# PSAT Problem Solving Practice Test 4

Question – 1

1. Which of the following is the cube of 3/25? Indicate the correct option.

• A. 0.0144

• B. 0.001728

• C. 0.0001728

• D. 0.00001728

• E. 0.00144

• Answer Explanation:(3/25)^3= 0.12^3=0.001728Option B is correct.

Question – 2

2. What part of the share of Amanda of 1/15 does Peter have if Peter has 3/40? Indicate the correct option.

• A. 120/3

• B. 3/120

• C. 1/45

• D. 9/8

• E. 8/9

• Answer Explanation:Let the required number be x1/15*x=3/40x=3/40*15= 45/40 = 9/8Peter has 9/8 part of Amanda’s share.Option D is true.

Question – 3

3. The average of n numbers is n. If each number is multiplied by n, which of the following will be the new average? Indicate the correct option.(Note:[x^2=x*x] )

• A. 2n

• B. n

• C. n^3

• D. n^2

• E. n/2

• Answer Explanation:Average = Sum of observations/number of observationsn = Sum/nSum = n*nEach observation is multiplied by n. Hence, the sum of the observations is equal to the old sum multiplied by n.New sum = Old sum*n = n*n*nAverage = n*n*n/n=n^2Option D is true.

Question – 4

4. One apple has the same nutrients as 4 biscuits and 3 biscuits have the same nutritional value as 4 bananas. What is the ratio of the number of apples to the number of bananas having the same nutrients? Indicate the correct option.

• A. 3:16

• B. 16:3

• C. 4:3

• D. 3:4

• E. 12:1

• Answer Explanation:1 apple = 4 biscuits3 biscuits = 4 bananas1 apple = 4 biscuits = 4*4/3 bananas = 16/3 bananas1 apple = 16/3 bananas3 apples = 16 bananasRequired ratio = 3:16Option A is true.

Question – 5

5. Peter bought oranges at \$5 per dozen. He sold half of his purchase at twice his investment and half of his purchase was rotten and could not be sold. How much was his profit percent? Indicate the correct option.

• A. 100%

• B. 50%

• C. 25%

• D. 10%

• E. 200%

• Answer Explanation:Let his purchase be of 10 dozen.His investment = \$5*10=\$50He sold 5 dozen at \$50*2=\$100He could not sell 5 dozen.Profit percent = (100-50)/50*100= 100%Option A is true.

Question – 6

6. A two-digit number is six times the sum of its digits and six less than three times the product of its digits. Which of the following is the number? Indicate the correct option.

• A. 54

• B. 45

• C. 36

• D. 63

• E. 72

• Answer Explanation:Let the two digit number be 10x+y, where x and y are the digits in the units and tens place.10x+y=6*(x+y) and 10x+y=3xy-610x+y=6x+6y10x-6x=6y-y4x=5yPut x=5y/4 in the second equation10(5y/4)+y=3(5y/4)y-650y/4+y=15y^2/4-650y+4y=15y^2-2415y^2-54y-24=05y^2-18y-8=05y^2-20y+2y-8=05y(y-4)+2(y-4)=0y=-2/5, y=4y=4 and x= 5*4/4=5The number is 54Option A is correct.

Question – 7

7. Some children are made to stand in a long row. Each child is given sweets equal to his position in the row. They have to walk up to some guests in a sequence and give their sweets to them. How many children shall have to give their sweets if at least 250 sweets have to be given to the guests? Indicate the correct option.

• A. 17

• B. 22

• C. 18

• D. 16

• E. 20

• Answer Explanation:The number of sweets given to the guests forms an AP.The first term of the AP, a, is 1 and the sum of n terms is at least 250 and the common difference d is 1.Sn=(n/2)[2a+(n-1)d]250<=(n/2)[2*1+(n-1)1]250<=(n/2)(n+1)250*2<=n(n+1)n(n+1)>=50022*23=506>=500The least possible value of n is 22.Hence, 22 children will have to give their sweets if at least 250 sweets have to be given.Option B is true.

Question – 8

8. What is the measure of each exterior angle of an equilateral triangle? Indicate the correct option.

• A. 90 degrees

• B. 120 degrees

• C. 80 degrees

• D. 180 degrees

• E. 300 degrees

• Answer Explanation:Each interior angle of an equilateral triangle is 60 degrees.Each exterior angle is 180-60=120 degrees.Option B is true.

Question – 9

9. Which of the following points lies in the third quadrant? Indicate the correct option.

• A. Abscissa is negative and ordinate is positive

• B. Abscissa is positive and ordinate is positive

• C. Abscissa is negative and ordinate is negative

• D. Abscissa is positive and ordinate is negative

• E. Abscissa is negative and ordinate is zero

• Answer Explanation:In the third quadrant, abscissa is negative and ordinate is negative.Only option C is true.

Question – 10

10. When a wire circumscribing a circle of area 616 sq.cm. is bent to form a square, how much lesser area does it enclose? Indicate the correct option.

• A. 14 sq.cm.

• B. 616 sq.cm.

• C. 484 sq.cm.

• D. 132 sq.cm.

• E. 88 sq.cm.

• Answer Explanation:Area of circle = 616 sq.cm.Radius of circle = Sqrt[616/pi]= sqrt[616*7/22]= sqrt[196]Radius = 14cmCircumference = 2*pi*radius= 2*22/7*14= 88Circumference of square = 88 cmSide of square = 88/4=22Area of square = 22*22= 484 sq.cm.Difference in area = 616 – 484 = 132 sq.cm.Option D is true.

Question – 11

11. Glory and Glen complete a piece of work in 8 days working together. In how many days would Glen complete the work if Glory is twice as efficient as Glen is? Indicate the correct option.

• A. 12

• B. 6

• C. 24

• D. 48

• E. 18

• Answer Explanation:Let the time taken by Glory be X and that taken by Glen be Y to complete the work.Glory is twice as fast as Glen and hence she takes half as much time as Glen does.Hence, 2X=YWork done by them in one day1/X+1/Y=1/81/(Y/2)+1/Y=1/82/Y+1/Y=1/83/Y=1/8Y=3*8=24Glen would complete it in 24 days.Option C is correct.

Question – 12

12. Robin’s takes 4 hours to water his garden working alone and Rubin takes 6 hours. They both take turns of one hour each to water the garden, starting with Robin. How much time will they take to water the garden? Indicate the correct option.

• A. 5 hours 20 minutes

• B. 4 hours 40 minutes

• C. 5 hours

• D. 4 hours

• E. 4 hours 50 minutes

• Answer Explanation:Garden watered in one hour by Robin = 1/4Garden watered in one hour by Rubin = 1/6Garden watered by them working together in two hours = 1/4+1/6= 5/12Garden watered in 4 hours = 2*5/12=10/12=5/6Remaining garden = 1-5/6=1/6Time taken by Robin to water 1/6 garden = 1/6*4=4/6 hours = 4/6*60=40 minutesOption B is correct.

Question – 13

13. Find the next number in the series 8, 24, 12, 36, 18, 54, 27, …. Indicate the correct option.

• A. 88

• B. 83

• C. 64

• D. 81

• E. 45

• Answer Explanation:8, 24, 12, 36, 18, 54, 278*3 = 2424/2 = 1212*3 = 3636/2 = 1818*3 = 5454/2 = 2727*3 = 81Option D is true.

Question – 14

14. If x+1/x=6, then which of the following is correct? Indicate the correct option.(Note:[x^2=x*x] )

• A. x^2+1/x^2=36

• B. x^2+1/x^2=34

• C. x^2+1/x^2=38

• D. x^2+1/x^2=40

• E. x^2+1/x^2=24

• Answer Explanation:x+1/x=6x^2+1/x^2+2*x*1/x=36x^2+1/x^2+2=36x^2+1/x^2=36-2=34Option B is correct..

Question – 15

15. 8th January 1993 was a Sunday. On which day does 8th January 1998 fall? Indicate the correct option.

• A. Sunday

• B. Monday

• C. Thursday

• D. Friday

• E. Saturday