divelab/Sys2Bench huggingface dataset:
Question: A runner runs the 40 miles from Marathon to Athens at a constant speed. Halfway through the run she injures her foot, and continues to run at half her previous speed. If the second half takes her 4 hours longer than the first half, how many hours did it take the runner to run the second half?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: The runner runs the first 20 miles at speed v and the second 20 miles at speed v/2.
The time T2 to run the second half must be twice the time T1 to run the first half.
T2 = 2*T1 = T1+4
T1 = 4 and so T2 = 8.
The answer is C.
Answer: C
Question: Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?
Options:
A)227
B)299
C)266
D)828
E)291
Rationale: Let the parts be x, y and [2379 - (x + y)]
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 2379
10k/11 + 20k/23 + 5k/6 = 2379
k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5
x = [10/11 * (3 * 11 * 23 * 6)/5] = 828
Hence, the first part is Rs. 828.
Answer: D
Answer: D
Question: A person covered one-fourth of the total distance at 18 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)21 (1/18)
B)21 (1/13)
C)21 (8/13)
D)22 (2/13)
E)21 (4/13)
Rationale: Let the total distance be x km
total time taken = (x/4)/18 + (3x/4)/24 = 13x/288
Average speed = x/(13x/288) = 22 (2/13)kmph.
Answer: D
Answer: D
Question: Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 12?
Options:
A)5x + 4y = 7
B)3x – 4y = 25
C)4y – 3x = 2
D)1.5y + 2x = 11
E)8x – 6y = 12
Rationale: Perpendicular lines have slopes which are negative reciprocals of each other.
The line 3x + 4y = 12 in slope-intercept form is y = -(3/4)x + 3
The slope of this line is - 3/4.
The slope of a perpendicular line is 4/3.
8x - 6y = 12 in slope-intercept form is y = (4/3)x - 2
The answer is E.
Answer: E
Question: The average of 10 consecutive odd numbers is 22. What is the sum of the first 3 numbers?
Options:
A)13
B)45
C)17
D)220
E)90
Rationale: 22 = (n + n+2 + n + 4 + ... + (n + 18))/10
22 = (10n + (2 + 4 + ... + 18))/10
220 = 10n + 2(1 + 2 + ... + 9)
220 = 10n + 2(9)(10)/2
220 = 10n + 90
220 - 90 = 10n
130 = 10n
n = 13
So the first three numbers are 13, 15, 17
13 + 15 + 17 = 45
Option B
Answer: B
Question: How many three digit numbers Q are divisible by 78 or 91?
Options:
A)17
B)19
C)20
D)21
E)22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples Q --11+9 -1 =19.
Hence Answer is 19.B
Answer: B
Question: How many positive integers less than 5,000 are evenly divisible by neither 17 nor 21?
Options:
A)4,514
B)4,480
C)4,521
D)4,428
E)4,349
Rationale: integers less than 5000 divisible by 17 5000/17 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 17 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 17 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4480 answer B.
Answer: B
Question: A trade analyst announced 8% reduction in the unit price of bike. As a result, the sales volume went up by 20%. What was the net effect on the sales revenue?
Options:
A)no change
B)decreases by 10.4%
C)increases by 10.4%
D)increases by 10%
E)None of these
Rationale: Explanation :
Reduction of price = (100 -8)% = 92% = 0.92
Increase of sale = (100+20)% = 120% = 1.20
Total effect = 0.92 X 1.20 = 110.4%, Increases by 10.4%
Answer : C
Answer: C
Question: What least number should be added to 1057, so that the sum is completely divisible by 23
Options:
A)A)4
B)B)1
C)C)2
D)D)3
E)E)5
Rationale: Explanation:
(1057 / 23) gives remainder 22
22 + 1 = 23, So we need to add 1
Answer: Option B
Answer: B
Question: If 3 taps are opened together a tank is filled in 3 hrs. One of the taps alone can fill it in 10 hrs. and another in 15 hrs. In how many hours will the third tap fill it ?
Options:
A)7 hrs.
B)4 hrs.
C)5 hrs.
D)6 hrs.
E)8 hrs.
Rationale: Part filled by three taps together in 1 hr =1/3 Part filled by one of the tap in 1 hr =1/10 Part filled by another tap in 1 hr =1/15 Part filled by third tap in 1 hr =1/3-(1/0+1/15) =5/30 Therefore the third tap can fill the whole tank in : 30/5 hrs. =6 hrs. Answer : D
Answer: D
Question: In the middle of a round pool lies a beautiful water lily. The water lily doubles in size every day. After exactly 20 days, the lily will cover the complete pool. After how many days will the water lily cover half of the pool?
Options:
A)16
B)18
C)19
D)10
E)20
Rationale: C
Because the water lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, after 19 days.
Conclusion: after 19 days, the water lily will cover half of the pool.
Answer: C
Question: There are two sections A and B of a class, consisting of 36 and 44 students respectively. If the average weight of sections A is 40 kg and that of section b is 35 kg. Find the average weight of the whole class?
Options:
A)36.25
B)37.25
C)38.25
D)17.25
E)27.25
Rationale: 36*40=1440
44*35=1540
1440+1540=2980
2980/(36+44)=37.25
ANSWER:B
Answer: B
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train?
Options:
A)150 meter
B)876 meter
C)200 meter
D)719 meter
E)169 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12
= 200 meter
Answer: C
Answer: C
Question: If both m and n are negative integers, which of the following must be positive?
Options:
A)m/n-1
B)m(n+1)
C)mn-5
D)m^2+n^2-1
E)mn+3n
Rationale: Given m and n are negative integers.
Now take m = -1 and n = -1. sub these values in options..
A) m/n-1 = -1/-1 - 1 = 0.
B. m(n+1) = 0
C. mn-5 = -4
D. m^2+n^2-1 = 1
E. mn+3n = -4
If we take any negative value , say m = -1 or n = -2 etc..only D satisfies...
ANSWER:D
Answer: D
Question: If a/x = 1/5 and a/y =1/ 4, then (x + y) =
Options:
A)A)2a
B)B)a/2
C)C)6a
D)D)7a
E)E)9a
Rationale: Ratio 1:
5a = x
Ratio 2:
4a = y
x+y = 9a
Answer is E
Answer: E
Question: Which fraction should be added to:
1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ....... + 1/(27 Ã— 28)
so that the result is equal to 1?
Options:
A)11/28
B)13/28
C)15/28
D)17/28
E)19/28
Rationale: The given expression
= 1/(2 Ã— 3) + 1/(3 Ã— 4) + 1/(4 Ã— 5) + ...... + 1/(27 Ã— 28)
= (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + .......... + (1/27 - 1/28)
= 1/2 - 1/28 = 13/28
Thus, the fraction we should add = 1 - 13/28 = 15/28
The answer is C.
Answer: C
Question: A part of certain sum of money is invested at 10% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
Options:
A)4:2
B)4:8
C)4:3
D)4:0
E)6:5
Rationale: 12:10
= 6:5
Answer: E
Answer: E
Question: A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days?
Options:
A)3.75 days
B)3.99 days
C)2.99 days
D)2.98 days
E)2.44 days
Rationale: 1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer: A
Answer: A
Question: A college has classes from 10:00 AM until 1:50 PM. In this duration, there are five periods. If 5 minutes are provided between each period to leave one class and enter the next class, how many minutes long is each period?
Options:
A)38 min
B)41 min
C)40 min
D)42 min
E)52 min
Rationale: The total time is 230 minutes.
There are four breaks of five minutes between the classes for a total of 20 minutes.
The total class time is 210 minutes.
210 / 5 classes = 42 minutes per class
The answer is D.
Answer: D
Question: The current birth rate per thousand is 42, whereas corresponding death rate is 15 per thousand. The net growth rate in terms of population increase in percent is given by
Options:
A).027%
B)27%
C)2.7%
D).0027%
E)none
Rationale: Sol.
Net growth on 1000 = (42 - 15) = 27.
Net growth on 100 = (27/1000 Ã— 100)% = 2.7%.
Answer C
Answer: C
Question: The sum of two numbers is 77. Five times one number is equal to 6 times the other. The bigger of the two numbers is
Options:
A)10
B)42
C)14
D)15
E)60
Rationale: a:b 5:6
a+b=77
5x+6x=77
x=7
then two numbers are 35,42. The bigger number is 42
ANSWER:B
Answer: B
Question: In a ratio, which is equal to 3 : 4, if the antecedent is 12, then the consequent is
Options:
A)6
B)9
C)16
D)10
E)12
Rationale: Sol.
We have 3/4 = 12/x ⇔ 3x = 48 ⇔ x = 16.
∴ Consequent = 16.
Answer C
Answer: C
Question: On dividing 127 by a number, the quotient is 5 and the remainder is 2. Find the divisor.
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: d = (D-R)/Q
= (127 - 2)/5
= 125/5 = 25
A
Answer: A
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)4556
B)2354
C)4576
D)6768
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: Consider a Number 3.1n7
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)1
B)5
C)4
D)3
E)2
Rationale: In this ques we are given the thousandth digit as 6, 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 6, the hundreth digit has to go up by 1, and correspondingly, the tenth digit should increase by one.i.e 0-9.say 2.
E
Answer: E
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
Options:
A)190
B)399
C)372
D)389
E)281
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50
= 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer: B
Answer: B
Question: If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?
Options:
A)42 days
B)22 days
C)32 days
D)82 days
E)72 days
Rationale: C
32 days
Given that 5 women is equal to 8 girls to complete a work.
So, 10 women = 16 girls.
Therefore 10 women + 5 girls = 16 girls + 5 girls = 21 girls.
8 girls can do a work in 84 days then 21 girls can do a work in (8*84/21) = 32 days.
Therefore 10 women and 5 girls can a work in 32 days
Answer: C
Question: Which of the following values is the greatest
Options:
A)a) 30% of 89
B)b) 22% of 78
C)c) 33% of 67
D)d) 44% of 56
E)e) 55% of 45
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says A
Answer: A
Question: How long will a boy take to run round a square field of side 55 meters, if he runs at the rate of 9km/hr?
Options:
A)88sec
B)45sec
C)1min
D)32sec
E)25sec
Rationale: Speed = 9 km/hr = 9*5/18 = 5/2 m/sec
Distance = 55*4 = 220m
Time taken = 220*2/5 = 88sec
Answer is A
Answer: A
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years ?
Options:
A)1 : 3
B)1 : 4
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Solution
22.20
Let the principal be P and rate of interest be R%.
∴ Required ratio =[(pxRx6/100) / (pxRx9/100)]=6PR/9PR
=6/9=2 : 3 .
Answer C
Answer: C
Question: The proportion of copper and zinc in the brass is 13:7. How much zinc will there be in 100 kg of brass?
Options:
A)65 kg
B)35 kg
C)88 kg
D)66 kg
E)44 kg
Rationale: 7/20 * 100
= 35
Answer:B
Answer: B
Question: If a: b = 3:4, b:c = 7:9, c:d = 5:7, find a:d?
Options:
A)5:12
B)7:12
C)3:11
D)5:11
E)7:11
Rationale: Explanation:
a/d = (3/4)*(7/9)*(5/7) => 5/12
ANSWER IS A
Answer: A
Question: A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface.
Options:
A)69 m sqaure
B)49 m sqaure
C)52 m sqaure
D)64 m sqaure
E)None of these
Rationale: Explanation:
Area of the wet surface =
2[lb+bh+hl] - lb = 2 [bh+hl] + lb
= 2[(5*1.40+7*1.40)]+7*5 = 69 m square
Option A
Answer: A
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 40kmph and Prasanna moves southward at a speed of 38 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
Options:
A)11
B)50
C)78
D)27
E)18
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 40kmph x 1hr = 40 km
Total southward Prasanna's distance = 38kmph x 1hr = 38 km
Total distance between Prasanna and Laxmi is = 40 + 38 = 78 km.
Answer: C
Answer: C
Question: A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is:
Options:
A)5m
B)12m
C)13m
D)14.5m
E)15.5m
Rationale: Let, length= x meters and breadth= y meters
Then xy=60 and (x2+y2) + x= 5
Therefore, x=60 and (x2+y2)= (5y-x)2
Or xy=60 and 24y2-10xy=0.
Therefore, 24y2-10*60=0 or y2= 25 or =5.
Therefore, x= (60/5)m= 12m. So, length of the carpet = 12m
ANSWER:B
Answer: B
Question: 6, 11, 21, 36, 56, ?
Options:
A)65
B)78
C)81
D)97
E)98
Rationale: The pattern is + 5, + 10, + 15, + 20,...
Answer : C.
Answer: C
Question: In a survey of 335 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
Options:
A)38/67
B)8/41
C)9/348
D)1/8
E)41/91
Rationale: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------281
Total--104----------------------------335
we have to find not part time and not uninsured . in other words not part time and insured = x/335 = (281-104+13)/335
= 38/67
Answer is A.
Answer: A
Question: What is the next number in the sequence : 12,15,21,24,30,33,39,51 __?
Options:
A)59
B)53
C)57
D)52
E)51
Rationale: next no. = previous + (sum of digits)
12 + (1+2) = 15
15 + (1+5) = 21
21 + (2+1) = 24
24 + (2+4) = 30
30 + (3+0) = 33
33 + (3+3) = 39
39 +(3+9) = 51
51 + (5+1) = 57
ANSWER:C
Answer: C
Question: To get the more profit, which is the best transaction?
Options:
A)C.P. = Rs. 18, profit = Rs. 9
B)C.P. = Rs. 25, profit = Rs. 12
C)C.P.= Rs. 20, profit = Rs. 8
D)C.P.= Rs. 30, profit = Rs. 18
E)None of these
Rationale: Explanation :
Solution: (A) Profit% = (9*100/18) =50%.
(B) profit% = (12*100/25) = 48%.
(C)profit% = (8*100/20) = 40%.
(D) profit% = (18*100/30) = 60%.
From the above results clearly, (D) is the best transaction.
Answer : D
Answer: D
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
Options:
A)2700
B)2900
C)3000
D)3100
E)3500
Rationale: Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
= 45 divided by 100x6000 =2700
Answer: Option A
Answer: A
Question: Suppose that we have the following set of equations
log2 x + log3 x + log4 x = 20
log4 y + log9 y + log16 y = 16
Compute logx y.
Options:
A)0.5
B)1.3
C)1.6
D)2.5
E)0.1
Rationale: We rewrite the rst equation as
20 = log2 x + log3 x + log4 x
20 =
log x
log 2
+
log x
log 3
+
log x
log 4
20 = log x (log2 10 + log3 10 + log4 10)
Similarly, we obtain that
16 = log y (log4 10 + log9 10 + log16 10)
16 = log y (log2
p
10 + log3
p
10 + log4
p
10)
16 =
1
2
log y (log2 10 + log3 10 + log4 10)
32 = log y (log2 10 + log3 10 + log4 10)
Dividing both equations by each other, we obtain
32
20
=
log y
log x
log2 10 + log3 10 + log4 10
log2 10 + log3 10 + log4 10
8/5
= logx y=1.6
correct answer C
Answer: C
Question: How much time does a train 160 metres long running at 72 km/hr take to pass a pole?
Options:
A)8s
B)2.5s
C)7.5s
D)7.6s
E)7.4s
Rationale: Explanation:
72 km/hr = 72 * 5/18 = 20 m/s
Speed = distance/time; v = d/t
20 = 160/t
t = 8s
ANSWER: A
Answer: A
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)1/113
B)1/117
C)1/216
D)2/113
E)2/117
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: To be eligible for retirement benefits at the Sieman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 66. If x, where x <66, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?
Options:
A)2x+2y=66
B)x+y=66
C)x+2y=66
D)2x+y=66
E)xy=66
Rationale: We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.
Now,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=66.
Answer: C
Answer: C
Question: A girl sold a book at a profit of 7%. Did she sold it for Rs.7.50 more, 22% would have been gained. Find the CP?
Options:
A)30%
B)40%
C)50%
D)55%
E)60%
Rationale: 50%
C
Answer: C
Question: The ratio of the ages of a man and his wife is 4:3. After 4 years,the ratio will be 9:7.If at the time of marriage the ratio was 5:3,then how many years ago were they married ?
Options:
A)8
B)10
C)12
D)14
E)15
Rationale: let the present ages of the man and his wife be 4x and 3x
then (4x+4)/(3x+4)= 9/7
[since given that after four years their ages will be 9/7]
by solving it we have x=8
so their present ages are 32 and 24 respectively
now suppose if they were married X years ago,
then (32-X)/(24-X)=5/3
by solving it we have 2X=24
so X=12
so they were married 12 years ago
ANSWER:C
Answer: C
Question: The center of a circle lies on the origin of the coordinate plane. If a point (x, y) is randomly selected inside of the circle, what is the probability that x > y?
Options:
A)1/8
B)1/6
C)3/8
D)1/2
E)3/4
Rationale: The line y=x divides the circle into two equal areas.
All the points below the line y=x satisfy the condition that x > y.
The answer is D.
Answer: D
Question: The least number which when increased by 8 each divisible by each one of 24, 32, 36 and 54 is :
Options:
A)427
B)859
C)869
D)856
E)None of these
Rationale: Solution
Required number = (L.C.M. of 24, 32, 36, 54) - 8 = 864 - 8 = 856. Answer D
Answer: D
Question: The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his wife?
Options:
A)6:9
B)6:5
C)6:8
D)6:2
E)6:1
Rationale: Let the present ages of Anil and his son be 7x and 3x years respectively.
Let the present age of the son's mother be m years.
(m + 6) / (3x + 6) = 2/1
m + 6 = 6x + 12 => m = 6x + 6
Ratio of the present ages of Anil and the son's mother = 7x / (6x + 6).
This cannot be found uniquely.
Answer:D
Answer: D
Question: What will be the remainder when (27^27) + 27 is divided by 28?
Options:
A)22
B)20
C)24
D)26
E)28
Rationale: x^n + 1 will be divisible by x+1 only when n is odd
27^27+1 will be divisible by 27+1
(27^27+1)+26, when divided by 28 will give 26 as remainder
Answer is D
Answer: D
Question: A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
Options:
A)205
B)200
C)180
D)195
E)None of these
Rationale: Explanation :
Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
Cloth0.128:25}::1:x
⇒0.128x=25
⇒x = 25/128 = 25000/128 = 3125/16 ≈ 195. Answer : Option D
Answer: D
Question: In a recent election, Geoff received 1 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,571 more votes to win the election, what is the value of x ?
Options:
A) 50
B) 54
C) 56
D) 60
E) 60.5
Rationale: Word problems are tricky in somehow more than other problem because you have the additional step to translate.
Breaking the problem: Geoff how many votes he receives ?? 60 votes
he needs 3571 more votes so : 60+3571= 3631
Now what's the problem wants ?? a x %........3631 is what % of total votes 6000........translating: 3631 = x/100 * 6000 ---> x = 60.51666666
x= 60.5 %..........E
Answer: E
Question: Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1320, how much does he invest in 12% stock at Rs. 120?
Options:
A)s. 4000
B)s. 4500
C)s. 5500
D)s. 6000
E)s. 6500
Rationale: Let investment in 12% stock be Rs. x.
Then, investment in 15% stock = Rs. (12000 - x).
12/120 * x + 15/125 * (12000- x) = 1320
x/10 + 3/25(12000-x) = 1320
5x + 72000 - 6x = 1320 x 50
x = 6000.
Answer = D
Answer: D
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)26 sec
B)28 sec
C)48 sec
D)72 sec
E)12 sec
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer:C
Answer: C
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)79.7 km/hr
B)89.2 km/hr
C)79.3 km/hr
D)79.2 km/hr
E)49.2 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: D
Answer: D
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 48 inches. Find b.
Options:
A)8
B)16
C)24
D)32
E)48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) and "b" is 4 (=2^2), so "b"=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) and "b" is 48 (2^4*3), so "b"=2^4 or 2^4*3 (16 or 48).
Combining 2 premises shows the answer is B(16).
Answer: B
Question: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 450 players took part in that tournament.
How many matches were played?
Options:
A)449 matches.
B)88 matches.
C)77 matches.
D)66 matches.
E)55 matches.
Rationale: Solution:
449 matches.
The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 449 matches were played.
Answer A
Answer: A
Question: The average of 11 results is 51, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
A)A)46
B)B)45
C)C)66
D)D)76
E)E)74
Rationale: 1 to 11 = 11 * 51 = 561
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 561 = 45
Answer:B
Answer: B