Test: Numeric Entry- 2


15 Questions MCQ Test Section-wise Tests for GRE | Test: Numeric Entry- 2


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*Answer can only contain numeric values
QUESTION: 1

A sum of money becomes 8 times itself in 15 years when placed at compound interest. In how many years will it double itself?Correct


Solution:

Let P, R and T be the principle, rate and time and A be the amount.
A = P(1+R/100)T
8P=P(1+R/100)15
8= (1+R/100)15
23= [(1+R/100)5]3
2 = (1+R/100)5
Hence, the amount doubles itself in 5 years.
[R^T=R*R*...*T times]

*Answer can only contain numeric values
QUESTION: 2

If (x3+1/x3) = 52, then find the value of (x+1/x). [x3=x*x*x]


Solution:

(x+1/x)3 = (x3+1/x3) + 3(x+1/x) (x+1/x)3
= 52 + 3(x+1/x) Let (x+1/x)
= y We have y3
=52+3y y3 - 3y - 52
= 0 Clearly
y = 4
Hence,
(x+1/x) = 4

*Answer can only contain numeric values
QUESTION: 3

    If x+1/x = 2, then find the value of x3+1/x3. [x3=x*x*x]


Solution:

x+1/x = 2 (x+1/x)3
= x3+1/x3 + 3*x*1/x(x+1/x)
Substituting the value of (x+1/x),
we get 23 = x3+1/x3 + 3(2) x3+1/x3
= 8 - 6
= 2

*Answer can only contain numeric values
QUESTION: 4

Find the value of k for which the equations 4x+5y = 3 and kx + 15y = 9 have infinitely many solutions


Solution:

For the equations to have infinitely many solutions,
4/k = 5/15 = 3/9
k = 4*15/5 = 4*3 = 12
The equations have infinitely many solutions for
k = 12

*Answer can only contain numeric values
QUESTION: 5

The difference between two numbers is 2 and the difference between their squares is 24. Find the larger number.


Solution:

Let the smaller number be x and the greater number be y.
y - x = 2 ...(1)
y2 - x2 = 24 ...(2)
Substituting y = x+2 from equation (1) in equation (2) we get
(x+2)2 -x2 = 24 x2+4x+4 -x2
= 24 4x+4=24 4x = 24-4 = 20
x = 20/4 = 5
y = x+2 = 5+2 = 7
The larger number is 7.
[x2=x*x]

*Answer can only contain numeric values
QUESTION: 6

Find the value of (bx-ay), if x/a+y/b = 2 and ax -by = a2-b2. [a2=a*a]


Solution:

x/a+y/b = 2 bx + ay = 2ab ...(1)
and
ax-by = a2-b2 ...(2)
Multiplying (1) by b and (2) by a, we get
(b2)x+aby + (a2)x -aby
= 2ab2 + a3 -ab2 (a2+b2)x
= a(a2+b2) x = a Putting x = a in (1),
we get
ba+ay = 2ab
y = 2b-b=b
Hence,
x = a and y = b bx-ay = ba-ab
= 0

*Answer can only contain numeric values
QUESTION: 7

 

Find the first term of a GP whose second term is 2 and the sum to infinity is 8.


Solution:

Let the first term of the GP be a and the common ratio be r
The second term is given by ar and the sum to infinity is given by
S=a/(1-r) ar = 2 and a/(1-r) = 8
r = 2/a and a = 8 - 8r
Hence, a = 8 - 8*2/a a^2 = 8a -16 a^2-8a+16=0 (a-4)^2=0 a = 4
Hence,
the first term of the GP = a = 4 [a^2=a*a]

*Answer can only contain numeric values
QUESTION: 8

How many elements does the power set of A contain if A = {x,y}?


Solution:

A = {x,y} The set A contains 2 elements.
The number of element in the power set of a set containing n elements is given by
2^n. Power set of A contains 2^2 = 4 elements.
[2^2=2*2]

*Answer can only contain numeric values
QUESTION: 9

The radius of the base of a solid cylinder is x cm and its height is 3 cm. It is re-cast into a cone of the same radius. Find the height of the cone in cm.


Solution:

Volume of a cylinder = pi*r^2*h,
where pi = 22/7 and r and h are the radius and height of the cylinder respectively.
Volume of cone = 1/3*pi*r^2*h
where pi = 22/7, and r and h are the radius and height of the cone respectively.
Volume of the given cylinder = pi*x^2*3
= 3*pi*x^2
Volume of cone = 1/3*pi*x^2*h = pi*x^2*h/3
Since the two volumes are equal
3*pi*x^2 = pi*x^2*h/3 3=h/3 h = 3*3 = 9 cm
The height of the cone is 9 cm.
[pi=22/7, r^2=r*r]

*Answer can only contain numeric values
QUESTION: 10

Cards numbered 1 through 10 are placed in an urn. One ticket is drawn at random. In how many chances out of 20 shall the card have a prime number written on it?


Solution:

There are 10 cards in the urn. Favourable numbers = 2, 3, 5, 7
Required probability
= 4/10 = 8/20
There are 8 chances out of 20 of drawing a prime number.

*Answer can only contain numeric values
QUESTION: 11

Find the value of a if (x-a) is the g.c.d. of x^2-x-6 and x^2+3x-18. [x^2=x*x]


Solution:

Since (x-a) is the g.c.d of the given polynomials, (x-a) is a factor of both the polynomials.
Putting the value a in place of x in the two polynomials,
we get a^2-a-6=0
and
a^2+3a-18=0 a^2-a-6
=a^2+3a-18 -a-6
=3a-18
3a+a =18-6
4a=12
a=3

*Answer can only contain numeric values
QUESTION: 12

The amount of money returned by Sam to Pam after two years was Rs.5500. How much money did Pam lend at 5% rate of simple interest?


Solution:

Let P, R, T and SI be the principle, rate, time and simple interest.
Amount = SI+ P = P*R*T/100 + P 5500
= P*5*2/100 + P 5500
= (P+10P)/10 P = 5500*10/11
= 5000 Rs.
5000 were lent

*Answer can only contain numeric values
QUESTION: 13

In a two-digit number, the sum of the digits is 12. The smaller digit subtracted from the larger digit gives us 4. How many such numbers are possible?


Solution:

Let the two digits be x and y such that x>y.
According to the conditions,
x+y = 12...(1)
x - y = 4...(2)
Adding (1) and (2), we get
x+y +x -y = 12+4 2x = 16
x = 8 y
= 12-8 = 4
The possible numbers are 84 and 48.
Hence, two such numbers are possible.

*Answer can only contain numeric values
QUESTION: 14

One man can complete a work in 25 days and one woman can complete it in 10 days. In how many days can 5 men and 3 women complete the work?


Solution:

One man can complete the work in 25 days.
Work completed by one man in one day = 1/25
One woman can complete the work in 10 days.
Work completed by one woman in one day
= 1/10
Work completed by 5 men and 3 women in one day
= 5*1/25+3*1/10
= 1/5+3/10 = (2+3)/10
= 5/10 =1/2
5 men and 3 women complete the work in 2 days.

*Answer can only contain numeric values
QUESTION: 15

Find n when n>0 and P(n,4) = 20*P(n,2).


Solution:

P(n,4) = 20*P(n,2) n!/(n-4)!
= 20*n!/(n-2)! (n-2)!
= 20*(n-4)! (n-2)(n-3)(n-4)!
= 20*(n-4)! (n-2)(n-3)
=20 n^2-5n+6-20=0
n^2-5n-14=0
n^2-7n+2n-14=0
n(n-7)+2(n-7)=0
n=-2,7
Since n>0,
we have n = 7

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