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Aptitude & Reasoning 14

1) (4-5x2) = 1

            Quantity A                                            Quantity B

             (4-5x)+(4-5x)2                                                 1

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 :

    (4 – 5x)2 equals 1 when either 4 – 5x = –1 or +1.

    If 4 – 5x equals –1, then

    (4 – 5x) + (4 – 5x)2 = –1 + 1 = 0

    And if 4 – 5x equals 1, then

    (4 – 5x) + (4 – 5x)2 = 1 + 1 = 2

    In the first case, Quantity A is less than Quantity B; and in the second case, Quantity B is less than Quantity A. Hence, we have a double case, and the answer is (D).

 2) If x = a + 2 and b = x + 1, then which of the following must be false?

Select ALL that apply.

(A) a > b

(B) a < b

(C) a = b

(D) a = b2

(E) b = a2

  • View Answer

    Ans : A, C, D

    Sol :

    We have the equations x = a + 2 and b = x + 1. Substituting the first equation into the second equation yields b = (a + 2) + 1 = a + 3. This equation shows that b is 3 units greater than a. Hence, b must be greater than a. So, (A) and (C) are false and therefore correct answers (remember, we are looking for statements that must be false).

    Next, assume a = b2 [Choice (D)]. Then a must be positive. If a is between 0 and 1, b is also between 0 and 1, which violates b = a + 3. Here, our assumption fails. If a were greater than 1, then b equals Ða, which must be less than a—but we know that b is greater than a. Again, our assumption fails. Accept choice (D).

    Next, assume b = a2 [Choice (E)]. This could be true. For example, consider b = a + 3 = a2. Subtracting a and 3 from both sides yields a2 – a – 3 = 0. The quadratic equation is in the form ax2 + bx + c = 0. Since the discriminant of the quadratic equation which is b2 – 4ac equals (–1)2 – 4(1)(–3) = 1 + 12 = 13, is positive, we will have valid real solutions (Note, the GRE is only interested in Real Numbers), which means that b = a2 is possible with given information. Hence, reject this choice (remember, we are looking for answers that must be false).

    The answer consists of (A), (C), and (D).

3) If 1/x + 1/y = 1/3, then xy/(x + y)=

(A) 1/5

(B) 1/3

(C) 1

(D) 3

(E) 5

  • View Answer

    Ans : D

    Sol :

    Multiplying the given equation 1/x + 1/y = 1/3 by xy yields

    y + x = xy/3, or x + y = xy/3

    Multiplying both sides of the equation x + y = xy/3 by 3/(x + y) yields

    xy/(x + y) = 3

    The answer is (D).

4) x > y > 0

   Quantity A                                     Quantity B

   x-y                                                        (x/3)+(y/3)

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 :

    If x=2 and y=1, then x-y=2-1=1=(3/3)=((2/3)+(1/3))=((x/3)+(y/3)). In this case, the Quantities are equal.

    If x=3 and y=1, then  x-y=3-1=2 ? ((3/3)+(1/3)) = (4/3) = ((x/3)+(y/3)). In this case, the Quantities are not equal and therefore the answer is (D).

5) Quantity A                       Quantity B

        h                                              10

image002

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 :

    Area = (1/2)h(h+2) = 40 or h(h+2) = 80

    Substitute h=10 (Quantity B) and observe that the left hand side greater than 80 . So, h<10

6) John swims laps 50% faster than Stacy

  Quantity A                                              Quantity B

   Number of laps Stacy swims                   Number of laps John swims

  In 70 minutes                                              in 50 minutes

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 :

       If Stacy’s rate is 1, then John’s rate is 1.5

       In 70 minutes, Stacy’s distance is 1(70) = 70

       In 50 minutes, John’s distance is 1.5(50) = 75

 7) Seven years ago, Scott was 3 times as old as Kathy was at that time. If Scott is now 5 years older than Kathy, how old is Scott?

(A) 12 ½  

(B) 13

(C) 13 ½

(D) 14

(E) 14 ½

  • View Answer

    Ans : E

    Sol :

    Let S be Scott’s age and K be Kathy’s age. Then translating the sentence “If Scott is now 5 years older than Kathy, how old is Scott” into an equation yields

                                  S = K + 5

    Now, Scott’s age 7 years ago can be represented as S = –7, and Kathy’s age can be represented as K = –7.

    Then translating the sentence “Seven years ago, Scott was 3 times as old as Kathy was at that time” into an equation yields S – 7 = 3(K – 7).

    Combining this equation with S = K + 5 yields the system:

    S – 7 = 3(K – 7)

    S = K + 5

    Solving this system gives S = 14 ½ . The answer is (E).

 8) The University of Maryland, University of Vermont, and Emory University have each 4 soccer players. If a team of 9 is to be formed with an equal number of players from each university, how many possible teams are there?

(A) 3

(B) 4

(C) 12

(D) 16

(E) 64

  • View Answer

    Ans : E

    Sol :

    The selection from the 3 universities can be done in 4x4x4 = 43 = 64 ways.

    The answer is (E).

9) ABC and DEF are right triangles. Each side of ?ABC is twice the length of the corresponding side of ?DEF.

           Quantity A                                                  Quantity B

      The area of ?DEF/The area of ?ABC                          1/2

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 :

    Since we are not given the sizes of the two triangles, we can choose any measurements such that each side of ?ABC is twice the length of the corresponding side of ?DEF. Suppose each leg of ?ABC is 2 units long and each leg of ?DEF is 1 unit long.

    Then the area of ?DEF is

    (1/2)(1)(1) = 1/2,

    and the area of ?ABC is

    (1/2)(2)(2) = 2.

    Forming the ratio yields.

    The area of ?DEF / The area of ?ABC

    = (1/2)/2 = 1/4

    Since 1/4 is less than 1/2, Quantity A is less than Quantity B. The answer is (B).

10)  Quantity A                   Quantity B

       ?12.5 + ?12.5                      ?25

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 :

    Whatever the value of ?12.5 is, it is greater than 3 since ?12.5 > ?9 = 3 . Hence, ?12.5 + ?12.5 > 3 + 3 = 6 > 5 = Quantity B

    The Answer is (A).

 11) The nth term of the sequence a1,a2,a3,……,an is defined as an = -(an-1). The first term a1 equals -1.

       Quantity A                                            Quantity B

         a5                                                                                      1

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 :

    The rule for the sequence is an = –(an – 1). Putting n = 2 and 3 in the rule yields

    a2 = –(a2 –1) = –a1 = –(–1) = 1 (given that a1 = –1)

    a3 = –(a3 – 1) = –a2 = –1

    Similarly, we get that each even numbered term (when n is even) equals 1 and each odd numbered term (when n is odd) equals –1. Since a5 is an odd numbered term, it equals –1. Hence, Quantity A equals –1 and is less than 1 (= Quantity B). The answer is (B).

12) ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the area of the square?

(A) 3

(B) 9

(C) 12

(D) 12?2

(E) 18

image004

  • View Answer

    Ans : E

    Sol :

    Side AB is the hypotenuse of ?AOB. Hence, by The Pythagorean Theorem, we have

    AB2 = AO2 + BO2 = 32 + 32 = 18. Hence, the area of the square ABCD equals side2 = AB2 = 18. The answer is (E).

13) In the figure, the areas of parallelograms EBFD and AECF are 3 and 2, respectively. What is the area of rectangle ABCD ?

(A) 3

(B) 4

(C) 5

(D) 4?3

(E) 7

image006

  • View Answer

    Ans : C

    Sol :

    The area of the rectangle ABCD is length x width = DC x AD.

    The area of the parallelogram AECF is FC x AD (base x height). Also, the area of parallelogram EBFD is DFxAD. Now, summing the areas of the two parallelograms AECF and EBFD yields

    FCxAD + DFxAD = (FC + DF)(AD) = DCxAD = the area of the rectangle ABCD.

    Hence, the area of rectangle ABCD equals the sum of areas of the two parallelograms, which is 2 + 3 = 5. The answer is (C).

14) In the rectangular coordinate plane shown, what are the coordinates of point E ?

(A) (2, 0)

(B) (2, 3)

(C) (6, 2)

(D) (6, 6)

(E) (6, 8)

image007

  • View Answer

    Ans : E

    Sol :

    From the figure, since EC is perpendicular to the x-axis, C is a point vertically below point B. Hence, both have the same x-coordinate.

     

    The line AC is horizontal and therefore its length equals the x-coordinate difference of A and C, which equals 6 – 0 = 6.

    The line DC is horizontal and therefore its length equals the x-coordinate difference of D and C, which is 6 – 2 = 4.

    The length of the vertical line BC equals the y-coordinate difference of B and C, which is 3 – 0 = 3.

    The length of the vertical line EC equals the y-coordinate difference of E and C.

    Now, in ?ABC, ÐA = a°, ÐB = 90° – a°, and ÐC = 90°. The sides opposite angles A and B are in the ratio

    BC/AC = 3/6 = 1/2.

    Similarly, in ?DEC, ÐE = a°, ÐD = 90° – a°, and ÐC = 90° (So, ABC and DEC are similar triangles and their corresponding sides are proportional). Hence, the sides opposite angles E and D are in the ratio

    DC/EC = 1/2.

    Hence, we have

    DC/EC = 1/2

    EC = 2DC

    EC = 2.4 = 8

    Hence, the y-coordinate of point E is 8, and the answer is (E).

15) Data Value                Frequency

         0                                    3

         1                                    6

         2                                   2

         3                                   1

         4                                  2

 Quantity A                                                        Quantity B

  Range of distribution                                                 5

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 :

    The range of the distribution is the difference between the largest and the smallest piece of data. In this case, the smallest data value is zero and the largest is 4 ;  4-0 = 4

16) If ABCD is a rectangle and ‘S’ is the midpoint of BC. Then which of the following could be a value for p ?

A)200

B)300

C)500

D)All of the above

E)None of the above

image010

  • View Answer

    Ans : B

    Sol :

    image011

    It can be noted that 4p is an obtuse angle, so p=300. Since ÐABS = 900

17) A 200ml solution is 25% salt. If 50ml of water is distilled from the solution, then what is the percentage of salt in the remaining solution ?

 Round off your answer to the nearest whole number.

 

  • View Answer

    Ans : 33

    Sol :

    Amount of Salt = 0.25×200 = 50

    (x/100)(200 – 50) = 50

    [Here the amount of salt remains the same because only water is removed from the solution]

    Or x = 33.33

18) The Fearson’s invested $1000 for three years at a rate of 5% compounded semi-annually. What is the interest earned by them at the end of two years ?

  • View Answer

    Ans : $ 159.69

     Sol :

    P = $1000

    r = 0.05/2 = 0.025

    n = 2×3 = 6 , conversion periods over the three years

    Therefore, the interest = 1000((1+0.025)^6) – 1000 = $159.69

19) A car travels at 30 mph for 1 ½ hours and then at 40 mph for 2 ½ hours. What is the average speed for the entire distance ?

 Round off your answer to the nearest whole number.

  • View Answer

    Ans : 36

     Sol :

    Average speed = (Total distance / Total time) = (30 * 3/2 + 40 * 5/2) / (3/2 + 5/2) = 36.25 mph

20) The table shows the distribution of a team of 16 engineers by gender and level. image013

The number of Male senior Engineers and the number of Female Lead Engineers is not yet known. If one engineer is selected from the team, which of the following could be the probability that the engineer is a male senior engineer when the numbers are known?

Select ALL that apply.

(A) 1/32

(B) 1/16

(C) 3/16

(D) 1/8

(E) 3/4

  • View Answer

    Ans : B, C, D

    Sol :

    The total number of engineers available is 16.

    The number of engineers shown in the table is 3 + 2 + 4 + 2 = 11.

    Hence, the number of engineers not shown in the table must be 16 – 11 = 5.

    Hence, the number of Male Senior Engineers must be 1, 2, 3, 4, or 5.

    Hence, the probability must be 1/16, 2/16 = 1/8, 3/16, 4/16 = 1/4, or 5/16 depending upon the number of male senior engineers available.

    Select choices (B), (C), and (D).

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