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Aptitude & Reasoning 13

1) Quantity A                            Quantity B

   (.9)8                                               (1.01)4

 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

  In Quantity A, a fractional value (a value less than 1) is multiplied by itself many times. So its value becomes increasingly smaller. (For example, 1?2 x 1?2 = 1?4; 1?4 x 1?2 = 1?8, and so forth.) In Quantity B, a number greater than 1 is multiplied by itself; its value grows larger. So Column B is greater.

  • View Answer


    Ans: B

 2) a > 0

b > 0

c > 0

 Quantity A                                                          Quantity B

 (3a)(3b)(3c)                                                           3abc

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

 Multiplying column A gives (3a)(3b)(3c) = 27abc. Because a, b, and c are all positive values, 9abc will always be greater than 3abc.

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    Ans: A

3) An off-season discount of 10% is being offered at a store for any purchase with list price above $500. No other discounts are offered at the store. John purchased a computer from the store for $459.

Quantity A                                                                               Quantity B

The list price (in dollars) of the computer that John purchased      500

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 :

    We do not know whether the $459 price that John paid for the computer was with the discount offer or without the discount offer.

    If he did not get the discount offer, the list price of the computer should be $459 and John paid the exact amount for the computer. In this case, Quantity A (= 459) is less than Quantity B.

    If the price corresponds to the price after the discount offer, then $459 should equal a 10% discount on the list price. Hence, if l represents the list price, then we have $459 = l(1 – 10/100) = l(1 – 1/10) = (9/10)l.

    Solving the equation for l yields l = (10/9)459 = 510 dollars (a case when discount was offered because the list price is greater than $500). Hence, it is also possible that John got the 10% discount on the computer originally list priced at $510. Here, list price (= Quantity A) is greater than 500 (= Quantity B).

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

4) The sale price is ‘s’ when the profit is ‘p’ . The sale price is ‘2s’ when the profit is ‘3p’.

                Quantity A                                             Quantity B

                p as a percentage                                      150%

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 :

    Let the cost be $100, then p = s – 100

    New profit = 2s – 100

    So, 3(s – 100) = 2s – 100

    s = 200

    Quantity A : p = (200-100)/100 = 100%

5) If 5 workers can assemble a car in 8 hours, how many hours would it take 12 workers to assemble the same car ?

A)3

B)33

C)5

D)10

E)19.2

  • View Answer

    Ans : B

    Sol :

     M1 T1 = M2 T2 or 5 x 8 = 12 x T2 or T = 3.3

 6) The average (Arithmetic Mean) of three different positive integers is 50. If the greatest of the three integers is 70, what is the least possible integer ?

A)1

B)10

C)11

D)20

E)21

  • View Answer

     Ans : C

    Sol :

    (a+b+c)/3 = 50

    a+b+70 = 150

    a+b = 80

    since 70 is the greatest of all the three, the next greatest integer is 69.

7) If 4 and 9 are lengths of 2 sides of a triangle, then which of the following can be the length of the third side ?

 Select ALL that apply.

A)4

B)9

C)10

D)13

  • View Answer

    Ans : B , C

    Sol :

    Only B and C hold good.

    A and D do not satisfy

    Sum of any two sides  > Third side

8) A vessel which is full contains 4/7 water and 3/7 milk. Another vessel which is full has 16 litres of water and 12 litres of milk. A third vessel which is full has milk and water in the ratio 4 4/5 : 3 3/5 . If all three vessels are emptied onto a fourth vessel, what could be the ratio of water to milk in it ?

A)1:4

B)12:13

C)4:3

D)5:3

E)4:1

  • View Answer

    Ans : B

    Sol :

    The ratios of the water and milk in the given three vessels are respectively

    (4/7) : (3/7) = 4:3 ,  16 : 12 = 4 : 3 and 4 4/5 : 3 3/5 = (24/5)(18/5) = 4 : 3

    Since all three vessels contain milk and water in the same ratio 4:3, the fourth vessel also will contain milk and water in the ratio 4:3 only.

9) Chelsea travelled from point A to point B and then from point B to point C. If she took 1 hour to complete the trip with an average speed of 50 mph, what is the total distance she travelled in miles?

(A) 20

(B) 30

(C) 50

(D) 70

(E) 90

  • View Answer

    Ans : D

    Sol :

    Let t be the entire time of the trip.

    We have that the car travelled at 80 mph for t/2 hours and at 40 mph for the remaining t/2 hours. Remember that

    Distance = speed x time.

    Hence, the total distance travelled during the two periods equals 80x(t/2) + 40 x(t/2) = 60t.

    Now, remember that

    Average Speed = Total Distance / Time taken = 60t/t = 60

    The answer is (D).

10) In the figure, ABCD and PQRS are two rectangles inscribed in the circle as shown and AB = 4, AD = 3, and QR = 4. What is the value of l ?

(A) 3/2

(B) 8/3

(C) 3

(D) 4

(E) 5

image002

  • View Answer

    Ans : E

     Sol :

    PQRS is a rectangle inscribed in the circle. Hence, diagonal PR must pass through the center of the circle. So, PR is a diameter of the circle.

    Similarly, BD is a diagonal of rectangle ABCD, which is also inscribed in the same circle. Hence, the two diagonals must be diameters and equal. So, we have PR = BD.

                Now, in the figure, let’s join the opposite vertices B and D of the rectangle ABCD :

    image003

    Applying The Pythagorean Theorem to the right triangle ABD yields BD2 = AB2 + AD2 = 42 + 32 = 16 + 9 = 25. By square rooting, we get BD = ?25 = 5 . Hence, PR also equals 5. Since, from the figure, l equals PR, l equals 5. The answer is (E).

11) If 2(22 ) +32+ 23= 5x, then x =

  • View Answer

    Ans : 2

    Sol :

    2(22) + 32 + 23 = 5x

    8 + 9 + 8 = 5x

    25 = 5x

    5x = 5x

    Since the bases are the same, 5, the exponents must equal each other: x = 2.

12) Each year, funds A and B grow by a particular percentage based on the following policy of the investment company:

(1) The allowed percentages of growths on the two funds are 20% or 30%.

(2) The growth percentages of the two funds are not the same in any year.

(3) No fund will grow by same percentage growth in any two consecutive years.

In the first year, Fund B was offered a growth of 30%.

Bob doesn’t know in which fund he invested 3 years back. What is the possible percentage by which the fund of $1000 that he invested might have grown in the last 3 years?

Select ALL that apply.

(A) 70%

(B) 80%

(C) 87.2%

(D) 92.2%

(E) 108.2%

  • View Answer

    Ans : C, E

    Sol :

    We have two cases here:

    I.Bob invested in Fund A.

    II.Bob invested in Fund B.

    In the first year, fund B was given a growth of 30%. Hence, according to clauses (1) and (2), fund A must have grown by 20% (the other allowed growth percentage clause (1)).

    In the second year, according to the clauses (1) and (3), the growth percentages of the two funds will swap between the only allowed values 30% and 20% (clause (1)). Hence, fund A grows by 30% and fund B grows by 20%.

    In the third year, according to clauses (1) and (3), the growth percentages will again swap between the only two allowed values 20% and 30% (clause (1)). Hence, fund A grows by 20% and fund B grows by 30%.

    The growth in Fund A is

    $1000(100 + 20% of 100)(100 + 30% of 100)(100 + 20% of 100) = $1000 (1.2)(1.3)(1.2) = 1.872 times = 87.2%.

    The growth in Fund B is

    $1000(100 + 30% of 100)(100 + 20% of 100)(100 + 30% of 100) = $1000 (1.3)(1.2)(1.3) = 2.082 times = 108.2%.

    Select the choices (C) and (E).

13) Mike drove from Dallas to Tulsa in 4 hours. He drove the first half of the distance at 50 mph, and the second half at 70 mph. What was the distance from Dallas to Tulsa ?

Round-off your answer to the nearest whole number.

  • View Answer

    Ans : 233 miles

    Sol :

    Let ‘s’ be the first half distance. Then,

    (25/x) = (15/x) + (15/6)

    or     s = 350/3

    So, total distance = 2s = 700/3 = 233.33 mph

     

14) The prices of a TV and a refrigerator are in the ratio 9:5. If the TV costs $4,200 more than the refrigerator does, what is the price of the refrigerator ?

A)$1050

B)$4200

C)$4600

D)$5250

E)$6000

  • View Answer

    Ans : D

    Sol :

    Let the price be 9x , 5x of the TV and refrigerator respectively.

    So, 9x = 4200 + 5x

    Or x = 1050

    Price of Refrigerator = 5x = $5250

15) The product of which three of the following numbers is the greatest?

Select ALL that apply.

(A) –9

(B) –5

(C) –3

(D) 0

(E) 4

(F) 7

(G) 10

  • View Answer

    Ans : A, B, G

    Sol :

    The product of n numbers is greatest when

    a) The individual n numbers are as far as possible from zero on the number line and the resultant

    product is positive.

    Or

    b) The individual n numbers are as close as possible to zero on the number line and the product is

    negative.

    With this as the criterion, choose the greater of Choice (A) –9, Choice (B) –5, and Choice (G) 10 so that the product is positive and the choices are as far as possible from zero on the number line.

    Or

    Choice (E) 4, Choice (F) 7, and Choice (G) 10 so that the product is positive and the choices are as far as possible from zero on the number line.

    (–9).(–5).10 = 450

    4 .7.10 = 280

    Select (A), (B), and (G).

16) a2 + 7a < 0

Quantity A                              Quantity B

a                                                         0

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 :

    Factoring out the common factor a on the left-hand side of the inequality a2 + 7a < 0 yields a(a + 7) < 0. The product of two numbers (here, a and a + 7) is negative when one is negative and the other is positive.

    Hence, we have two cases:

    1) a < 0 and a + 7 > 0

    2) a > 0 and a + 7 < 0

    Case 2) is impossible since if a is positive then a + 7 cannot be negative.

    Case 1) is valid for all values of a between 0 and –7. Any number in the range is less than 0. So, Quantity A is less than Quantity B, and the answer is (B).

    Method II: Since a square, a2, is positive or zero, the inequality a2 + 7a < 0 is possible only if 7a is

    negative, which means a is negative. Hence, a < 0, and Quantity B is larger. The answer is (B).

17)  If (x+5)[(1/x)+(1/5)] = 4, then x =

(A) 1/5

(B) 1/2

(C) 1

(D) 5

(E) 10

  • View Answer

    Ans : D

    Sol :

    We are given the equation

    (x+5)((1/x)+(1/5)) = 4

    (x+5)((x+5)/5x) = 4

     (x + 5)2 = 4x(5)

    X2 + 52 + 2x(5) = 4x(5)                since (a + b)2 = a2 + b2 + 2ab

    X2 + 52 – 2x(5) = 0

    (x – 5)2 = 0                                since (a – b)2 = a2 + b2 – 2ab

    x – 5 = 0                                   by taking the square root of both sides

    x = 5

    The answer is (D) only.

18)The first fourth of a 60-mile trek took twice as long as the rest of the trek. If the first fourth took 4 hours, what is the average speed of the entire trek ?

  • View Answer

    Ans : 10

    Sol :

    Average speed = 60/(4+2) = 10 mph

    [Rest of the trip took half the time as the first fourth]

19) A coin is tossed five times. What is the probability that the fourth toss would turn a head?

(A) 1/8

(B) 1/4

(C) 1/2

(D) 3/4

(E) 4/5

  • View Answer

    Ans : C

    Sol :

    The fourth toss is independent of any other toss. The probability of a toss turning heads is 1 in 2, or simply 1/2. Hence, the probability of the fourth toss being a head is 1/2. The answer is (C).

20) PQXY , QRWX , RSVW , STUV are all equal rectangles. What fraction of PTUY is shaded ?

Express your answer as a fraction.

image005

  • View Answer

    Ans : 1/12

     Sol :

     In the rectangle RSVW, Area = length x breadth

    Area of shaded part = (1/6)(Area of rectangle)(Why?)

     So totally 1/3 part is shaded in the two rectangles.

    For the rectangle , PTUY, (1/3)/4 is shaded.

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