divelab/Sys2Bench huggingface dataset:
Question: Cars emerging from a motorway arrive at a junction that splits the road into two separate lanes. The number of cars per hour that continue in either lane is constant. If 35 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane per hour. Alternatively, if 35 cars per hour were diverted from the right lane to the left lane, the number of cars entering the left lane per hour would be four times as great as the number of cars entering the right lane per hour. How many cars enter the left lane per hour?
Options:
A)170
B)140
C)119
D)98
E)85
Rationale: as per question 14 cars diverted from left lane to right lane. Thus we get equation R+35=2(L-35)
as per question 14 cars diverted from right lane to left lane .thus we get equation L+35=4(R-35)
7L =595 THUS L =85
E
Answer: E
Question: If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.
Options:
A)10 km
B)8 km
C)6 km
D)4 km
E)8 km
Rationale: Sol. Let the required distance be x km
Difference in the time taken at two speeds=1 min =1/2 hr
Hence x/5-x/6=1/5<=>6x-5x=6
ïƒ³x=6
Hence, the required distance is 6 km
ANSWER C
Answer: C
Question: A,B,C can do a piece of work in 20days, 30days and 40days respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?
Options:
A)3days
B)1day
C)5days
D)10days
E)7days
Rationale: A+B 1day work = 1/20 + 1/30 = 1/12
A+C 1day work = 1/20 + 1/40 = 3/40
work done in 2 days = 1/12 + 3/40 = 19/120
19/120 work is done by A in 2days
Whole work will be done in 2*19/120 = 3days approximately
Answer is A
Answer: A
Question: In a city 100% votes are registered, in which 60% vote for congress and 40% vote for BJP. There is a person A, who gets 75% of congress votes and 8% of BJP votes. How many votes got by A?
Options:
A)48.9 %
B)78.2 %
C)48.2 %
D)48.7 %
E)48.6 %
Rationale: Assume total votes are 100. So A got
75% of 60 = 45
8% of 40 = 3.2
A total of 48.2 %
Answer:B
Answer: B
Question: A sum fetched a total simple interest of Rs. 2700 at the rate of 6 p.c.p.a. in 3 years. What is the sum?
Options:
A)25000
B)20000
C)18000
D)14000
E)15000
Rationale: Sol.
Principal = Rs. [100 * 2700 / 6 * 3] = Rs. [270000 / 18] = Rs. 15000.
Answer E
Answer: E
Question: If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
Options:
A)16m
B)18m
C)15m
D)14m
E)11m
Rationale: Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (80 * 5) / 25 = 16m
Hence, A beats B by 16m.
ANSWER: A
Answer: A
Question: I gain 70 paise on Rs.70. My gain percent is
Options:
A)0.1%
B)1%
C)7%
D)10%
E)None
Rationale: Solution
Gain%	=(0.70/70×100)%
= 1%.
Answer B
Answer: B
Question: Vinay spends 48% of his monthly income on household items, 22% of his monthly income on buying cloths, 5% of his monthly income on medicines and saves the remaining amount which is Rs. 10000. Find his monthly income.
Options:
A)Rs. 48000
B)Rs. 36000
C)Rs. 50000
D)Rs. 45000
E)None of these
Rationale: Savings 25 % - 12000
Expenditure 75% - 36000
Total - 48000
Answer : A
Answer: A
Question: The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of?
Options:
A)6:6
B)6:3
C)6:5
D)6:8
E)6:1
Rationale: 4:5
3:2
-------
12:15:10
12:10
6:5
Answer: C
Answer: C
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 8 days. In how many days Peter complete the work separately.
Options:
A)20 days
B)27 days
C)23 days
D)25 days
E)24 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 8 days which means that the whole job(1) can be completed in X days.
<=> 8/20->8 <=> X=8/(8/20)=20 Thus the answer is A.
Answer: A
Question: The average (arithmetic mean) of eight numbers is 46.1. If the sum of half of these numbers is 158.4, what is the average of the other half?
Options:
A)12.8
B)24.2
C)52.6
D)72.1
E)96.8
Rationale: arithmetic mean = sum / total numbers
sum = 46.1 * 8 = 368.8
sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum = 368.8-158.4 = 210.4
Arithmetic mean of the 4 nos = 210.4/4 = 52.6
Hence, C is the answer.
Answer: C
Question: In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many Q eggs does the plant process per day?
Options:
A) 100
B) 300
C) 400
D) 3,000
E) 4,000
Rationale: Straight pluggin in for me. As usual, I started with C and got the answer.
Lets' back calculate and see what we get
Let us consider eggs processed each day to be 400
So Initial ratio of eggs processed and rejected is 96:4 or 24:1
So out of 400 eggs, there will be 384 eggs processed and 16 rejected.
Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there Q=384+12=396 eggs accepted and 4 rejected...and the ratio will be 99:1
Bingo...this is what the questions says....
Its always a good idea to start with C.
Answer: C
Question: What is the least number which should be added to 2782 so that the sum is exactly divisible by 5, 6, 4, and 3?
Options:
A)26
B)32
C)38
D)46
E)52
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 2782 by 60, the remainder is 22.
The number to be added = 60 - 22 = 38.
The answer is C.
Answer: C
Question: Bob starts out in his car traveling 30 mph. Four hours later, Mr. Speedster starts out from the
same point at 60 mph to overtake Bob. In how many hours will he catch him?
Options:
A)4 hours
B)6 hours
C)8 hours
D)2 hours
E)9 hours
Rationale: Making the d = rt chart
d = r x t
Bob 30 x + 4
Mr. Speedster 60 x
Since Mr. Speedster traveled the least amount of time, we called that x. This is a TYPE A
problem, the distances are equal.
DBob = DSpeedster
30(x + 4) = 60x
30x + 120 = 60x
120 = 30x
4 = x It will take 4 hours to catch Bob.
correct answer A
Answer: A
Question: Speed of a goods train is 72 km/hr. This train crosses a 250 meter plaƞorm in 26 seconds. Then find
the length of goods train.
Options:
A)250 meters
B)260 meters
C)270 meters
D)280 meters
E)None of these
Rationale: Explanation:
First convert speed from km/hr to m/sec
So, Speed = 72*(5/18) = 20 m/sec
Time = 26 seconds
Let the length of the train be x meters.
We know, Distance = Speed*Time.
[you can remember this formula as remembering DUST = D*ST... Distance=Speed*Time]
x+250 = 20*26
=> x = 270 meters
So length of the goods train is 270 meter
Answer: C
Answer: C
Question: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Options:
A) 4
B) 6
C) 9
D) 10
E) 5
Rationale: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and bottom, hence 4+1 = 5.
E
Answer: E
Question: In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)14 km/hr
B)13 km/hr
C)12 km/hr
D)11 km/hr
E)10 km/hr
Rationale: Let speed of the boat in still water = a and speed of the stream = b
Then
a + b = 14
a - b = 8
Adding these two equations, we get 2a = 22
=> a = 11
ie, speed of boat in still water = 11 km/hr
ANSWER:D
Answer: D
Question: 252 can be expressed as a product of primes as
Options:
A)2 x 2 x 3 x 3 x 7
B)2 x 2 x 2 x 3 x 7
C)3 x 3 x 3 x 3 x 7
D)2 x 3 x 3 x 3 x 7
E)None of these
Rationale: Solution
Clearly, 252 = 2 x 2 x 3 x 3 x 7.Answer A
Answer: A
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
Options:
A)Rs.429
B)Rs.480
C)Rs.420
D)Rs.418
E)Rs.429
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer:B
Answer: B
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
Options:
A)134456 m
B)144556 m
C)153600 m
D)156680 m
E)167800 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: C
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ?
Options:
A)1288
B)2797
C)3944
D)1299
E)1082
Rationale: Let the side of the square plot be 'a' ft.
Given area of the plot (a x a) = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 x 58 = Rs. 3944.
Answer: C
Answer: C
Question: ----------------YES---------NO----UNSURE Subject M----500--------200-----100 Subject R----400--------100-----300 A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either yes or no or unsure, and the numbers of students who gave these answers are listed in the table above. If 140 students answered yes only for subject M, how many of the students did not answer yes for either subject?
Options:
A)100
B)260
C)360
D)400
E)500
Rationale: Since 140 students answered yes only for subject M, then the remaining 360 students who answered yes for subject M, also answered yes for subject R. So, 360 students answered yes for both subjects.
If 360 students answered yes for both subjects, then 400-360=40 students answered yes only for subject R.
So, we have that:
200 students answered yes only for subject M;
40 students answered yes only for subject R;
300 students answered yes for both subjects;
Therefore 800-(200+40+300)=260 students did not answer yes for either subject.
Answer: B.
Answer: B
Question: In what time will a train 60 m long cross an electric pole, it its speed be 144 km/hr?
Options:
A)2.5 sec
B)2.8 sec
C)7.5 sec
D)2.3 sec
E)1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 60/40
= 1.5 sec.
Answer:E
Answer: E
Question: In a 1000 m race, A beats B by 400 meters or 25 seconds. Find the speed of B?
Options:
A)8
B)9
C)7
D)16
E)2
Rationale: Since A beats B by 400 m or 25 seconds, i
t implies that B covers 400 m in 25 seconds.
Hence speed of B = 400/25 = 16 m/s.
Answer: D
Answer: D
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)
Options:
A)77
B)656
C)20
D)88
E)12
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Answer: C
Question: 60 boys can complete a work in 40 days.how many men need to complete twice the work in 20 days
Options:
A)160
B)170
C)180
D)190
E)240
Rationale: one man can complete the work in 40*60=2400 days = one time work
to Complete the work twice it will be completed in
let M be the no. of worker assign for this therefore the eqn becomes
M*20=2*2400
M=240 workers
ANSWER:E
Answer: E
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 4 out of 5 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
Options:
A)2/25
B)4/75
C)8/75
D)3/5
E)4/5
Rationale: Probability of sand dune blown out = 2/3
Probability that it has treasure = 1/5
Probability that it has lucky coupon = 4/5
total probability = 2/3 * 1/5 * 4/5 = 8/75
ANSWER:C
Answer: C
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 190 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40 sec
E)50 sec
Rationale: Explanation:
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 190 = 550 meter
Time taken to cross the platform = 550/(25/2) = 550×2/25 = 44 seconds
Answer: Option C
Answer: C
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 36m/h. what is the speed of the person while he was going to his office?
Options:
A)8km/h
B)9km/h
C)10km/h
D)11km/h
E)24km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=36
\inline \Rightarrow 1.5k = 36
\inline \Rightarrow k=24km/h
E
Answer: E
Question: I'm building a wall out of square blocks (1 ft x 1 ft) and want the wall to be perfectly square. Currently the unfinished wall has a width of 50 feet and an area of 2000 square feet. How many more blocks do I need to add to make the wall a perfect square with the present width?
Options:
A)200
B)10
C)50
D)500
E)150
Rationale: If the wall has a width of 50 and an area of 2000, then the current height is 2000/50 = 40
We must expand the height to 50 feet by adding 10 more rows.
Each row has a width of 50, so 500 more blocks are required to finish the wall.
The answer is D.
Answer: D
Question: A sum of money at simple interest amount to Rs 720 after 2 years and to Rs 1020 after a further period of 5 years.The sum is:
Options:
A)600
B)450
C)650
D)500
E)550
Rationale: Simple Interest for 5 year = Rs.(1020 - 720) = Rs. 300.
Simple Interest for 2 year = Rs.(300/5×2) = Rs. 120.
Principal = Rs. (720 - 120) = Rs. 600.
ANSWER : A
Answer: A
Question: A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 5 for 85 cents. How many were sold at the first rate?
Options:
A)46
B)21
C)9
D)15
E)12
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 5 at the second rate. You simple subtract the answer choices for the first rate from 300 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 5.
300 - 46 = 255 => not a multiple of 5 so exclude
300 - 21 = 279 => not a multiple of 5 so exclude
300 -9 = 291 => not a multiple of 5 so exclude
300 - 15 = 285 => a multiple of 5 so keep
300 - 12 = 288 => not a multiple of 5 so exclude
Hence, answer choice 15 is correct.
D
Answer: D
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 15 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
Options:
A)61%
B)70%
C)75%
D)85%
E)95%
Rationale: find the product of the two increases: (1.4) * (.15) , which is 1.61 and a 61% increase.
A
Answer: A
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Options:
A)4/5 km
B)9/5 km
C)7/5 km
D)5/5 km
E)4/9 km
Rationale: Explanation:
x/3 – x/4 = 4/60
x = 4/5 km
Answer: Option A
Answer: A
Question: A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?
Options:
A)28%
B)20%
C)38%
D)30%
E)22%
Rationale: 900 ---- 180
100 ---- ? => 20%
Answer:B
Answer: B
Question: The ratio of pens to pencils is 5 to 6. There are 5 more pencils than pens. How many pencils are there?
Options:
A)24
B)30
C)36
D)42
E)48
Rationale: Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 5
x = 5
The number of pencils is 30.
The answer is B.
Answer: B
Question: When magnified 1,000 times by an electron microscope, the image of a certain circular piece of tissue has a diameter of 1 centimeter. The actual diameter of the tissue, in centimeters, is
Options:
A) 0.005
B) 0.002
C) 0.001
D) 0.0005
E) 0.0002
Rationale: It is very easy if x is the diameter, then the magnified length is 1000x.
ince 1000x=1 then x=1/1000=0.001.
The answer is C
Answer: C
Question: If a certain sample of data has a mean of 22.0 and the value 40.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
Options:
A)3.75
B)7.15
C)3.25
D)3.0
E)2.75
Rationale: 40.0 is more than 2.5 standard deviations from 22 --> 40 > 222 + 2.5*{SD} --> 2.5*{SD} < 18 --> {SD} < 7.2. Only option B offers the standard deviation less than 7.2
Answer: B
Answer: B
Question: Find the cost price of an item if by selling at Rs.900, a profit of 20% is made?
Options:
A)Rs.780
B)Rs.720
C)Rs.700
D)Rs.750
E)Rs.729
Rationale: SP = 900
CP = (SP)*[100/(100+P)]
= 900 * [100/(100+20)]
= Rs.720
Answer: B
Answer: B
Question: Rob also compared the Empire State Building and the Petronas
Towers. What is the height difference between the two if the Empire
State Building is 435m tall and the Petronas Towers is 445m tall?
Options:
A)10
B)17
C)23
D)45
E)12
Rationale: 445-435=10.Answer is A.
Answer: A
Question: A boat can travel with a speed of 22 km/hr in still water. If the speed of the stream is 5 km/hr, find the time taken by the boat to go 216 km downstream
Options:
A)5 hours
B)4 hours
C)3 hours
D)2 hours
E)8 hours
Rationale: Explanation :
Speed of the boat in still water = 22 km/hr
speed of the stream = 5 km/hr
Speed downstream = (22+5) = 27 km/hr
Distance travelled downstream = 216 km
Time taken = distance/speed = 216/27 = 8 hours. Answer : Option E
Answer: E
Question: he average of 30 numbers is zero. Of them, at the most, how many may be greater than zero?
Options:
A)29
B)1
C)10
D)30
E)8
Rationale: Average of 30 numbers = 0.
Sum of 30 numbers (0 x 30) = 0.
It is quite possible that 29 of these numbers may be positive and if their sum is a the 30th number is (-a).
Answer: Option A
Answer: A
Question: What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12% p.a.?
Options:
A)Rs.10123.67
B)Rs.10123.08
C)Rs.10123.20
D)Rs.10123.22
E)Rs.10123.12
Rationale: Amount = [25000 * (1 + 12/100)3]
= 25000 * 28/25 * 28/25 * 28/25
= Rs. 35123.20
C.I. = (35123.20 - 25000)
= Rs.10123.20
Answer: C
Answer: C
Question: If the quantity 2^2+ 2^4 + 2^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
Options:
A)12
B)9
C)4
D)2
E)5
Rationale: (a+b)(a-b) = a^2 - b^2
2^2+ 2^4 + 2^6 = 2^2 (1+2^2+2^4)
if the above expression is solved even then every term of the expression will remain a multiple of 2^2 which is out of parenthesis
hence, b must be a multiple of 2^2 i.e. 4
Answer: option C
Answer: C
Question: A train covers a distance of 12 km in 10 min. If it takes 3 sec to pass a telegraph post, then the length of the train is?
Options:
A)70m
B)16 m
C)60 m
D)80 m
E)88 m
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec
= 20 m/sec.
Length of the train = 20 * 3
= 60 m.
Answer: C
Answer: C
Question: If (2x + 1) times (x + 4) is an odd integer, then x must be:
Options:
A)an odd integer
B)an even integer
C)a prime number
D)a composite number
E)a negative integer
Rationale: Solution:
(2x + 1) times (x + 4) means (2x + 1)(x + 4)
(2x + 1)(x + 4) = 2x^2+9x+4
For 2x^2+9x+4 to be odd, 9x+4 must be odd since 2x^2 is always even.
So 9x must be odd, hence x must be odd.
Therefore x is an odd integer.
Answer: A
Answer: A
Question: If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Options:
A)1
B)5
C)3
D)2
E)6
Rationale: log10 5 + log10 (5x + 1) = log10 (x + 5) + 1
log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10
log10 [5 (5x + 1)] = log10 [10(x + 5)]
5(5x + 1) = 10(x + 5)
5x + 1 = 2x + 10
3x = 9=> X = 3
ANSWER C
Answer: C
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
3/11 × [4/3 + 5/4 × ........ 121/120]
3/11 × 4/3 × 5/4 × .... 121/120
121/11 = 11.
A
Answer: A
Question: In an IT company 35% of employees are given Development Department and 40% of employees are given Testing Department and 20% are given both.What is the probability for an employee is given Development or testing department
Options:
A)95%
B)85%
C)55%
D)5%
E)none of these
Rationale: (dUt)=d(n)+t(n)-dnt
=35+40-20
ANSWER:C
Answer: C
Question: Some amount out Rs.7000 was lent at 6% per annum and the remaining was lent at 4% per annum. If
the total simple interest from both the fractions in 5 years was Rs.1600, the sum lent of 6% per annum
was
Options:
A)Rs. 2400
B)Rs. 2200
C)Rs. 2000
D)Rs. 1800
E)None of these
Rationale: Explanation :
Total simple interest received , I = Rs.1600
Principal , p = 7000
period, n = 5 years
Rate of interest, r = ?
Simple Interest, I = pnr100=>1600=7000×5×r100=>r=1600×1007000×5=16035=327%
By the rule of alligation, we have
Rate of interest % from part1 Rate of interest % from part2
6 4
Net rate of interest %
32/7
32/7 - 4 =4/7 6 - 32/7 = 10/7
=> Part1 : part2 = 4/7 : 10/7 = 4 : 10 = 2 : 5
Given that total amount = Rs.7000
The amount lent of 6% per annum (part1 amount) = 7000×27=Rs.2000
Answer : Option C
Answer: C
Question: The average of marks obtained by 120 boys was 37. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
Options:
A)100
B)110
C)120
D)130
E)140
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 37
24X = 4440 - 1800
=> X = 2640/24
X = 110.
Hence, the number of boys passed = 110.
ANSWER:B
Answer: B
Question: The sum of three digits a number is 17. The sum of square of the digits is 109. If we substract 495 from the number, the number is reversed. Find the number.
Options:
A)2,4,2
B)8,3,6
C)2,2,2
D)3,3,4
E)1,3,4
Rationale: Let the number be abc.
Then a + b + c= 17 .....(1)
a2+b2+c2=109a2+b2+c2=109 .....(2)
100a+10b+c -495 = 100c+10b+a ......(3)
From 3, we get a - c = 5
So the possibilities for (a, c, b) are (6,1,10), (7,2,8), (8,3,6), (9,4,4)
From the above, (8,3,6) satisfies the condition.
Answer:B
Answer: B
Question: John is three times as old as Sam. If John will be twice as old as Sam in six years, how old was Sam one years ago?
Options:
A)2
B)4
C)5
D)8
E)16
Rationale: j= 3s
after 6 years
j +6 = 2(s+6)
j= 2s+6
2s +6 = 3s
s= 6
one years ago
s= 6-1= 5
C is the answer
Answer: C
Question: Three numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
Options:
A)5/18
B)5/27
C)7/36
D)5/54
E)7/108
Rationale: The number of ways to select w, x, and y is: 6*6*6=216
The number of ways to choose three different numbers from the set is 6C3=20.
There are six permutations for each group of three different numbers, but only one permutation satisfies w < x < y.
P(w < x < y) = 20/216 = 5/54
The answer is D.
Answer: D