The average height of 10 students is 155 cm. Later on it is discovered that while calculating the average, the reading of 157 cm was wrongly read as 147cm .The correct average is:

• A. 196
• B. 154
• C. 200
• D. 156

Explanation: A, B, C are incorrect as 156cm is the correct average height D is correct as Total height of 10 students = 10 x 155 = 1550 cm Since 157cm was incorrectly read as 147cm 1550 - 147 + 157 = 1560 1560/10 =156cm

412. How many minutes are there in 2h hours and 6m minutes?

• A. 60m+12m
• B. 120m+6m
• C. 60m+6m
• D. 120hm+60m

Explanation: A, C and D are incorrect as 2 hour 6 mins is equal to 120 mins+6 mins B is correct as 1 hour = 60 minutes 2 hour = 120 mins 120 + 6 mins is the answer

413. g(x)=kx3+3 For the function g defined above, k is a constant and g(-1)=5. What is the value of g(1) ?

• A. -3
• B. -1
• C. 1
• D. 3

Explanation: First step is to find k 5=k(-13)+3 5 - 3 = - 1k - 2 =kOption A) Putting A) equal to the function -3 = k (13) + 3 k= -6 This is a Wrong option Option B) Putting B) equal to the function -1= k (13) + 3 K = - 4 This option is also wrong Option C) Putting C) equal to the function 1=k(13) + 3 k= - 2 Gives correct value for k, this is the answer. Option D) Putting D) equal to the function 3= k(13) + 3 k=0 So the correct answer is C.

414. In 2005, 120 students at Lincoln High School had smartphones. By 2010, 345 students in the same school had smartphones. Which of the following best describes the annual rate of change in the number of smartphones students had from 2005 to 2010 at Lincoln High School?

• A. The average increase in the number of smart phones per year is 40
• B. The average increase in the number of smart phones per year is 45
• C. The average increase in the number of smart phones per year is 50
• D. The average increase in the number of smart phones per year is 55

Explanation: We have to find the increase in n.o of students per year with the change of 5 years Students having phone in 2005:120 Students having smartphones in 2010: 345=345 - 120 =225 =225/5 Increase for each year= 45 Hence, Option B is the correct answer.

415. y=2x+4 x-y=-1 Which ordered pair (x,y) satisfies the system of equations shown above?

• A. ( -2, -3)
• B. ( -3, -2)
• C. ( -1, 2)
• D. ( -2,0)

Explanation: Using simultaneous linear equation substituting x and y in the 1st equation Option A) Y - 2x =4 -3 - 2(- 2) =4 - 3 + 4=4 Option A is hence incorrect as it does not satisfy the equations. Option B) substituting x and y in the 1st equation Y - 2x=4 -2 - 2 ( -3)=4 -2 +6= 4 4 =4 Substituting option B in 2nd equation -3 - (-2)= - 1 - 3 +2= - 1 -1 = - 1 B is the answer Option C) Substituting option C in 2nd equation 2 - (-1) =- 1 As 3 is not equal to -1 this option is wrong Option D) Substituting option D in 2nd equation -2 - 0 =-1 - 2 is not equal to -1 This option is also incorrect

416. At the beginning of a trip, the tank of Chloe's car was filled with 12 gallons of gas. When she travels constantly on the highway 60 miles per hour, the car consumes 1 gallon of gas per 35 miles. If she traveled 5 hours and 15 minutes on the highway with a constant speed of 60 miles per hour, how many gallons of gas are left in the tank?

• A. 3
• B. 4
• C. 5
• D. 6

Explanation: For this to be solved we have to find the gallons of gas used If car travels 60 miles in one hour Car uses 1 gallon for 35 miles let's find the gallons it uses for 60 miles or in an hour 1 /35 x /60 ( cross multiplying) 60 *1 =35*x 12 /7=x Now multiply it with the hours of the journey Time of the journey : 5 hours and 15 minutes 15 minutes in hours :15/60 =¼Gallons used in the journey:5 ¼ * 12 /7 21/4 *12/7 252/28 =9 gallons Now add 9 to the options whichever adds up to 12 is the answer Option A) 3+9=12 Correct Option B) 9+4=13 Option C) 9+5=14 Option D) 6+9=15 None adds upto 12 except A so A is the answer.

417. A rock climber is climbing up a 450 feet high cliff. By 9:30 AM. the climber reached 90 feet up the cliff and by 11:00 AM he has reached 210 feet up the cliff. If he climbs with a constant speed, by what time will he reach the top of the cliff?

• A. 1:45 PM
• B. 2:00 PM
• C. 2:15 PM
• D. 2:30 PM

Explanation: Constant speed is equal distance covered in equal time periods So he will cover the rest of the distance by the same time intervals as before Distance covered : 210 ft As we have the time interval from 9: 30 to 11:00 A.M we will use the distance covered in this interval only in the ratio method Distance covered in interval 9 : 30 to 11:AM 210 - 90= 120 ft Distance remaining : 450 - 210=240 So using ratio method Ft./hrs 120/1.5=240/ x Cross multiplying =120 * x=1.5 * 240 x = 3 hrs 3 hrs is the time interval between 11 and the reaching time of the climber. So, Reaching time - option =3 hrs (converting in 24 hour clock before subtraction by adding 12 to the options) Option A) =12:00+ 1 : 45 =13 45 =13 45 - 11 = 2 hrs 45 mim Option gives wrong outcomes Option B) 12 :00 + 2 14 00 hrs 14 - 11 = 3 hrs Option is giving correct outcome Option C) 12:00 + 2 :15 14 :15 - 11= 3 hrs 15 min Option gives wrong outcomes Option D) 12:00 +2:30 =14:30 14 : 30 - 11 = 3 hrs 30 mins Option gives wrong outcomes

418. Tim has 140 paperback and hard cover copies in his book shelf. If the hard cover copies do not exceed one sixth the number of paperback copies, what is the minimum number of paperback copies in Tim's book shelf?

• A. 114
• B. 116
• C. 118
• D. 120

Explanation: Number of paperback copies = x Number of hardcover copies ≤ x/6. (Maximum Number of hardcover copies = x/6) Total number of books = 140 Therefore, we can write the equation: x + (x/6) = 140 Multiplying both sides by 6, we get: 6x + x = 840 7x = 840 x = 120 Therefore, the minimum number of paperback copies on Tim's bookshelf is 120.

419. The number of students in a geometry class is four fifths the number of students in a Spanish class. The total number of students in both classes does not exceed 54. What is the greatest possible number of students in the Spanish class?

• A. 30
• B. 32
• C. 34
• D. 36

Explanation: Number of students in the Spanish class=x Since the number of students in the geometry class is four fifths the number of students in the Spanish class, the number of students in the geometry class =(4/5)x. The total number of students in both classes does not exceed 54, so we can set up the following inequality: x + (4/5)x ≤ 54 Simplifying this inequality, we get: (9/5)x ≤ 54 Multiplying both sides by 5/9, we get: x ≤ 30 So the greatest possible number of students in the Spanish class is 30, which is option A.

420. At a sporting goods store, Jay paid $172 for a pair of shoes and a pair of pants. The pants cost less than two thirds of what the shoes cost. What is the minimum price of the shoes to the nearest dollar?

• A. 103
• B. 110
• C. 120
• D. 90

Explanation: Let x be the price of the shoes and y be the price of the pants. Then we have: x + y = 172 ...(1) y < (2/3)x ...(2) To find the minimum price of the shoes, we need to maximize the price of the pants. From equation (1), we get: y = 172 - x Substituting this value of y in equation (2), we get: 172 - x < (2/3)x Multiplying both sides by 3, we get: 516 - 3x < 2x Adding 3x to both sides, we get: 516 < 5x Dividing both sides by 5, we get: x > 103.2 Rounding up to the nearest dollar, we get: x > 103 Therefore, the minimum price of the shoes to the nearest dollar is $103. Answer: A) 103.