divelab/Sys2Bench huggingface dataset:
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1200. How many workers were part of the latter production run?
Options:
A)A)6
B)B)14
C)C)11
D)D)15
E)E)23.5
Rationale: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1200 .. thus for the current period = 1200 -500 = 700
(5n+45)K= 700
k = 700/5n+45........................................2
equate 1 and 2
500/5n+20 = 700 /5n+45
500(5n+45) = 700(5n+20)
25n + 225 = 35n + 140
-10n = -85
n = 8.5
thus n+5 = 14
hence B
Answer: B
Question: a series of natural number 1+2+3+4+5+6+7+8+9+10 is divisibel by 11 so we has to find how many such series is possible upto n where n is less than 1000.
Options:
A)90
B)99
C)180
D)96
E)92
Rationale: the total multiple of 11 less then 1000 are 90 .
and for every multiple there are two such series which are divisible by 11.
. .
. sum of series = n(n+1)/2
for multiple 11 we can take n=10 and 11
for 22 '' '' ''' n=21 and 22
and so on and for 990 multiple of 11 we can take n=989 and 990
so total series formed are 90*2= 180
ANSWER:C
Answer: C
Question: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number G of people surveyed by the company?
Options:
A)46
B)G=80
C)G=90
D)G=100
E)200
Rationale: 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
Answer: D
Question: A firm is divided into four departments, each of which contains four people. If a project is to be assigned to a team of three people, none of which can be from the same department,what is the greatest number of distinct teams to which the project could be assigned?
Options:
A)4^3
B)4^4
C)4^5
D)6(4^4)
E)4(3^6)
Rationale: First member: 4*4=16 choices;
Second member: 4*3=12 choices (as one department already provided with a member);
Third member: 4*2=8 choices (as two departments already provided with members);
So, we have: 16*12*8.
Since the order of the members in a team does not matter (we don't actually have 1st, 2nd and 3rd members) then we should divide above by 3! to get rid of duplication: 16*12*8/3!=4^4.
ANSWER:B
Answer: B
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction M of the work will be done by Adam?
Options:
A) 1/4
B) 12/47
C) 1/3
D) 5/12
E) 20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
M>( 60/47 *12)/60 =12/47
Answer B
Answer: B
Question: A car during its journey travels 30 minutes at a speed of 60 kmph, another 45 minutes at a speed of 60 kmph, and 2 hours at a speed of 80 kmph.The average speed of the car is
Options:
A)63.07 kmph
B)64 kmph
C)72.30 kmph
D)64.02 kmph
E)None of these
Rationale: First car travels 30 min at speed of 60 kmph
distance = 60 x 1/2 = 30 m
Then car travels 45 min at a speed of 60 kmph
distance = 45 min at speed of 60 kmph
distance = 60 x 3/4 = 45 m
at last it travels 2 hours at speed of 70 kmph
distance = 80 x 2 = 160 m
Total distance = 30 + 45 + 160 = 235
Total time= 1/2 + 3/4 + 2 = 3.25
Average speed of the car = 235/3.25 = 72.30
ANSWER:C
Answer: C
Question: What is the greatest of 3 consecutive integers whose sum is 21 ?
Options:
A)6
B)7
C)8
D)9
E)5
Rationale: The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 21;
=> 3n = 18;
=> n = 6
The greatest of the three numbers is therefore 6 + 2 = 8 Answer: C
Answer: C
Question: 5357 x 51 = ?
Options:
A)273232
B)273243
C)273247
D)273250
E)273207
Rationale: 5357 x 51	= 5357 x (50 + 1)
= 5357 x 50 + 5357 x 1
= 267850 + 5357
= 273207
E)
Answer: E
Question: Equal weights of two alloys containing tin, copper and lead in the ratio 6:8:7 and 1:2:4 are melted and mixed together. What is the ratio of tin, copper and lead in the resultant alloy?
Options:
A)11:8:3
B)3:1:8
C)17:28:27
D)9:4: 11
E)9:14: 11
Rationale: Let the weight of the two alloys be w each
Required ratio =
(6w/21+1w/7): (8w/21+2w/7 ): (7w/21+4w/7)
= 9w/21 : 14w/21 : 11w/21
= 9:14: 11
ANSWER:E
Answer: E
Question: Which of the following fraction is the smallest?
Options:
A)12/14
B)13/19
C)17/21
D)7/8
E)None of these
Rationale: Explanation:
12/14 = 0.857, 13/19 = 0.684, 17/21 = 0.8095 and 7/8 = 0.875
Since 0.684 is the smallest, so 13/19 is the smallest fraction.
ANSWER: B
Answer: B
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
Options:
A)6620
B)3277
C)2688
D)2998
E)2789
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer:A
Answer: A
Question: A man covers a certain distance by car driving at 30 km/hr and he returns back to the starting point riding on a scooter at 10 km/hr. Find his average speed for the whole journey.
Options:
A)8 Km/hr
B)17 Km/hr
C)15 Km/hr
D)12 km/hr
E)None of these
Rationale: Explanation:
= (2 x a x b)/(a + b)
= (2 x 30 x 10)/(30 + 10)
= (2 x 30 x 10)/40
= 15 km/hr
Answer: Option C
Answer: C
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1125 as rent for parking his cars, what is the total rent paid by all the four agencies?
Options:
A)2388
B)2778
C)1279
D)6150
E)2771
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1125
45k = 1125 => k = 25
246k = 246(25) = Rs. 6150
Thus the total rent paid by all the four agencies is Rs. 6150.
Answer: D
Answer: D
Question: A sum of money at simple interest amounts to Rs. 830 in 3 years and to Rs. 854 in 4 years. The sum is:
Options:
A)647
B)698
C)758
D)847
E)976
Rationale: S.I. for 1 year = Rs. (854 - 830) = Rs. 24.
S.I. for 3 years = Rs.(24 x 3) = Rs. 72.
Principal = Rs. (830 - 72) = Rs. 758.
Answer:C
Answer: C
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 5 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
Options:
A) 60
B) 80
C) 50
D) 120
E) 140
Rationale: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+5=42 members have not passed the test, thus 0.7*Total=35 --> Total=50.
Answer: C.
Answer: C
Question: A company pays project contractors a rate of a dollars for the first hour and b dollars for each additional hour after the first, where a > b.
In a given month, a contractor worked on two different projects that lasted 6 and 8 hours, respectively. The company has the option to pay for each project individually or for all the projects at the end of the month. Which arrangement would be cheaper for the company and how much would the company save?
Options:
A)Per month, with savings of $(5a + 5b)
B)Per month, with savings of $(5a - 5b)
C)The two options would cost an equal amount.
D)Per project, with savings of $(5a + 5b)
E)Per project, with savings of $(5a - 5b)
Rationale: Per Project, company will pay as follows:
For 6 hours work = a+5b
For 8 hours work = a+7b
Total = 2a+12b
Per Month, company will pay for 14 hours work = a+13b
Total per contract - total per month
6a+8b - (a+13b)
5a-5b
Since a>b Amount 6a+8b(per contract amount) > a+13b (per project amount) by 5a-5b.
Hence per month payment will be cheaper by 5a-5b .
OA B
Answer: B
Question: A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
Options:
A)78
B)40
C)68
D)88
E)None
Rationale: EXPLANATION
We have: l = 30 ft and lb = 720 sq. ft.
So, b = 24 ft.
Length of fencing = (l + 2b) = (30 + 48) ft = 78 ft.
Answer A
Answer: A
Question: Car Z travels 45 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
Options:
A)320
B)360
C)400
D)408.3
E)440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 45 miles/hour, the car will run 45 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 36 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 36 miles/gallon * 10 gallons = 360 miles.
Answer B.
Answer: B
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 180meters, after what time will they meet at the starting point?
Options:
A)20sec
B)12sec
C)30sec
D)50sec
E)1min
Rationale: They meet every 180/7+8 = 12sec
Answer is B
Answer: B
Question: 5 skilled workers can build a wall in 20days; 8
semi-skilled workers can build a wall in 25 days; 10
unskilled workers can build a wall in 30days. If a te
am has 2 skilled, 6 semi-skilled and 5 unskilled
workers, how long will it take to build the wall?
Options:
A)15days
B)16days
C)14days
D)18days
E)17days
Rationale: For Skilled
5 workers --------20 days
5 workers 1 day work= 1/20
1 worker's 1 day work= 1/(5*20)
Similarly,
For Semi-Skilled------
1 worker's 1 day work= 1/(8*25)
For Unskilled------
1 worker's 1 day work= 1/(10*30)
For 2 skilled,6 semi-skilled and 5 unskilled
workers
One day work= 2*[1/(5*20)] +6*[1/(8*25)] + 5*[ 1/(10*30)] = 1/15
Therefore no. of days taken= 15
ANSWER:A
Answer: A
Question: Twenty coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
A)2^19
B)2^10
C)3 * 2^8
D)3 * 2^9
E)3 * 2^10
Rationale: Fix the third coin as H. The remaining 19 coins have 2^19 outcomes.
A
Answer: A
Question: The manufacturing cost of a shoe is Rs.180 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
Options:
A)Rs 222
B)Rs 216
C)Rs 220
D)Rs 210
E)Rs 217
Rationale: Explanation :
Total cost of a watch = 180 + (500/100) = 185.
Gain = 20% => SP = 1.2CP = 1.2 X 185 = 222
Answer : A
Answer: A
Question: Shopkeeper rise price by 33% and gives successive discount of 10% and 15%. What is overall % gain or loss?
Options:
A)1.745%
B)4.745%
C)3.745%
D)6.745%
E)7.745%
Rationale: Let d initial price be 100
33 % rise
now price = 133/100*100 = 133
10% discount
Then price = 133 * 90/100 = 119.7
15 % discount
Then price = 119.7 * 85/100 = 101.745
So Gain = 101.745 - 100 = 1.745
Gain % = Gain * 100 /CP
==> 1.745 * 100 /100 = 1.745%
ANSWER:A
Answer: A
Question: A relay race covers 1 1/2 miles,and each runner on a team will run 1/4 of a mile. How many runners are needed for a team?
Options:
A)9
B)6
C)3
D)10
E)4
Rationale: Number of runners=total distance/distance each runner runs
=1 1/2 ÷ 1/4
=3/2 ÷ 1/4 = 3/2*4/1
=12/2
= 6.
Answer is B.
Answer: B
Question: Today Jennifer, who is 30 years old, and her daughter, who is 6 years old, celebrate their birthdays. How many years will pass before Jennifer’s age is twice her daughter’s age?
Options:
A)18
B)20
C)22
D)24
E)25
Rationale: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
After x years passes Jennifer’s age will be (30+x) years old, and her daughter’s age will be (6+x) years old. Since the Jennifer’s age is twice her daughter’s age (30+x)= 2 * (6+x) ---> 30+x=12+2x ---> x= 18.
The answer is (A).
Answer: A
Question: A 3-digit positive integer consists of non zero digits. If exactly two of the digits are the same, how many such integers are possible?
Options:
A)72
B)144
C)216
D)283
E)300
Rationale: here is the answer in pure probability terms.
let the 3 digit number be XYZ
now none of them contain zero --> they can vary from 1 - 9
so lets take the value of X, X can be from 1 - 9, hence X can be selected in 9 ways
since Y =X, after selecting X you can select Y in 1 way only
Z can be an selected from 1 -9 (minus 1 because it cannot be the same as X) in exactly 8 ways
hence total number of ways of selecting the number is 9 * 8 = 72.
BUT we are asked for all possible numbers that can be formed.
So XYZ ( or XXZ in this case) can be moved around in 3 ways
XXZ
XZX
ZXX
hence the total number of numbers is 72 *3 = 216
ANSWER:C
Answer: C
Question: There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
Options:
A)320
B)120
C)400
D)420
E)514
Rationale: Sol. Let the original average expenditure be Rs. x. Then,
42 (x - 1) - 35x=42	ïƒ³	7x= 84	ïƒ³	x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
ANSWER D
Answer: D
Question: How many odd numbers are possible between 1 to 10000000? find out the number of odd number of digits?
Options:
A)2999
B)3500
C)4000
D)4599
E)4999999
Rationale: There are always one odd and one even no. And the question is odd no. Between 1 to 10000000
So we have to find no. Between 1 to 10000 so we should not includes 1
10000000/2 -1=4999999
ANSWER:E
Answer: E
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 3.5t seconds, then what is the length of the platform?
Options:
A)0.5L
B)1.5L
C)2.5L
D)3.5L
E)4.5L
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 3.5t
(L+P) / (L/t) = 3.5t
P = 2.5L
The answer is C.
Answer: C
Question: In how many days does B alone complete the work
1. B and C together can complete the work in 8 days
2. A and B together can complete the work in 12 days
Options:
A)Statement 1 alone is sufficient
B)Statement 2 alone is sufficient
C)Statement 1 and 2are sufficient
D)Statement 1 and 2are not sufficient
E)None of these
Rationale: Explanation:
We cannot find the work done by B.
If C+A work is given we can find it by
B’s work = (A+B+C) work - (A+C) work
Answer: Option D
Answer: D
Question: A project scheduled to be carried out over a single fiscal year has a budget of $12,600, divided into12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was $5,580. By how much was the project over its budget?
Options:
A) $380
B) $540
C) $1,050
D) $1,380
E) $1,430
Rationale: Difficulty level: 600
Each month's budget = 12600/12 = 1050
Budget for 4 months = 4*1050 = 4200
Actual amount spent = 5580
Amount spent over the budget = 5580 - 4200 = 1380
Answer (D),
Regards,
Answer: D
Question: A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by 1/2. What is the number of students in the class?
Options:
A)20
B)30
C)10
D)40
E)50
Rationale: Let the total number of students = x
The average marks increased by 1/2 due to an increase of 83 - 63 = 20 marks.
But total increase in the marks = (1/2)x=x/2
Hence we can write as
x/2=20
⇒x=20×2=40
Answer is D.
Answer: D
Question: The length of a rectangle is halved, while its breadth is tripled. Wat isthe % change in area?
Options:
A)20%
B)40%
C)50%
D)60%
E)70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: C
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 10 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
Options:
A)80%
B)105%
C)120%
D)124.2%
E)138%
Rationale: 0,08R = x/100*0.1R
Answer A
Answer: A
Question: Can you solve it?
2+3=8,
3+7=27,
4+5=32,
5+8=60,
6+7=72,
7+8=??
Options:
A)68
B)78
C)88
D)98
E)56
Rationale: 2+3=2*[3+(2-1)]=8
3+7=3*[7+(3-1)]=27
4+5=4*[5+(4-1)]=32
5+8=5*[8+(5-1)]=60
6+7=6*[7+(6-1)]=72
therefore
7+8=7*[8+(7-1)]=98
x+y=x[y+(x-1)]=x^2+xy-x
correct answer is D)98
Answer: D
Question: If x and y are positive integers, and 3x^2=3y, then which of the following must be a multiple of 9?
I. x^2
II. y^2
III. xy
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II and III
Rationale: 4x^2 = 3y
since x,y are positive integers, x^2 = x*x is divisible by 3 -> x is divisible by 3 and y is divisible by x^2
-> x^2 and y is divisible by 9 -> y^2 is divisible by 9
(1),(2), and (3) must be true
Answer is A
Answer: A
Question: Find the unit's digit in (264)^102 + (264)^103
Options:
A)4
B)1
C)5
D)0
E)2
Rationale: Required unit's digit = unit's digit in (4)^102 + (4)^103.
Now, 4^2 gives unit digit 6.
Therefore, (4)^102 gives unit digit 6.
Therefore, (4)^103 gives unit digit of the product (6 x 4) i.e., 4.
Hence, unit's digit in (264)m + (264)103 = unit's digit in (6 + 4) = 0.
Answer is D.
Answer: D
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
Options:
A)7
B)2
C)8
D)6
E)3
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
Answer: C
Question: For which of the following does g(a)−g(b)=g(a−b) for all values of a and b?
Options:
A)g(x)=x^2
B)g(x)=x/2
C)g(x)=x+5
D)g(x)=2x−1
E)g(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. g(a) = a^2 and g(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. g(a) = a/2 and g(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: B
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)Rs.345
B)Rs.270
C)Rs.275
D)Rs.324
E)Rs.300
Rationale: Explanation:
I = (500*9*6)/100 = 270
Answer IS B
Answer: B
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)18 2/17
B)18 2/11
C)18 2/15
D)18 2/19
E)18 2/12
Rationale: 13 CP = 11 SP
11 --- 2 CP
100 --- ?
=>18 2/11%
Answer:B
Answer: B
Question: 3+33+333+3.33=?
Options:
A)362.33
B)372.33
C)702.33
D)702
E)None of them
Rationale: 3
33
333
3.33
----------
372.33
----------
Answer is B
Answer: B
Question: How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?
Options:
A)38
B)56
C)22
D)088
E)11
Rationale: Explanation:
Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the numberof years for which it is invested, r is the rate of interest per annum
In this case, Rs. 1250 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 1250 = 8750.
8750 = [(1250 x n x 12.5)/100]
=> n = 700 / 12.5 = 56 years.
Answer: B) 56years
Answer: B
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (3 Ø 1) Ø 2 = ?
Options:
A)2
B)4
C)8
D)16
E)32
Rationale: 3 Ø 1 = 2^3/2^1 = 4
4 Ø 2 = 2^4/2^2 = 4
The answer is B.
Answer: B
Question: The profit obtained by selling an article for Rs. 66 is the same as the loss obtained by selling it for Rs. 52. What is the cost price of the article?
Options:
A)Rs. 40
B)Rs. 50
C)Rs. 49
D)Rs. 59
E)None of these
Rationale: S.P 1- C.P = C.P – S.P 2
66 - C.P = C.P - 52
2 C.P = 66 + 52;
C.P = 118/2 = 59
ANSWER:D
Answer: D
Question: If 13 = 13w/(1-w) ,then (2w)2 =
Options:
A)1/4
B)1/2
C)1
D)2
E)3
Rationale: 13-13w=13w
26w=13
w=1/2
2w=1
2w*2=1*2=2
ANSWER:D
Answer: D
Question: If a*b*c=130, b*c*d = 65, c*d*e=750 and d*e*f=250 the (a*f)/(c*d) = ?
Options:
A)1/2
B)2/3
C)3/4
D)4/3
E)None of these
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/750 => f/c = 1/3
a/d* f/c = 2 * 1/3 = 2/3
Answer : B
Answer: B
Question: A can do a piece of work in 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each.how long will they take it to do working together
8 2/5 hours a day?
Options:
A)3 days
B)4 days
C)5 days
D)6 days
E)7 days
Rationale: A's work per hour=1/63
B's work per hour=1/42
A & B's work per hour together=(1/63)+(1/42)=5/126
so a & B together complete the work in 126/5 hours...
if they work 8 2/5=42/5 hours a day,
it will take (126/5)/(42/5) days=(126/5)*(5/42)=3 days...
ANSWER:A
Answer: A
Question: Find value of x from given equation 2x + 1 = -17
Options:
A)-8
B)-9
C)-7
D)7
E)6
Rationale: 1. Subtract 1 from both sides:
2x + 1 - 1 = -17 - 1
2. Simplify both sides:
2x = -18
3. Divide both sides by 2:
4. Simplify both sides:
x = -9
B
Answer: B
Question: For any integer k greater than 1, the symbol k* denotes the product of all integers between 1 and k, inclusive. If k* is a multiple of 1701 what is the least possible value of k?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: 1701 = 3*3*3*3*3*7
Thus k must include numbers at least up to the number 12 so that there are at least five appearances of 3 (that is: 3, 6, 9=3*3, and 12).
The answer is C.
Answer: C
Question: A, B, K start from the same place and travel in the same direction at speeds of 30 km/hr, 40 km/hr, 100 km/hr respectively. B starts two hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
Options:
A)4.2
B)4.8
C)5.6
D)6.4
E)7.2
Rationale: In 2 hours, A travels 60 km.
B can catch A at a rate of 10 km/hr, so B catches A 6 hours after B starts.
So A and B both travel a distance of 240 km.
C needs 2.4 hours to travel 240 km, so C leaves 5.6 hours after A.
The answer is C.
Answer: C
Question: What is the solution of the equations x - y = 10 and (x + y)-1 = 2 ?
Options:
A)x = 3.2, y = 2.3
B)x = 5.25, y = 4.75
C)x = 2, y = 1.1
D)x = 1.2, y = 0.3
E)None
Rationale: Answer
x - y = 10 ...(i)
and 1/(x + y)-1=2
⇒ 1/ (x + y) = 2
⇒ 2(x + y) =1
⇒ x + y = 1/2 ...(ii)
On solving Eqs.(i) and (ii),we get
x = 5.25
and y = 4.75
Correct Option: B
Answer: B
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)4 years
B)8 years
C)10 years
D)None of these
E)15 years
Rationale: Explanation:
Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20 => x = 4.
Age of youngest child = x = 4 years.
ANSWER IS A
Answer: A