divelab/Sys2Bench huggingface dataset:
Question: Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.55%, what fraction of the products was checked by worker y?
Options:
A)1/3
B)1/4
C)1/5
D)1/6
E)1/8
Rationale: x: 0.5% is 0.05%-points from 0.55%.
y: 0.8% is 0.25%-points from 0.55%.
Therefore the ratio of products checked by y:x is 1:5.
Thus, worker y checked 1/6 of the products.
The answer is D.
Answer: D
Question: The difference between the ages of two persons is 20 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the younger person is?
Options:
A)30
B)35
C)25
D)28
E)32
Rationale: Let their ages be x years and (x+20) years
Then, (x+20) - 15 = 2(x-15)
x +5 = 2x-30
x = 35
Answer is B
Answer: B
Question: 20-5*4^2+15 = ?
Options:
A)287
B)-13
C)-45
D)13
E)None
Rationale: 20-5*4^2+15
= 20-5*16+15
=20-48+15=-45..
C
Answer: C
Question: A car rental company charges for mileage as follows: 3 dollars per mile for the first n miles and 4 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?
Options:
A)5d-n
B)6d-n
C)7d-n
D)8d-n
E)4d-n
Rationale: Total Distance in miles = d
Millage Charge = 3n + (d-n) 4
3n --> For the first n Miles
(d-n)4--> Total no of miles after traveling the first n miles is d-n and the rate after n miles is 4 .
If we solve the equation , We will get 4d-n
Answer : E
Answer: E
Question: In an examination series, which consists of 5 exams, Arvind scored an average of 60 marks in
the first 3 exams and an average of 70 in the last 4 exams, what is the average score of
Arvind for the first and last two exams if his average scores of all the five exams are 65?
Options:
A)31
B)32
C)63
D)64
E)65
Rationale: let a,b,c,d,e be the five exams
(a+b+c+d+e)/5=65
a+b+c+d+e=325
first 3 exams avg is (a+b+c)/3=60
a+b+c=180
d+e=325-180=145
avg of last 4 exams is (b+c+d+e)/4=70
b+c+d+e=280
a=325-280=45
avg of first and last two exams are(a+d+e)/3=(45+145)/3=(190)/3=63.33
ANSWER:C
Answer: C
Question: A bakery has 6 employees. It pays annual salaries of $15,000 to each of 2 employees, $17,000 to 1 employee, and $18,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees?
Options:
A)$16,200
B)$16,500
C)$16,800
D)$17,000
E)$17,400
Rationale: average = 2(15000)+(17000)+3(18000) / 6 = $16,833
The answer is C.
Answer: C
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
Options:
A)9.30 a.m
B)10 a.m
C)10.40 a.m
D)11 a.m
E)11.40 am
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
answer B
Answer: B
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
Options:
A)87 min
B)82 min
C)86 min
D)47 min
E)72 min
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
Answer:D
Answer: D
Question: The greatest number by which the product of three consecutive multiples of 4 is always
Options:
A)384
B)81
C)162
D)243
E)None of these
Rationale: Explanation:
4*8*12 = 384
Option A
Answer: A
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 23 percent are juniors and 75 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
Options:
A)42
B)48
C)56
D)64
E)72
Rationale: 200 are sophomores.
The number of freshmen is 600 - 160 - 0.23(800) = 256
The answer is C.
Answer: C
Question: A shopkeeper sold an article at $1110 and gained a 20% profit. What was the cost price?
Options:
A)$850
B)$875
C)$900
D)$925
E)$950
Rationale: Let x be the cost price.
1.2x = 1110
x = 1110/1.2 = 925
The answer is D.
Answer: D
Question: A traveller makes 3/4 of his journey by train and 2/3 of the rest by car. If he walks the remaining 12 Kms, the total distance traveled by him is
Options:
A)124 Kms
B)134 Kms
C)144 Kms
D)244 Kms
E)None of the above
Rationale: (1-(3/4))(1-(2/3)of distance = 12 km
(1/12) of distance = 12 km
Hence distance = 144 km
ANSWER:C
Answer: C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options:
A)35
B)10
C)40
D)50
E)55
Rationale: Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) = 90 years.
Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.
Husband's present age = (90 - 50) = 40 years.
ANSWER C
Answer: C
Question: In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?
Options:
A)7 : 2
B)7 : 3
C)7 : 5
D)7 : 7
E)7 : 9
Rationale: By the rule of alligation:
Cost of 1 kg pulses of 1st kindCost of 1 kg pulses of 2nd kind
Rs. 15	Mean Price
Rs. 16.50	Rs. 20
3.50	1.50
Required rate = 3.50 : 1.50 = 7 : 3.
Option B
Answer: B
Question: A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
Options:
A)3
B)4
C)6
D)8
E)9
Rationale: Sol.
Let the number be x.
Then, 3(2x +9) = 75
⇔ 2x + 9 = 25
⇔ 2x = 16
⇔ x = 8
Answer D
Answer: D
Question: A woman swims downstream 54 km and upstream 6 km taking 6 hours each time, what is the speed of the woman in still water?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 54 --- 6 DS = 9
? ---- 1
6 ---- 6 US = 1
? ---- 1 M = ?
M = (9 + 1)/2 = 5
Answer:D
Answer: D
Question: can you find the last number in the number sequence given below
10: 10 : 20 : 45 : 110 : 300 :?
Options:
A)870
B)930
C)540
D)630
E)730
Rationale: Correct Answer : B
? = last no * multiplication factor (increase by 0.5 every time) + sum factor (Increase by 5 every time)
10*0.5+5 = 10
10*1.0+10=20
20*1.5+15=45
45*2.0+20=300
300*3.0+30=930
Answer: B
Question: A pump can fill a tank with water in 4 hours. Because of a leak, it took 20 hours to fill the tank. The leak can drain all the water of the tank in?
Options:
A)1
B)3
C)5
D)4
E)2
Rationale: P --> Pump, L ---> Leak
Pipe----------P---------L------------(P-L)--
Time---------4---------x-------------20
*
Rate---------5---------x-------------1
Work-------20---------20-----------20
Time required to empty the tank if leakage present = 20/((5) - 1)
= (20)/(4)
= 5
Ans -C
Answer: C
Question: On what sum of money will be difference between the simple interest and compound interest for 2 years at 5% p.a be equal to Rs. 25
Options:
A)Rs.10000
B)Rs. 20000
C)Rs. 22000
D)Rs. 12000
E)Rs. 14000
Rationale: p(r/100)^2 =25 p(5/100)^2 =25=Rs.10000 Answer : A
Answer: A
Question: A chemist mixes one liter of pure water with x liters of a 40% salt solution, and the resulting mixture is a 20% salt solution. What is the value of x?
Options:
A)1/4
B)1/3
C)1/2
D)1
E)3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 40%
Concentration of salt in the mixed solution = 20%
The pure solution and the salt solution is mixed in the ratio of --> (40 - 20)/(20 - 0) = 1/1
1/x = 1/1
x = 1
Answer: D
Answer: D
Question: A boy was asked to find 7/9 of a x. But he divided the x by 7/9, Thus he got 32 more than theanswer. Find the x.
Options:
A)60
B)61
C)62
D)63
E)65
Rationale: x/7/9 = 9x/7 = 32 + y
Actualy he should do 7x/9 = y
y = (9x/7) - 32
y = (9x - 224)/7
(9x - 224)/7 = 7x/9
81x - 2016 = 49x
81x - 49x = 2016
32x = 2016
x = 63
D
Answer: D
Question: Will must choose a 2-character computer password, consisting of 2 letter from the alphabet , in any order.From how many different passwords can Will choose?
Options:
A)390
B)2,340
C)4,680
D)1300
E)14,040
Rationale: 26C1*25C1 = 650.
=>650 * 2 ! = 1300.
Option E is correct answer...but OA is D.
Answer: D
Question: If John invested $ 2 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
Options:
A)(1.5)^4
B)4(1.5)
C)(1.05)^4
D)(2.05)^4
E)1 + 4(0.05)
Rationale: In this prompt, the answer choices show that we don't actually have to calculate anything - we just need to 'format' the calculation correctly. We're told that the interest is COMPOUNDED ANNUALLY, so we need the Compound Interest Formula, with a Principal of $2, an R of 5% (which would 'translate' as .05) and a T of 4. We'd have....
D
Answer: D
Question: If y = x +2, Find the range of real values of y satisfying the inequalities 16x - 6 > 42 and 7x - 24 < 60"
Options:
A)5 < y < 14
B)3 < y < 12
C)1 < y < 10
D)y < 10
E)y < 12
Rationale: 16x – 6 > 42 => 16x >48 => x>3 ...(1)
And 7x – 24 < 60 = > 7x x 3 and y - 2 5 or y < 14
Combining the above range, we get, 5 < y < 14
ANSWER:A
Answer: A
Question: The sum of the squares of three numbers is 41, while the sum of their products taken two at a time is 20. Their sum is:
Options:
A)10
B)5
C)9
D)15
E)None of these
Rationale: x^+y^2+z^2=138
xy+yz+zx=131
as we know.. (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+zx)
so (x+y+z)^2=41+(2*20)
(x+y+z)^2=81
so x+y+z=9
ANSWER:C
Answer: C
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
Options:
A)-33
B)-34
C)-46
D)45
E)46
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: A
Question: The average age of 20 men in the class is 14.6 years. Five new men join and the new average becomes 15.56 years. What was the average age of five new men?
Options:
A)15.5
B)19.4
C)15.25
D)15.3
E)15.6
Rationale: Total age of 20 men = 14.6 x 20 = 292
Now, total age of 25 men = 389.
Total age of five men added later = 389 - 292 = 97.
Hence, the total average of five men = 97/5 = 19.4
ANSWER:B
Answer: B
Question: Whats the probability of getting 5 Sunday(my favorite day) in a 31 day month ?
Options:
A)3/3
B)2/9
C)6/7
D)1/5
E)3/7
Rationale: E
3/7
Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.
Answer: E
Question: Pipe A can fill a tank in 10 hours, pipe B in 8 hours, and pipe C in 40 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: The part filled by A + B + C in 1 hour
= 1/10 + 1/8 + 1/40
= 10/40 = 1/4
All the three pipes together will fill the tank in 4 hours.
The answer is C.
Answer: C
Question: The diameter of a circle is 4/π. Find the circumference of the circle.
Options:
A)8
B)4 π
C)4
D)6
E)5
Rationale: circumference = 2*pi*r= 2*pi*4/pi
=> 8
A
Answer: A
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)17%
B)77%
C)44%
D)16%
E)47%
Rationale: g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: C
Question: Set E includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: First, reach to the point of getting the equation E : x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: D
Question: There are 138 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
Options:
A)10
B)11
C)12
D)16
E)14
Rationale: IMO 17
Take each answer choice and substract it from 135 and the divided this with 11.
D
Answer: D
Question: In a coconut grove, (x + 4) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 4) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
Options:
A)3
B)4
C)8
D)9
E)None of the above
Rationale: (x+4)×60+x×120+(x−4)×180/(x+4)+x+(x−4)=100
⇒ 360x−480/3x = 100
⇒ 60x = 480 ⇒ x = 8
Answer C
Answer: C
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
Options:
A)700
B)720
C)740
D)760
E)780
Rationale: Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
120x=85(x+2)+40
35x=210
x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720 hectares.
So answer is B.
Answer: B
Question: For a certain exam,a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean.What was the mean score for the exam?
Options:
A)74
B)76
C)78
D)80
E)82
Rationale: Mean-2SD=60
Mean+3SD=100
by solving above we get,
SD (absolute value)=8
Mean=76
Ans. B
Answer: B
Question: Three consecutive even numbers are such that thrice the first number exceeds double the third number by five. What is the third number?
Options:
A)13
B)15
C)17
D)19
E)21
Rationale: Let the three numbers be x, x+2, and x+4.
3x = 2(x+4) + 5
x = 13 and then the third number is x+4 = 17.
The answer is C.
Answer: C
Question: A(n+1)=1+(1/A(n)) and A(1)=1. What is the value of A(8)?
Options:
A)30/17
B)32/19
C)34/21
D)36/23
E)38/25
Rationale: A(n+1)=1+(1/A(n))
A(1) = 1
A(2) = 2
A(3) = 3/2
A(4) = 5/3
A(5) = 8/5
A(6) = 13/8
A(7) = 21/13
A(8) = 34/21
The answer is C.
Answer: C
Question: Present ages of Kiran and Syam are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Syam's present age in years?
Options:
A)20
B)24
C)25
D)28
E)30
Rationale: Ratio = 5:4
age of kiran = 5x
age of syam = 4x
after 3 yrs = 11:9
(5x+3):(4x:3) = 11:9
x=33-27 = 6
syam age= 4x=4*6=24
ANSWER B
Answer: B
Question: How many positive integers will divide evenly into 190?
Options:
A)4
B)6
C)8
D)12
E)16
Rationale: The question is asking how many factors 190 has.
190 = 2*5*19
The number of factors is 2^3 = 8
The answer is C.
Answer: C
Question: Suresh started a business with Rs.20,000. Kiran joined him after 4 months with Rs.30,000. After 2 months, Suresh withdrew Rs.5,000 of his capital and 2 more months later, Kiran brought in Rs.20,000 more. What should be the ratio in which they should share their profits at the end of the year?
Options:
A)21:32
B)32:21
C)12:17
D)17:12
E)None of these
Rationale: Explanation :
Here capital is not the same.
Suresh invest 20000 for initial 6 months and 15000 for the next 6 months.
Hence his term of ratio
=( 20000*6 + 15000*6)
Kiran invest Rs.30000 for 4 months and Rs.50000 for next 4 months.
Hence his term of ration
= (30000*4 : 50000*4)
Suresh : Kiran = ( 20000*6 + 15000*6) : (30000*4 : 50000*4)
= (20*6 + 15*6) : (30*4 + 50*4)
= (20*3 + 15*3) : (30*2 : 50*2)
= 105:160
= 21:32. Answer : Option A
Answer: A
Question: Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 84. Find the third number?
Options:
A)A)37
B)B)85
C)C)48
D)D)43
E)E)84
Rationale: Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 84
6x = 84 => third number is 84.
Answer: Option E
Answer: E
Question: After decreasing 40% in the price of an article costs Rs.1050. Find the actual cost of an article?
Options:
A)1200
B)1750
C)1050
D)1570
E)1005
Rationale: CP* (60/100) =1050
CP= 17.5 * 100 => CP
= 1750
Answer:B
Answer: B
Question: If n is a natural number, then (6n2 + 6n) is always divisible by?
Options:
A)6 and 12 both
B)6 only
C)12 only
D)6 or 12
E)None
Rationale: (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even.
A)
Answer: A
Question: A is twice as fast as B. If B alone can do a piece of work in 30 days, in what time can A and B together complete the work?
Options:
A)10
B)88
C)66
D)28
E)12
Rationale: A can do the work in 30/2 i.e., 15 days.
A and B's one day's work = 1/15 + 1/30 = (2 + 1)/30 = 1/10
So A and B together can do the work in 10 days.
Answer: A
Answer: A
Question: By selling 20 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
Options:
A)80
B)60
C)50
D)30
E)10
Rationale: 80% --- 20
120% --- ?
80/120 * 20 = 30
Answer:D
Answer: D
Question: P is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2P is divided by 4 ?
Options:
A)3
B)2
C)1
D)0
E)-1
Rationale: Let P = 4q + 3. Then 2P = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2P is divided by 4, the remainder is 2.
ANSWER:B
Answer: B
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)11 km/hr
B)50 km/hr
C)76 km/hr
D)88 km/hr
E)17 km/hr
Rationale: :
Speed of the train relative to man = (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: B
Question: Of 30 applicants for a job, 13 had at least 4 years' experience, 18 had degrees, and 3 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
Options:
A)14
B)13
C)9
D)6
E)5
Rationale: D. 6
30 - 3 = 27
27 - 13 - 18 = -6
Then 6 are in the intersection between 4 years experience and degree.
Answer D
Answer: D
Question: The size of a flat-screen television is given as the length of the screen’s diagonal. How many square inches greater is the screen of a square 21-inch flat-screen television than a square 19 -inch flat-screen television?
Options:
A)42
B)40
C)38
D)36
E)48
Rationale: If we take a square with side length x and draw a diagonal, we get two isosceles right triangles.
If we focus on one such right triangle, we see that the legs have length x.
square 21-inch flat-screen television
The diagonal (hypotenuse) = 21
So, we can apply the Pythagorean Theorem to get x² + x² = 21²
Simplify: 2x² = 21²
Divide both sides by 2 to get: x² = 21²/2
Since the area of the square = x², we can see that the area of this square is 21²/2
square 19-inch flat-screen television
The diagonal (hypotenuse) = 19
So, we can apply the Pythagorean Theorem to get x² + x² = 19²
Simplify: 2x² = 19²
Divide both sides by 2 to get: x² = 19²/2
Since the area of the square = x², we can see that the area of this square is 19²/2
DIFFERENCE IN AREAS =21²/2-19²/2
= (21+19)(21-19)/2 =40
B
Answer: B
Question: If a 5 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?
Options:
A)100%
B)200%
C)300%
D)400%
E)500%
Rationale: The area A of the large cube is 5*5*6 = 150 square cm.
The area of the 125 small cubes is 125*6 = 750 = 5A, an increase of 400%.
The answer is D.
Answer: D
Question: A train travels at an average of 40 miles per hour for 4 hours and then travels at a speed of 60miles per hour for 2hours. How far did the train travel in the entire 6 hours?
Options:
A)100miles
B)150miles
C)200miles
D)250miles
E)300miles
Rationale: Total distance traveled = (40*4)+(70*2) = 160+140 = 300 miles
Answer is E
Answer: E
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
Options:
A)20
B)40
C)80
D)100
E)200
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10
x - y = 20 .... (i)
and x + 20 = 2(y - 20)
x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
answer :D
Answer: D
Question: In an exam 80% of the boys and 40% of the girls passed. The number of girls who passed is 120, which is 2/3rd of the number of boys who failed. What is the total number of students who appeared for the exam?
Options:
A)1200
B)380
C)3800
D)2180
E)3180
Rationale: Let the Number of boys = x , Number of girls =y
40y/100 =120
y = 300
120= 2/3* 20x/100 = 2x/15
x = 900
Total = x+y = 300+900 =1200
ANSWER:A
Answer: A
Question: In an examination, 35% candidates failed in one subject and 42% failed in another subject while 14% failed in both the subjects. If 2500 candidates appeared at the end of the examination how many passed in either subject but not in both?
Options:
A)975
B)1020
C)1175
D)1225
E)1525
Rationale: Failed in 1st subject = 35*2500/100 = 875
Failed in 2nd subject = 42*2500/100 = 1050
Failed in both = 14*2500/100 = 350
Failed in 1st subject only = 875-350 = 525
Failed in 2nd subject only = 1050-350 = 700
Passed in either subject but not in both = 700+525 = 1225
Answer is D
Answer: D
Question: A man incurs a loss of 5% be selling a watch for Rs. 1140. what price should the watch be sold to earn 5% profit.
Options:
A)1200
B)1260
C)1350
D)1250
E)1355
Rationale: (100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
= 95/1140 =105/x
= 1260
ANSWER B
Answer: B
Question: The average age of a husband and a wife is 23 years when they were married five years ago but now the average age of the husband, wife and child is 21 years(the child was born during the interval). What is the present age of the child?
Options:
A)7
B)5
C)8
D)4
E)2
Rationale: 28 * 2 = 56
21 * 3 = 63
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7 years.Answer: A
Answer: A
Question: By using the numbers 1, 2, 3, 7 and 9 only once, how many five digit numbers can be made that are divisible by 25?
Options:
A)5
B)4
C)Not possible
D)3
E)6
Rationale: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, not possible.
Answer: C.
Answer: C
Question: If 2log(4*5^2) = x, find x
Options:
A)5
B)6
C)7
D)4
E)8
Rationale: 2(log2^2*5^2)=x
2log(5*2)^2=x
2*2log(5*2)=x
4log10=x
log10 base 10=1
so
4*1=x
x=4
ANSWER:D
Answer: D
Question: A man swims downstream 72 km and upstream 45 km taking 5 hours each time; what is the speed of the current?
Options:
A)1.7
B)2.8
C)3.6
D)2.7
E)1.1
Rationale: 72 --- 5 DS = 14.4
? ---- 1
45 ---- 5 US = 9
? ---- 1 S = ?
S = (14.4 - 9)/2 = 2.7
Answer:D
Answer: D
Question: A and B together have $ 1210. If of A's amount is equal to of B's amount,What is the ratio between A and B?
Options:
A)2:3
B)3:2
C)4:5
D)5:3
E)cannot be determined
Rationale: (4/15)a=(2/5)b
a=((2/15)*(15/4))b
a=(3/2)b
a/b=3/2
a:b=3:2
Option B
Answer: B