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Aptitude & Reasoning 15

1) A bag contains green, blue and yellow balls. The ratio of green to blue balls is 2:7. The ratio of green to yellow balls is 3:5

      Quantity A                                          Quantity B

       Number of blue balls                     Number of yellow balls

A)Quantity A is greater

B)Quantity B is greater

C)The two quantities are equal

D)The relationship cannot be determined from the information Given

  • View Answer

    Ans : A

     Sol :

     Let g, b and y be the numbers of green, blue and yellow balls respectively. Using the given ratios, we can write the following fractions

     g / b = 2 / 7 and g / y = 3 / 5

     The first fraction gives

     b / g = 7 / 2

     We now evaluate the product of fractions g / y and b / g as follows

    (g / y) * (b / g) = (3 / 5) * (7 / 2)

     Note that (g / y) * (b / g) simplifies to b / y, hence

    b / y = 21 / 10

     The above fraction indicates that the number of blue balls (A) is greater than the number of yellow balls (B).

    So the Answer is (A)

2)  Quantity A                               Quantity B

    2×310 + 2×310 + 2×310              3×310

 

A)Quantity A is greater

B)Quantity B is greater

C)The two quantities are equal

D)The relationship cannot be determined from the information Given

  • View Answer

    Ans : A

     Sol :

     Simplify expressions in A and B

    A : 2×310 + 2×310 + 2×310 = 2× ( 310 + 310 + 310 )

     = 2× ( 3×310 ) = 2×311

     B : 3×310 = 311

     Quantity A is greater than quantity B

     Answer (A).

    b / y = 21 / 10

     The above fraction indicates that the number of blue balls (A) is greater than the number of yellow balls (B).

    So the Answer is (A)

3) ABC is a triangle such that the measure of angle A is 45°. The measure of angle C is twice the measure of angle B.

       Quantity A                                               Quantity B

      The measure of angle A                         The measure of angle B

 A)Quantity A is greater

B)Quantity B is greater

C)The two quantities are equal

D)The relationship cannot be determined from the information Given

 

 

  • View Answer

    Ans : C

     Sol :

     Quantity A is known. Let us calculate quantity B. The measure of angle C is twice the measure of angle B is translated as follows.

    C = 2 B

     The sum of the measures of the three angles A, B and C of the triangles is 180°

     A + B + C = 180

     Substitute A by 45 and C by 2B in the above equation

     45 + B + 2B = 180

     Solve for B

    3 B = 135

     B = 135 / 3 = 45°

     The measures of angle A and B are equal

     Answer (C).

4) x = -10-2

    Quantity A                                     Quantity B

        x3                                                              x2

 

A)Quantity A is greater

B)Quantity B is greater

C)The two quantities are equal

D)The relationship cannot be determined from the information Given

  • View Answer

    Ans : B

     Sol :

     Evaluate expressions in A and B for the given value of x

     A:  x3 = (- 10-2)3 = (-1)3(10-2)3

    = – 10-6

     B : x2 = (- 10-2)2 = (-1)2(10-2)2

     = 10-4

     Quantity B is greater than quantity A

     Answer (B)

5) Quantity A                                               Quantity B

Area of rectangle of perimeter 240             Area of square of perimeter 240

 

A)Quantity A is greater

B)Quantity B is greater

C)The two quantities are equal

D)The relationship cannot be determined from the information Given

 

  • View Answer

    Ans : D

     Sol :

    Given the perimeter of a rectangle, we cannot calculate its area and therefore the relationship between the quantities in A and B cannot be determined from the information given.

     So the Answer  is (D).

6) The arithmetic mean (average) of the numbers a and b is 17. The geometric mean of the numbers a and b is 8. The geometric mean of two numbers is defined to be the square root of their product.

      Quantity A                                Quantity B

            a                                              b

  • View Answer

    Ans : D

    Sol :

    The arithmetic mean of the numbers a and b is 17. Hence, (a + b)/2 = 17, or a + b = 34.

    The geometric mean of the numbers a and b is 8. Hence,

    ?ab = 8, or ab = 82 = 64.

    Solving the equation a + b = 34 for a yields a = 34 – b. Substituting this into the equation ab = 64 yields

                      (34 – b)b = 64

                      34b – b2 = 64

                      34b – b2 – 64 = 0

                      b2 – 34b + 64 = 0

                      (b – 32)(b – 2) = 0

                      b – 32 = 0 or b – 2 = 0

                      b = 32 or b = 2

    Now, if b = 32, then a = 34 – b = 34 – 32 = 2. In this case, Quantity B is larger.

    Now, if b = 2, then a = 34 – b = 34 – 2 = 32. In this case, Quantity A is larger.

    Hence, we have a double case, and the answer is (D).

7) 1 pound = 16 Ounces

      Quantity A                                                        Quantity B

     Weight of 16,000 ounces of rice                  Weight of 1,000 pounds of coal

  • View Answer

    Ans : C

    Sol :

    Quantity B has 1,000 pounds of coal, and there are 16 ounces in 1 pound. So, Quantity B has 1,000 pounds = 1,000(16 ounces) = 16,000 ounces. Hence, each Quantity weighs 16,000 ounces. The answer is (C).

8) The average of a set of six positive numbers is 30.

Quantity A                                                                               Quantity B

The average of the numbers in the set after             The average of the remaining numbers in

replacing the smallest number in the set with 0      the set after removing the smallest number                                                                                 from the set

  • View Answer

    Ans : B

    Sol :

    Let a, b, c, d, e, and f be the numbers in the set, and let f be the smallest number in the set.

    When the smallest number (f) in the set is replaced by 0, the numbers in the set are a, b, c, d, e, and 0.

    Quantity A equals the average of these six numbers, which equals

     

    (a + b + c + d + e + 0) / 6 = (a + b + c + d + e) / 6

    Instead, if the smallest number in the set is removed, the remaining numbers in the set would be a, b, c, d, and e. Now there are only 5 numbers in the set. Hence, Quantity B, which equals the average of the remaining numbers (five numbers) in the set, equals

    (a + b + c + d + e) / 5

    Since all the numbers in the set are positive (given), the sum of the five numbers a + b + c + d + e is also positive. Note that dividing a positive number by 5 yields a greater result than dividing it by 6.

    Hence,

    (a + b + c + d + e) / 5 is greater than (a + b + c + d + e) / 6.

     Thus, Quantity B is greater than Quantity A, and the answer is (B).

9) What is the perimeter of ?ABC shown in the figure ?

(A) 2 + 4?2

(B) 4 + 2?2

(C) 8

(D) 4 + 4?2

(E) 4 + 4?2

image002

  • View Answer

    Ans : B

    Sol :

    Equating the vertical angles at points A and C in the figure yields ÐA = 2z and y = z. Summing the

    angles of the triangle to 180° yields

    ÐA + ÐB + ÐC = 180

    2z + y + z = 180                              we know that ÐA = 2z, ÐB = y, and ÐC = z

    2z + z + z = 180                               we know that y = z

    4z = 180

    z = 180/4 = 45

    So, ÐA = 2z = 2(45) = 90, ÐB = y = z = 45 and ÐC = z = 45. Hence, ?ABC is a right triangle. Also, since angles ÐC and ÐB are equal (equal to 45), the sides opposite these two angles, AB and AC, must be equal.

    Since AC equals 2 (from the figure), AB also equals 2. Now, applying The Pythagorean Theorem to the triangle yields

    BC2 = AB2 + AC2

          = 22 + 22                        given that AB = AC = 2

          = 4 + 4

          = 8

          BC = 2?2                     square rooting both sides

    Now, the perimeter of ?ABC = AB + BC + CA = 2 + 2?2 + 2 = 4 +2?2 .

    The answer is (B).

10) A closed rectangular tank contains a certain amount of water. When the tank is placed on its 3 ft. by 4 ft. side, the height of the water in the tank is 5 ft. When the tank is placed on another side of dimensions 4 ft. by 5 ft. what is the height, in feet, of the surface of the water above the ground ?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

  • View Answer

    Ans : B

    Sol :

    When based on the 3 ft.4 ft side, the height of water inside the rectangular tank is 5 ft. Hence, the volume of the water inside tank is length.width.height = 3.4.5 cu. ft.

    When based on 4 ft.5 ft side, let the height of water inside the rectangular tank be h ft. Then the volume of the water inside tank would be length.width.height = 4.5.h cu. ft.

     

    Equating the results for the volume of water, we have 3.4.5 = v = 4.5.h. Solving for h yields

    h = (3.4.5)/(4.5) = 3 ft.

    The answer is (B).

11)In the figure, X =

A)400

B)500

C)600

D)700

E)900

image004

  • View Answer

    Ans : A

     Sol :

    image006

    X = 1800 – (900+500) = 400

    (or)

    X is alternate angle to q , So , X = q

12) John invests $ 100 in a certificate of deposit (CD) that yields 6% simple interest annually. How much money will john have in his account after six months ?

A)$ 3

B)$ 6

C)$ 103

D)$ 106

E)$ 110

  • View Answer

    Ans : C

    Sol :

    Simple interest = pnr/100 = (100*6*6)/(100*12) = $ 3

    Total amount = 100 + 3 = $ 103

 13) Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce, making a profit of 20 percent. What was the ratio of the mixture?

(A) 1 : 10

(B) 1 : 5

(C) 2 : 7

(D) 3 : 8

(E) 5 : 7

  • View Answer

    Ans : B

    Sol :

    Let 1 : k be the ratio in which Joseph mixed the two types of rice. Then a sample of (1 + k)

    ounces of the mixture should equal 1 ounce of rice of the first type, and k ounces of rice of the second type. The rice of the first type costs 5 cents an ounce and that of the second type costs 6 cents an ounce.

    Hence, it cost him

    (1 ounce x 5 cents per ounce) + (k ounces x 6 cents per ounce) = 5 + 6k

    Since he sold the mixture at 7 cents per ounce, he must have sold the net 1 + k ounces of the mixture at 7(1 + k).

     

    Since he earned 20% profit doing this, 7(1 + k) must be 20% more than 5 + 6k. Hence, we have the equation

    7(1 + k) = (1 + 20/100)(5 + 6k)

    7 + 7k = (120/100)(5 + 6k)

    7 + 7k = (6/5)(5 + 6k)

    7 + 7k = 6/5 . 5 + 6/5 . 6k

    7 + 7k = 6 + 36k/5

    1 = k/5

    k = 5

    Hence, the required ratio is 1 : k = 1 : 5. The answer is (B).

14) A set has exactly five consecutive positive integers starting with 1. What is the percentage decrease in the average of the numbers when the greatest one of the numbers is removed from the set?

(A) 5

(B) 8.5

(C) 12.5

(D) 15.2

(E) 16.66

  • View Answer

    Ans : E

    Sol :

    The average of the five consecutive positive integers 1, 2, 3, 4, and 5 is

    (1 + 2 + 3 + 4 + 5)/5 = 15/5 = 3.

    After dropping 5 (the greatest number), the new average becomes (1 + 2 + 3 + 4)/4 = 10/4 = 2.5.

    The percentage drop in the average is

    ((Old average – New average) / Old average)*100

    = ((3-2.5)/3)*100

    = 16.66%

    The answer is (E).

15)Three workers A, B, and C are hired for 4 days. The daily wages of the three workers are as follows:

A’s first day wage is $4.

Each day, his wage increases by 2 dollars.

B’s first day wage is $3.

Each day, his wage increases by 2 dollars.

C’s first day wage is $1.

Each day, his wage increases by the prime numbers 2, 3, and 5 in that order.

Which one of the following is true about the wages earned by A, B, and C in the first 4 days?

 

(A) A > B > C

(B) C > B > A

(C) A > C > B

(D) B > A > C

(E) C > A > B

  • View Answer

    Ans : A

    Sol :

    The payments to Worker A for the 4 days are the four integers 4, 6, 8, and 10. The sum of the payments is 4 + 6 + 8 + 10 = 28.

    The payments to Worker B for the 4 days are the four integers 3,5,7 and 9. The sum of the payment is 3+5+7+9 = 24 .

    The payments to Worker C for the 4 days are 1, 1 + 2 = 3, 3 + 3 = 6, and 6 + 5 = 11. The sum of the

    payments is 1 + 3 + 6 + 11 = 21.

    From the calculations, A > B > C. The answer is (A).

16)  What is the remainder when 72.82 is divided by 6?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

  • View Answer

    Ans : D

    Sol :

    72.82 = (7 . 8)2 = 562.

    The number immediately before 56 that is divisible by 6 is 54. Now, writing 562 as (54 + 2) 2,

    we have 562 = (54 + 2) 2

                = 542 + 2(2)(54) + 22                   by the formula (a + b) 2 = a2 + 2ab + b2

                = 54[54 + 2(2)] + 22

                = 6 x 9[54 + 2(2)] + 4                 here, the remainder is 4

    Since the remainder is 4, the answer is (D).

17) If N is average (Arithmetic Mean) of five numbers, which of the following must be true ?

 Select ALL that apply.

A)At least one of the five numbers is greater than or equal to N

B)At least one of the five numbers is less than or equal to N

C)At least two of the five numbers are greater than or equal to N

  • View Answer

    Ans : A , B

     Sol :

    Plug-in values for the three numbers and verify.

    Can you think of a generalized logical approach to this ?

18) ABCD is a square X and Y are the mid points of BC and AX. Which of these statements are true ?

Select ALL that apply

A)AY < CY B)XY > BX

C)AX < AB

image009

  • View Answer

    Ans : A, B

     Sol :

    image010

    A)Angle CXY > 900 (Why?)

    So, CY is the longest in triangle CXY

    AY (or XY) < CY

     

    B)If AB = 2a , BX = a then AX = ?5a or XY = (?5)a/2

    XY > BX

     

    C)AX > AB

     

19) Pete has 5 different ties that match with 3 different shirts. How many shirt-and-tie combinations can he make if he selects one shirt and one tie ?

  • View Answer

    Ans : 15

     Sol :

    There are 5 different choices of ties, and 3 different choices of shirts. Multiply these choices : 5×3 = 15 different shirt-and-tie combinations.

20) Kathy, Linda and Nancy are trainee chefs. It takes Kathy and Linda 2 hours to prepare a main course. Linda and Nancy can do it in 3 hours. If Linda alone takes 4 hours to prepare the main course, in how many hours would Kathy and Nancy complete the main course together ?

  • View Answer

    Ans : 3 hours

     Sol :

    Let us assume, Kathy = k , Linda = l , Nancy = n

    Kl/(k+l) = 2     and     ln/(l+n) = 3

    Since l = 4 , k = 4  and n = 12

    So, kn/(k+n) = (4×12)/(4+12) = 48/16 = 3 hours

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