divelab/Sys2Bench huggingface dataset:
Question: A man can swim in still water at 5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.78
B)1.667
C)1.15
D)1.5
E)1.2
Rationale: M = 5
S = x
DS = 5 + x
US = 5 - x
5 + x = (5 - x)2
5 + x = 10 -2x
3x = 5
x = 1.667
Answer:B
Answer: B
Question: In the parking lot there are 28 vehicles, 18 of them are buses, and the rest are cars. The color of 14 vehicles is red, of which 11 are buses. How many cars can be found in the parking lot which are not colored red?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The number of cars is 28-18 = 10.
The number of red cars is 14-11=3.
The number of cars which are not red is 10-3=7.
The answer is A.
Answer: A
Question: In how many different number of ways 4 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)A)160
B)B)170
C)C)190
D)D)210
E)E)120
Rationale: 6p2 = 6 × 5 x 4= 120
Option 'E'
Answer: E
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)1245 m^2
B)1345 m^2
C)2520 m^2
D)2560 m^2
E)2678 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: A train crosses a platform of 170 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)A)150m
B)B)170m
C)C)180m
D)D)70m
E)E)350m
Rationale: Length of the train be ‘X’
X + 170/15 = X + 250/20
4X + 680 = 3X + 750
X = 70m
Answer: D
Answer: D
Question: In how many different ways can the letters of the word 'EVE' be arranged?
Options:
A)3 ways
B)20 ways
C)30 ways
D)60 ways
E)40 ways
Rationale: Totally there are 3 letters on the word EVE. it contains 2E,1V.
The no of ways is 3!/2!=3 ways.
ANSWER:A
Answer: A
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
Options:
A)7508
B)7500
C)7506
D)7566
E)7508
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs.7500
Answer: B
Answer: B
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 65520 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
Options:
A)130000
B)12500
C)14000
D)12000
E)None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 65520.
(75/100 * 96/100 * 70/100 * x) = 65520.
=> x = (65520*100*100*100)/(75*96*70) = 130000
Answer : A
Answer: A
Question: In how many different number of ways 4 boys and 4 girls can sit on a bench such that girls always sit together.
Options:
A)A)720
B)B)2000
C)C)2880
D)D)780
E)E)790
Rationale: 2880
Option 'C'
Answer: C
Question: How many values of c in x^2 - 5x + c, result in rational roots which are integers?
Options:
A)23
B)27
C)25
D)12
E)82
Rationale: Explanation:
By the quadratic formula, the roots of x2−5x+c=0x2−5x+c=0 are −(−5)±−52−4(1)(c)−−−−−−−−−−−√2(1)−(−5)±−52−4(1)(c)2(1) = 5±25−4c−−−−−−√25±25−4c2
To get rational roots, 25−4c25−4c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.
Now let 25 - 4c = 1, then c = 6
If 25 - 4c = 9, then c = 4
If 25 - 4c = 25, then c = 0 and so on...
So infinite values are possible.
Answer:C
Answer: C
Question: ? x 48 = 173 x 240
Options:
A)545
B)685
C)865
D)495
E)534
Rationale: Let y x 48 = 173 x 240
Then y = (173 x 240) / 48
=173 x 5
= 865 .
ANSWER :C
Answer: C
Question: What percent of a day is five hours?
Options:
A)20.83%
B)16x1/2%
C)18x2/3%
D)22x1/2%
E)None of these
Rationale: Explanation :
Required percentage = (5/24100)%
= (125 / 6)%.
= 20.83%.
Answer : A
Answer: A
Question: A and B started a business investing Rs. 24,000 and Rs 18,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
Options:
A)4 : 3
B)9:2
C)18:20
D)1:4
E)18:4
Rationale: A: B =24000 : 18000 = 8 : 6 = 4 : 3
ANSWER:A
Answer: A
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)7
C)5
D)9
E)6
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: A
Question: If a man lost 4% by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)1
B)8
C)9
D)4
E)32
Rationale: 96% ---- 48
144% ---- ?
96/144 * 48= 32
Answer: E
Answer: E
Question: Train X and train Y pass one another traveling in opposite directions. Twelve minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?
Options:
A)28
B)40
C)53
D)72
E)80
Rationale: Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30
d=100 and t = 12 min i.e 12/60 hr
using RTD table, (2R+30) * 12/60 = 100 ==> R= 235 miles/hr
So the rate of train X is 265 miles/hr (since R+30)
The distance traveled by Train X in 12 min is R*T = 265 * 12/60 = 53 miles (C)
Answer: C
Question: The forth proportional to 5,8,15 is?
Options:
A)15
B)12
C)18
D)20
E)24
Rationale: Let the fourth proportional to 5,8,15 be x
then 5:8::15:x
5x = 8*15
x = 24
Answer is E
Answer: E
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is?
Options:
A)200
B)400
C)450
D)500
E)None
Rationale: Let the numbers be x and y.
Then, xy = 9375 and x = 15.
y
xy = 9375
(x/y) 15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
Option is B
Answer: B
Question: On a trip, a cyclist averaged 12 miles per hour for the first 18 miles and 10 miles per hour for the remaining 18 miles. If the cyclist returned immediately via the same route and took a total of 7.3 hours for the round trip, what was the average speed (in miles per hour) for the return trip?
Options:
A)8.4
B)8.6
C)8.8
D)9
E)9.2
Rationale: The time to go 36 miles was 18/12+18/10=1.5+1.8=3.3 hours.
The average speed for the return trip was 36 miles/4 hours= 9 mph.
The answer is D.
Answer: D
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are white,black, red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the nine socks?
Options:
A)12
B)15
C)21
D)36
E)72
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
9P2 = 9!/7! = 9*8 = 72 .........Answer is - E
Answer: E
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Options:
A)Rs. 3700
B)Rs. 3800
C)Rs. 3900
D)Rs. 4000
E)Rs. 4900
Rationale: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5 x.
2
15x + 2y = 4000
15x + 2 x 5 x = 4000
2
20x = 4000
x = 200.
So, y = 5 x 200 = 500.
2
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
C)
Answer: C
Question: Consider a Number 3.1n3
n represent the hundredths digit in the number shown above. If the number is rounded to the nearest hundredth, which of the following could be the tenths digit in the rounded number?
Options:
A)2
B)1
C)3
D)4
E)5
Rationale: In this ques we are given the thousandth digit as 3, so the hundreth digit can take any value from 0-9. For the hundreth digit i considered 2 set of values (i) 0, 1, 2, 3 and (ii) 4, 5, 6, 7, 8, 9. Given that the thousandth digit is 3, the hundreth digit has to go up by 0, and correspondingly, the tenth digit should remain same.i.e 0-9.say 1
B
Answer: B
Question: Tomy started a software business by investing Rs.50,000. After 6months, Nanda joined her with a capital of $80,000. After 3years, they earned a profit of $24,500. What was Simran's share in the profit?
Options:
A)$8,500
B)$9,500
C)10,500 dollars
D)$11,500
E)$12,500
Rationale: Tomy : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Tomy 's share = $24500 x	3/7	= $10,500.
C
Answer: C
Question: If the radii of umbra and penumbra cast by an object on a wall are of the ratio 2:6, what is the area of the penumbra ring around the umbra of the latter’s radius is 40 cms?
Options:
A)40288.57 centimeter square
B)40388.57cm^2
C)40488.57cm^2
D)40588.57cm^2
E)40688.57cm^2
Rationale: et the radius of umbra and penumbra are 2k and 6k.
Then as given radius of umbra=40cm
so 2k=40
k=20
radius of penumbra=20*6=120
area of penumbra ring around the umbra= area of penumbra-area of umbra
22/7*[(120)^2-(40)^2]
=40288.57cm^2
ANSWER:A
Answer: A
Question: A circle in the coordinate plane passes through points (-3, -2) and (1, -4). What is the smallest possible area of that circle?
Options:
A)13π
B)26π
C)262√π
D)5π
E)64π
Rationale: The distance between the two points is sqrt(20).
radius = sqrt(20)/2
Area= pi*(sqrt(20)/2)^2
D. 5π
Answer: D
Question: A cube with volume of 125 cm^3 is dropped in a fish tank with dimensions 3 m x 1 m x 2 m. If the tank is full of water, how much water will remain after the cube is droppped?
Options:
A)5.9999999 m^3
B)5.725 m^3
C)5.650 m^3
D)5.999875 m^3
E)5999.725 m^3
Rationale: Volume of fish tank = 3m x 1m x 2m = 6 m^3
125 cm^3 x (1 m^3 / 1,000,000 cm^3) = 0.000125 m^3
6-.000125 = 5.999875 m^3
Answer is D
Answer: D
Question: Two pipes can fill a tank in 20 minutes and 15 minutes. An outlet pipe can empty the tank in 10 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
Options:
A)36
B)42
C)48
D)54
E)60
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/20 + V/15 - V/10 = V/60 per minute
The tank will be filled in 60 minutes.
The answer is E.
Answer: E
Question: The fourteen digits of a credit card are to be written in the boxes shown above. If the sum of every three consecutive digits is 18, then the value of x is :
Options:
A)1
B)3
C)8
D)7
E)9
Rationale: Sol : A
Explanation:
Let us assume right most two squares are a , b
Then Sum of all the squares = 18 x 4 + a + b .......... (1)
Also Sum of the squares before 7 = 18
Sum of the squares between 7, x = 18
and sum of the squares between x , 8 = 18
So Sum of the 14 squares = 18 + 7 + 18 + x + 18 + 8 + a + b (2)
Equating 1 and 2 we get x = 3
Answer:B
Answer: B
Question: f(x) = 1/(1-x) find(f(f(f(x)))
Options:
A)1
B)x
C)2x
D)3x
E)0
Rationale: f(x) = 1/(1-x)
==>f(f(x)) = f(1/(1-x))
= 1/(1-(1/(1-x)))
= 1/((1-x-1)/(1-x))
= 1/(-x/(1-x))
= x-1/x
==> (f(f(f(x)))=f(x-1/x)
= 1/(1-(x-1/x))
= 1/((x-x+1)/x)
= 1/(1/x)
= x
ANSWER:B
Answer: B
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.192 in 4 Years?
Options:
A)5%
B)6%
C)3%
D)9%
E)1%
Rationale: 192 = (800*4*R)/100
R = 6%
Answer: B
Answer: B
Question: A children's gift store sells gift certificates in denominations of $3 and $5. The store sold 'm' $3 certificates and 'n' $5 certificates worth $93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?
Options:
A)5
B)7
C)6
D)31
E)18
Rationale: Explanatory Answer
Step 1: Key data
1. Total value of all certificates sold = $93.
2. Certificates sold were in denominations of $3 and $5.
3. Both 'm' and 'n' are natural numbers.
Step 2: Approach
The value of all certificates sold, 93 is divisible by 3.
So, a maximum of 31 $3 certificates and no $5 certificates could have been sold.
However, the question states that both 'm' and 'n' are natural numbers.
Hence, at least 1 $5 certificate should have been sold.
Let us reduce the number of $3 certificates from theoretical maximum count of 31 by say 'x' and correspondingly increase $5 certificates by 'y'.
Evidently, 3x = 5y because the value of $3 certificates reduced should be the same as the value of $5 certificates increased.
It means that x has to be a multiple of 5 and y has to be a multiple of 3.
Or $3 certificates reduce in steps of 5 certificates.
Step 3: List down possibilities
The following combinations are possible
1. m = 26, n = 3
2. m = 21, n = 6
3. m = 16, n = 9
4. m = 11, n = 12
5. m = 6, n = 15
6. m = 1, n = 18
An alternative way to think of the same concept - Replacing five $3 certificates with three $5 certificates leads to no change in the overall value of certficates sold and gives us a new combination each time. We need to see how many such combinations are possible.
Answer C
Answer: C
Question: A pump can fill a tank with a water in 2 hours. Because of a leak, it took 3 and 1/3 hours to fill the tank. The leak can drain all the water of the full tank in how many hours?
Options:
A)5 hrs
B)7 hrs
C)12 hrs
D)14 hrs
E)16 hrs
Rationale: The rate of the pump + leak = 3/10
1/2 - leak's rate = 3/10
leak's rate = 1/5
The leak will empty the tank in 5 hours.
The answer is A.
Answer: A
Question: A man counted his animals, 80 heads and 250 legs (ducks and goats). how many goats are there?
Options:
A)30
B)40
C)50
D)45
E)70
Rationale: let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=250 and divide 2d+4g=250 by 2 we get d+2g=125 -----------> eq2
subtract eq1 from eq2
we get no of goats=45
ANSWER:D
Answer: D
Question: To asphalt 1km road, 30 men spent 12 days working 8 hours per day. How many days, 20 men will spend to asphalt a road of 2km working 8 hours a day?
Options:
A)40
B)36
C)42
D)44
E)46
Rationale: Man-hours required to asphalt 1 km road=30*12*8=2880
Man-hours required to asphalt 2 km road=2880*2=5760
Man-hours available per day=20*8=160
Therefore number of days=5760/240=36 days
Ans=B
Answer: B
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
Options:
A)1000
B)2288
C)2777
D)2999
E)2711
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer:A
Answer: A
Question: During the second quarter of 1984, a total of 4,976,000 domestic cars were sold. If this was 24% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
Options:
A)714,240
B)2,261,760
C)2,400,000
D)3,690,240
E)4,012,903
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 24% greater than the number sold during the first quarter = (1 + 24/100)x = 1.24 x
1.24 x = 4,976,000
=> x = 4,012,903
So, answer will be E
Answer: E
Question: One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
Options:
A)600/53km/h
B)1200/53 km/h
C)1800/53 km/h
D)1600/53 km/h
E)None of these
Rationale: Solution: Let distance be 120 KM, hence 30 KM is covered by @ 25 kmph and 40 km covered by @ 30 kmph and rest 50 km has been covered@ 50 km.
Now, average = (120/total time taken);
= {120/[(30/25)+(40/30)+(50/50)}]
= 3600/106 = 1800/53 km/h.
Answer: Option C
Answer: C
Question: I travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours. How long did the first part of my journey last?
Options:
A)4 hours
B)2 hours
C)3 hours
D)2 hours 24 minutes
E)None
Rationale: Explanatory Answer
The total time of journey = 5 hours.
Let 'x' hours be the time that I traveled at 40 kmph
Therefore, 5 - x hours would be time that I traveled at 60 kmph.
Hence, I would have covered x*40 + (5 - x)60 kms in the 5 hours = 240 kms.
Solving, for x in the equation 40x + (5 - x)*60 = 240, we get
40x + 300 - 60x = 240
=> 20x = 60 or x = 3 hours.
Answer C
Answer: C
Question: A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6,7,8,9}. If no digit may be repeated and each password must be at least 8 digits long, how many passwords are possible?
Options:
A)8! + 9!
B)2 x 9!
C)8! x 9!
D)17!
E)18!
Rationale: If we choose the 9 different digits then they can be arranged in 9! ways.
The number of possible 8-digit passwords is 9*8*...*2 = 9!
The total number of passwords is 9! + 9! = 2*9!
The answer is B.
Answer: B
Question: A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 4 for 85 cents. How many were sold at the first rate?
Options:
A)45
B)21
C)9
D)16
E)13
Rationale: This can be solved like a classical mixture problem but numbers are awkward to deal with.
It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 100 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 4.
100 - 45 = 255 => not a multiple of 4 so exclude
100 - 21 = 279 => not a multiple of 4 so exclude
100 -9 = 291 => not a multiple of 4 so exclude
100 - 16 = 284 => a multiple of 4 so keep
100 - 13 = 287 => not a multiple of 4 so exclude
Hence, answer choice 16 is correct.
D
Answer: D
Question: The price of an item is discounted 5 percent on day 1 of a sale. On day 2, the item is discounted another 5 percent, and on day 3, it is discounted an additional 10 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
Options:
A)80%
B)82.5%
C)83%
D)84%
E)85.5%
Rationale: Let initial price be 100
Price in day 1 after 5% discount = 95
Price in day 2 after 5% discount = 90.25
Price in day 3 after 10% discount = 81.23
So, Price in day 3 as percentage of the sale price on day 1 will be = 81.23/95*100 => 85.5%
Answer will definitely be (E)
Answer: E
Question: If 8 boys can color 48 m long cloth in 2 days, then 6 boys can color 36 m long cloth in
Options:
A)day
B)days
C)days
D)days
E)days
Rationale: The length of cloth painted by one boy in one day = 96 / 8 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 boys = 36/ 6 × 6 = 1 day.
A)
Answer: A
Question: If the price of a certain computer increased 20 percent from d dollars to 351 dollars, then 2d =
Options:
A)540
B)585
C)619
D)649
E)700
Rationale: Before Price increase Price = d
After 30% Price increase Price = d+(20/100)*D = 1.2d = 351 (Given)
i.e. d = 351/1.3 = $292,5
i.e. 2d = 2*292.5 = 585
Answer: option B
Answer: B
Question: an article with cost price of 280 is sold at 30% profit. what is the selling price?
Options:
A)198
B)364
C)369
D)207
E)210
Rationale: sp=1.30*280=364
ANSWER:B
Answer: B
Question: After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6500. Find the actual price of the good.
Options:
A)s. 6000
B)s. 9000
C)s. 10800
D)s. 9503
E)s. 9980
Rationale: Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6500
1 = 6500/68.4
100 = (6500*100)/68.4 = Rs. 9503.
Answer: Option D
Answer: D
Question: In the gure below, arc SBT is one quarter of a circle with center R and radius
r. The length plus the width of rectangle ABCR is 8, and the perimeter of the shaded region
is 10 + 3. Find the value of r.
Options:
A)6
B)6:25
C)6:5
D)6:75
E)7
Rationale: Set x = RC and y = AR. It must then be x+y = 8 (by hypothesis) and x2+y2 = r2
(since the rectangle ABCR has one vertex in the circle). The perimeter of the shaded area is
then AS + SBT + TC + AC = (r 􀀀 y) + r=2 + (r 􀀀 x) +
p
x2 + y2 = 3r + r=2 􀀀 (x + y) =
3r + r=2 􀀀 8. All we need to so is solve for r in the equation 18 + 3 = (3 +
2 )r.
correct answer A
Answer: A
Question: If k, (k+200), (k+350), and 15*K are all multiples of V, then V could equal which of the following ?
Options:
A)20
B)V=25
C)V=75
D)100
E)150
Rationale: {Multiple of V} - {Multiple of V} = {Multiple of V}.
(K+200) - k = 200 = {Multiple of V}.
(K+350) - k = 350 = {Multiple of V}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Answer: B
Question: list of salaries of 8 employees are listed below. What is the median salary?
$40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $33,000
Options:
A)$32,000
B)$28,500
C)$30,200
D)$30,800
E)$31,500
Rationale: Ordering the data from least to greatest, we get:
$27,000, $29,000, $30,000, $31,000, $33,000, $35,500, $40,000, $43,000
Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.
$31,000 + $33,000 = $64,000
The median salary is $32,000.
Answer : A
Answer: A
Question: Tharak covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?
Options:
A)3 hours 12 minute
B)2 hours
C)4 hours 40 minutes
D)3 hours 20 minutes
E)3 hours 18 minute
Rationale: Let x be no. Of hours, and he travelled at 20kmph.
And balance distance (8-x)hr at 70kmph.
Total distance=20x+(8-x)hr =400
20x+(8-x)70=400
20x+560-70x=400
20x-70x=400-560
-50x=-160
x=3.2 =3 hr 12minutes
ANSWER:A
Answer: A
Question: In how many different ways can 5 girls and 4 boys form a circle such that the boys and the girls alternate?
Options:
A)576
B)425
C)215
D)321
E)None of these
Rationale: Explanation :
In a circle, 5 boys can be arranged in 4! ways
Given that the boys and the girls alternate.
Hence there are 4 places for girls which can be arranged in 4! ways
Total number of ways = 4! x 4! = 24 x 24 = 576. Answer : Option A
Answer: A
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
Options:
A)Rs. 1851
B)Rs. 1941
C)Rs. 1951
D)Rs. 1961
E)Rs. 1861
Rationale: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25) = Rs. 17576 C.I. = 17576 - 15625 = Rs. 1951.
ANSWER:C
Answer: C
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
Options:
A)Rs. 3100
B)Rs. 6240
C)Rs. 6500
D)Rs. 9600
E)Rs. 8600
Rationale: To get Rs. 10, Investment is 96
To get Rs. 650, investment is (96/10)*650 = 6240
ANSWER:B
Answer: B
Question: Find the product of place value and face value of 5 in 65231
Options:
A)28000
B)25000
C)27000
D)26000
E)28000
Rationale: Place value of 5 in 65231 = 5 x 1000 = 5000
Face value = 5
required product = 5000 x 5 = 25000
Answer :B
Answer: B
Question: The average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student. The weight of the student is
Options:
A)62 kg
B)60 kg
C)64 kg
D)72 kg
E)None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 8 kg
=> (96-x)/4 = 8
=> x = 64
Answer : C
Answer: C
Question: The cost of 4 bags and 12 purses is Rs.1520, what is the cost of 10 bags and 30 purses?
Options:
A)Rs.3600
B)Rs.3500
C)Rs.3800
D)Rs.3900
E)None of these
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.1520
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.3800.
Answer: Option C
Answer: C
Question: Johnny travels a total of one hour to and from school. On the way there he jogs at 4 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour. How far is it to the school?
Options:
A)2 miles
B)6.6 miles
C)4.8 miles
D)8 miles
E)10 miles
Rationale: Answer: B) 6.6 miles.
Average speed for round trip = 2*a*b/(a+b), where a,b are speeds
so, average speed was = 2*4*20/(4+20) = 6.6m/hr
the distance between schoolhome should be half of that. ie. 6.6 miles
answer B
Answer: B