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Test: Numeric Entry- 1


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15 Questions MCQ Test Section-wise Tests for GRE | Test: Numeric Entry- 1

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*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 1

The denominator of a fraction is 4 less than the numerator. If the denominator is decreased by 2 and the numerator is increased by 1, then the numerator is eight times the denominator. Find the numerator of the fraction.


Detailed Solution for Test: Numeric Entry- 1 - Question 1

Let the fraction be x/y
According to the conditions y = x - 4 x - y = 4 ...(1)
8*(y-2) = (x+1) 8y-16=x+1 x-8y = -17...(2)
Subtracting (1) from (2),
we get x - 8y - x + y
= -17 - 4 -7y = 21 y
= 3 x = 4 + y
= 4+ 3 = 7
The numerator is 7

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 2

A father is four times as old as his son is. Five years back he was seven times as old as his son was then. What is the present age of the father?


Detailed Solution for Test: Numeric Entry- 1 - Question 2

Let the age of the son and father be x and y respectively. 5 years back, their ages were (x-5) and (y-5)
According to the given conditions
4x = y 4x-y = 0 ...(1)
7(x-5) = (y-5) 7x - 35
= y -5 7x -y = 30 ...(2)
Subtracting (1) from (2),
we get 7x - y - 4x + y = 30 - 0 3x = 30 x = 10 years
y = 4*10 = 40 years
The present age of the father is 40 years.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 3

Find a number whose 20% is 35% of 144.


Detailed Solution for Test: Numeric Entry- 1 - Question 3

Let the number be x.
20% of x = 35% of 144
= 35*144/100
= 50.4 20% of x = 50.4 20x/100 = 50.4 x
= 50.4*100/20 = 252
The required number is 252

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 4

Find the positive value of x, for which AB = 5 units for points A(3,x/2) and B(-1,x+1).


Detailed Solution for Test: Numeric Entry- 1 - Question 4

AB = 5
AB =
5=
Squaring both sides,
we get
25 = 16 + x2/4+1+x x2/4 + x -8
=0 x2+4x-32=0 x2+8x-4x-32
=0 x(x+8)-4(x+8)=0 (x-4)(x+8)=0
x = 4 [x2 = x*x]

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 5

When two lines are parallel, what is the difference of their slopes equal to?


Detailed Solution for Test: Numeric Entry- 1 - Question 5

When two lines are parallel, their slopes are equal. The differene of their slopes is equal to 0.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 6

Find the distance of the mid-point of the line joining L(5,1) and M(-1,-1) from the point O(2,0).


Detailed Solution for Test: Numeric Entry- 1 - Question 6

Mid point of LM is given by
((5-1)/2, (1-1)/2)
= (4/2,0/2) =(2,0)
The distance of (2,0) from O(2,0) is equal to 0.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 7

For what value of k is the line (k-3)x-(4-k2)y+k2-7k+6=0 parallel to the x axis? [k2=k*k]


Detailed Solution for Test: Numeric Entry- 1 - Question 7

For the line to be parallel to the x axis, its slope is 0 Slope = - coefficient of x/coefficient of y = -(k-3)/(4-k2) = 0
Hence, k-3=0 k=3 For k=3,
the given line is parallel to the x axis.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 8

    Find the radius of the circle x2+y2-12x+11=0 [x2=x*x]


Detailed Solution for Test: Numeric Entry- 1 - Question 8

x2+y2-12x+11=0
(x2-12x)+y2+11=0
(x-6)2+(y+0)2 -36 +11 = 0
(x-6)2+(y+0)2 = 36-11=25
(x-6)2+(y+0)2 = 52
The radius of the circle is 5 units.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 9

The sum of three numbers is 132. The first number is twice the second and the third number is one-third of the first. Find the first number


Detailed Solution for Test: Numeric Entry- 1 - Question 9

Let the second number be 3x.
The first number will be 2*3x = 6x
The third number will be
1/3*6x = 2x 6x+3x+2x = 132
11x=132 x
= 132/11
= 12
The first number will be 6x = 6*12 = 72

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 10

Find the value of [27(2/3)]/[64(-4/3)]. [272=27*27]


Detailed Solution for Test: Numeric Entry- 1 - Question 10

[27(2/3)]/[64(-4/3)] =
[(33)(2/3)]/[(43)(-4/3)]
= [3(3*2/3)]*[4(3*4/3)]
= (32)*(44) = 9*256 = 2304

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 11

    Three-fourth of a number is 150 greater than three-fourteenth of the number. Find the number.


Detailed Solution for Test: Numeric Entry- 1 - Question 11

Let the number be x.
According to the conditions,
3x/4 -150
= 3x/14 x/4 - 50
= x/14 x*14 - 50*4*14
= x*4 14x - 2800
= 4x 10x = 2800 x
= 280

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 12

 

If a/(a+b) = 17/23, then fill in the blank (a+b)/(a-b) = -------/11


Detailed Solution for Test: Numeric Entry- 1 - Question 12

a/(a+b) = 17/23
Hence,
when a+b = 23,
a = 17
Thus,
b = 23
- a = 23 - 17
= 6 (a+b)/(a-b)
= (17+6)/(17-6) = 23/11
Hence, the number to be filled in the blank is 23.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 13

5 men can complete a work in 2 days, 4 women can complete it in 3 days and 5 children can complete it in 3 days. In how many days can 1 man, 1 woman and 1 child complete it working together?


Detailed Solution for Test: Numeric Entry- 1 - Question 13

Work done by one man in 2 days = 1/5
Work done by one man in one day = 1/(5*2) = 1/10
Work done by one woman in one day = 1/(4*3) = 1/12
Work done by one child in one day = 1/(5*3) = 1/15
Work done by one man, one child and one woman in one day
= 1/10+1/12+1/15 = (6+5+4)/(5*2*2*3 )
=15/(15*4) = 1/4
They will take 4 days to complete the work.

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 14

In a kilometer race A can give B a start of 50 meters and B can give C a start of 40 meters. A start of how many meters can A give C in a 2 km race?


Detailed Solution for Test: Numeric Entry- 1 - Question 14

When A completes 1000 meters, B covers 950 meters.
When B completes 1000 meters, C covers 960 meters.
Distance covered by A/ distance covered by B = 1000/950
Distance covered by B/distance covered by C = 1000/960
Distance covered by A = 1000/950 * distance covered by B = 1000/960 * 1000/950*distance covered by C Distance covered by C,
when A covers 2 km =
(950*960)/(1000*1000)*2000
= 1824 metres
A gives C a start of
2000-1824 = 176 meters

*Answer can only contain numeric values
Test: Numeric Entry- 1 - Question 15

On what sum is the difference in compound interest and simple interest for 3 years at 5% per annum Rs.61?


Detailed Solution for Test: Numeric Entry- 1 - Question 15

Let CI and SI be the compound interest and simple interest.
Let P, R, T be the principle, rate and time.
SI = P*R*T/100 = P*3*5/100
= 15P/100 CI = P[(1+R/100)T-1]
= P[(1+5/100)3-1] CI-SI
= 61 P[(21/20)3-1] - 15P/100 = 61 P[9261/8000 -1 -3/20]
= 61 P[(9261-8000-1200)/8000
= 61 P = 61*8000/(61)
= 8000
The sum invested was Rs.8000 [100T=100*100*...T times]

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