divelab/Sys2Bench huggingface dataset:
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
Options:
A)42, 33
B)42, 36
C)44, 33
D)44, 36
E)None of these
Rationale: Explanation :
Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=> (x + 9) = (56/100)(2x + 9)
=> (x + 9) = (14/25)(2x + 9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
Answer : Option A
Answer: A
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 2700, then his salary per month in rupees is:
Options:
A)4000
B)6000
C)18000
D)10000
E)None of these
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 2700, Salary = 18000 Rs.
Answer:C.
Answer: C
Question: Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 772.
Options:
A)120 ,122 , 124 ,126
B)120 ,122 , 124 ,128
C)120 ,121 , 122 ,123
D)125 , 127 ,129, 131
E)None of these
Rationale: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two
x + (x + 2)
twice the sum of the last two is written as
2 ((x + 4) + (x + 6)) = 4 x + 20
sum of the first two added to twice the sum of the last two is equal to 772 is written as
x + (x + 2) + 4 x + 20 = 772
Solve for x and find all four numbers
x = 125 , x + 2 = 127 , x + 4 = 129 , x + 6 = 131
Answer D
Answer: D
Question: A shepherd had 17 sheep. All but nine died. How many was he left with ?
Options:
A)Nil
B)8
C)9
D)17
E)18
Rationale: Explanation:
'All but nine died' means 'All except nine died' i.e. 9 sheep remained alive.
Answer: C
Answer: C
Question: If s is a positive even integer, and n and m are consecutive integers, then (n - m)^s/(m - n)^s =
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: s= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^s)/((m-n)^s)= ((n-m)/(m-n))^s = (-1)^s
Since we are raising the difference of n and m to power s , which is even , the answer will be 1 .
Answer D
Answer: D
Question: For every positive even integer n, the function h(n) is defined to be the product of all even integers from 2 to n, inclusive. For instance, h(10)= 2x4x6x8x10. What is the greatest prime factor of h(28)+h(30)?
Options:
A)5
B)7
C)13
D)29
E)31
Rationale: h(28)+h(30)
Since h(n) is the product of all even integers from 2 to n, we can say that all the factors of h(28) will be there in h(30)
so we can write the expression as h(28) (1+30)= h(28) *31
31 is the greatest prime factor since all the prime factors in h(28) will be smaller than 31.
E is the answer
Answer: E
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
Options:
A)77
B)30
C)108
D)66
E)12
Rationale: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108Kmph.Answer:C
Answer: C
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 38 min, then the slower pipe alone will be able to fill the tank in?
Options:
A)229
B)787
C)152
D)128
E)121
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/38
4/x = 1/38 => x = 152 min.
Answer: C
Answer: C
Question: What is the unit digit in (4137)^754?
Options:
A)1
B)3
C)7
D)9
E)None of these
Rationale: Unit digit in (4137)^754=unit digit in {{(4137)^4}^188 * (4137)^2}=(1*9)=9.
Correct Option: D
Answer: D
Question: The arithmetic mean of the scores of a group of students in a test was 40. The brightest 10% of them secured a mean score of 60 and the dullest 20% a mean score of 30. The mean score of remaining 70% is?
Options:
A)25
B)30
C)40
D)42
E)48
Rationale: Let the required mean score be x
10*60 + 20*30 + 70*x = 40*100
600+600+70x = 4000
x = 40
Answer is C
Answer: C
Question: The fraction 878(21/10000) in decimal form is
Options:
A)None of these
B)878.0021
C)878.00021
D)878.021
E)Cannot be determined
Rationale: Explanation :
878(21/10000) = 878 + (21/10000) = 878 + 0.0021 = 878.0021. Answer : Option B
Answer: B
Question: There are 280 female managers in a certain company. Find the total number of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
Options:
A)600
B)650
C)700
D)750
E)None of these
Rationale: as per question stem 2/5M (Portion of Men employees who are managers) + 280 (Portion of Female employees who are managers) = 2/5T (Portion of Total number of employees who are managers), thus we get that 2/5M+280= 2/5T, or 2/5(T-M)=280, from here we get that T-M=700, that would be total number of female employees and the answer (C)
Answer: C
Question: If 7a - 3b = 10b + 40 = -12b - 2a, what is the value of 9a + 9b?
Options:
A)-5
B)-3
C)0
D)3
E)5
Rationale: (i) 7a - 13b = 40
(ii) 2a + 22b = -40
Adding (i) and (ii):
9a + 9b = 0
The answer is C.
Answer: C
Question: A bag contains 6 black and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)3/4
B)2/5
C)1/7
D)1/8
E)4/3
Rationale: Let number of balls = (6 + 4) = 10.
Number of white balls = 4.
P (drawing a white ball) =4/10=2/5.
Option B.
Answer: B
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] + 5 = f(3x – 6)
Options:
A)0
B)4
C)6
D)7
E)13
Rationale: Answer = C = 6
f(x) = 3x – 5
2*[f(x)] + 5 = f(3x – 6)
2(3x-5) + 5 = 3 (3x-6) - 5
6x - 5 = 9x - 23
x = 6
Answer: C
Question: Ashok secured average of 76 marks in 6 subjects. If the average of marks in 5 subjects is 74, how many marks did he secure in the 6th subject?
Options:
A)66
B)74
C)78
D)86
E)None of these
Rationale: Explanation:
Number of subjects = 6
Average of marks in 6 subjects = 76
Therefore total marks in 6 subjects = 76 * 6 = 456
Now, No. of subjects = 5
Total marks in 5 subjects = 74 * 5 = 370
Therefore marks in 6th subject = 456 – 370 = 86
ANSWER D
Answer: D
Question: What is the smallest positive integer x such that 66-x is the cube of a positive integer
Options:
A)5
B)7
C)47
D)9
E)2
Rationale: Given 66-x is a perfect cube
so we will take 64 = 4*4*4
66-x = 64
x =66-64 = 2
correct option is E
Answer: E
Question: Which one of the following is a prime number?
Options:
A)45
B)90
C)81
D)29
E)91
Rationale: 73 is divisible by 1 and itself So, it is a prime number.
D
Answer: D
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.00 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)s.666
B)s.1140
C)s.999
D)s.1085
E)s.1020
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.0 = 666
ANSWER:A
Answer: A
Question: In a given set of S = {1,2,3,4,5,6,7,8} what is the median of the set S?
Options:
A)4
B)4.5
C)5
D)3.5
E)6
Rationale: median = 4+5 / 2 = 9/2 = 4.5
Answer is B
Answer: B
Question: A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper?
Options:
A)20%
B)25%
C)32%
D)46.66%
E)50%
Rationale: Solution: While buying,
He buys 1100 gram instead of 1000gram.
Suppose he bought 1100 grams for Rs. 1000.
While selling,
He sells only 900 grams when he takes the money for 1 kg.
Now, according to the problem,
he sells at a 8% profit (20% markup, 10% discount).
Hence, his selling price is Rs. 1080 for 900 grams.
Now,
1100grams for Rs. 1000
Hence, 1188 grams for Rs. 1080
Selling: 900 grams for Rs. 1080.
Hence, % profit = 288/900 = 32%.
(using goods left by goods sold formula)
Answer: Option C
Answer: C
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)None
Rationale: EXPLANATION
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer C
Answer: C
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)22
B)88
C)77
D)51
E)21
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88
Answer: B
Answer: B
Question: The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
Options:
A)55
B)44
C)66
D)60
E)12
Rationale: H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
Answer:D
Answer: D
Question: The ratio of the radius of two circles is 1: 4, and then the ratio of their areas is?
Options:
A)1: 16
B)1: 6
C)1: 9
D)1: 3
E)1: 2
Rationale: r1: r2 = 1: 4
Πr12: Πr22
r12: r22 = 1: 16
Answer:A
Answer: A
Question: Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?
Options:
A)10.30 am
B)10 am
C)9 am
D)11 am
E)12 am
Rationale: Assume both trains meet after x hours after 7 am
Distance covered by train starting from P in x hours = 20x km
Distance covered by train starting from Q in (x-1) hours = 25(x-1)
Total distance = 110
=> 20x + 25(x-1) = 110
=> 45x = 135
=> x= 3
Means, they meet after 3 hours after 7 am, ie, they meet at 10 am
ANSWER:A
Answer: A
Question: A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
Options:
A)1/7
B)2/9
C)1/12
D)4/17
E)2/3
Rationale: Total number of balls = 7+2 = 9
n(S) = 9C3 = 9*8*7 / 3*2 = 84
n(E) = 2C2* 7C1 = 7
Probability = 7/84 = 1/12
Answer is C
Answer: C
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 50,000 as total savings, how much has he saved in Public Provident Fund ?
Options:
A)Rs. 20,000
B)Rs. 30,000
C)Rs. 60,000
D)Rs. 90,000
E)None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (50000 – x) respectively. Then,
1/3x=1/2(50000-x)
=> x/3 + x/2 = 25000
=> 5x/6 = 25000
=> x= 25000 x 6 /5= 30000
Savings in Public Provident Fund = Rs. (50000 – 30000) = Rs. 20000
Answer A
Answer: A
Question: What is the units digit of the expression 13^27 +1?
Options:
A)1
B)3
C)4
D)8
E)9
Rationale: Power of 3 follows repetition pattern of = 3, 9, 7, 1, 3, 9, 7, 1 ....
Repetition after 4 powers = (3, 9, 7, 1)
13^27 = 27th Power = 24+3
24/4 = 6 (6 repetitions) + 3 = "7"
7+1=8
Answer D
Answer: D
Question: Two bullet train s 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Options:
A)15.8 sec.
B)12.8 sec.
C)11.16 sec.
D)10.8 sec.
E)08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 170) m = 310 m.
Required time = 310x9/250 = 11.16 sec.
ANSWER C
Answer: C
Question: The equation f= 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at f = -5, the equation for l is
Options:
A)+ y + 15 = 0
B)- 3x - 11 = 0
C)+ y - 16.5 = 0
D)- y - 7 = 0
E)+ y + 13.5 = 0
Rationale: Is optionC: -3f + y -6.5= 0=C
Answer: C
Question: The captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Options:
A)20 years
B)21 years
C)22 years
D)23 years
E)25 years
Rationale: Explanation:
Let the average age of the whole team by x years.
11x â€“ (28 + 31) = 9(x -1)
11x â€“ 9x = 50
2x = 50
x = 25
So, average age of the team is 25 years.
Answer E
Answer: E
Question: If the price of 357 apples is Rs.1517.25, what will be the approximate price of 49 dozens of such apples
Options:
A)Rs. 2500
B)Rs. 2300
C)Rs. 2200
D)Rs. 1400
E)None of these
Rationale: Let the required price be x
More apples, More price(direct proportion)
Hence we can write as
apples357:(49×12)}::1517.25:x
⇒357x = (49 × 12) × 1517.25
⇒x = (49 × 12 × 1517.25)/357 = (7 × 12 × 1517.25)/51
= (7 × 4 × 1517.25)/17 = 7 × 4 × 89.25 ≈ 2500. Answer A
Answer: A
Question: The product S of the first 10 prime numbers is closest to which of the following?
Options:
A)6.5 x 10^7
B)6.5 x 10^8
C)6.5 x 10^9
D)6.5 x 10^10
E)6.5 x 10^11
Rationale: The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=S
2*3*5*7*11*13*17*19=~10*50*100*200*667=10^7*667=6.67*10^9.
Answer: C.
Answer: C
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 24 gallons of gasoline?
Options:
A)190
B)284.6
C)300
D)292
E)312
Rationale: so 12.2 * 24 = 292..
IMO option D is correct answer..
Answer: D
Question: There are two positive numbers in the ratio 4:8. If the larger number exceeds the smaller by 16, then find the smaller number?
Options:
A)25
B)20
C)77
D)88
E)44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 4x = 16
4x = 16 => x = 4
=> Smaller number = 5x = 20.
Answer: B
Answer: B
Question: The parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)22.51
B)22.0
C)22.15
D)22.17
E)22.63
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(18 + 10) = 56 cm Parameter of the square = 56 cm
i.e. 4a = 56
a = 14
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(âˆ)(14)
= 1/2(22/7)(14) = 308/14 = 22 cm to two decimal places
Answer: B
Answer: B
Question: A woman sold 300 oranges at $12.10, some at the rate of 3 for 35 cents and the rest at 7 for 85 cents. How many were sold at the first rate?
Options:
A)45
B)21
C)9
D)15
E)13
Rationale: This can be solved like a classical mixture problem but numbers are awkward to deal with.
It's easier to just look at the answer choices. You know that a multiple of 3 oranges has to be sold at the first rate, and a multiple of 7 at the second rate. You simple subtract the answer choices for the first rate from 300 and check whether the remainder (i.e. the number of oranges sold at the second rate) is a multiple of 7.
300 - 45 = 255 => not a multiple of 7 so exclude
300 - 21 = 279 => not a multiple of 7 so exclude
300 -9 = 291 => not a multiple of 7 so exclude
300 - 15 = 285 => not a multiple of 7 so exclude
300 -13=287 => a multiple of 7 so keep
Hence, answer choice 13 is correct.
E
Answer: E
Question: How many liters of oil at Rs.40 per liter should be mixed with 240 liters of a second variety of oil at Rs.60 per liter so as to get a mixture whose cost is Rs.52 per liter?
Options:
A)120
B)150
C)160
D)180
E)200
Rationale: 8:12 = 2:3
If 240 lrs of the 2nd variety taken then the 1st variety should be taken as 160 lr
ANSWER C
Answer: C
Question: A bag contains 3 red, 3 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
Options:
A)5/8
B)7/12
C)11/16
D)17/24
E)37/48
Rationale: P(no red balls) = 7/10*6/9*5/8 = 7/24
P(at least one red ball) = 1 - 7/24 = 17/24
The answer is D.
Answer: D
Question: How many integers from 0 to 44, inclusive, have a remainder of 1 when divided by 3 ?
Options:
A)13
B)16
C)17
D)18
E)19
Rationale: Explanation:
1 also gives 1 remainder when divided by 3, another number is 4, then 7 and so on.
Hence we have an arithmetic progression: 1, 4, 7, 10,..... 43, which are in the form 3n+1.
Now we have to find out number of terms.
tn=a+(n-1)d, where tn is the nth term of an AP, a is the first term and d is the common difference.
so, 43 = 1+(n-1)3
or, (n-1)3 = 42
or, n-1 = 12
or, n = 13
A
Answer: A
Question: Divide 50 into two parts so that sum of the reciprocal is 1/12 ?
Options:
A)10,20
B)20,20
C)30,20
D)40,20
E)50,20
Rationale: let two no be x,y
x+y=50 ....eq(1)
1/x+1/y=1/12...eq(2)
x+y/xy=1/12(using eq(1))
xy=600
now, (x-y)^2=(x+y)^2 -4xy
using above
x-y=10.....eq(3)
solving eq(1) & eq(2)
x=30 & y=20
ANSWER:C
Answer: C
Question: emblem is coded as 216;
crude is coded as 125
Crickets will be ?
Options:
A)243
B)644
C)512
D)380
E)464
Rationale: coding follows (no. of letters)^3
emblem = 216 = 6^3
crude = 125 = 5^3
Crickets = 8^3 =512
ANSWER:C
Answer: C
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
Options:
A)331/8%
B)331/3%
C)381/3%
D)351/3%
E)231/3%
Rationale: 100
150
------
150-------50
100-------? => 331/3%
Answer: B
Answer: B
Question: Population of a city in 20004 was 1000000. If in 2005 there is an increment of 30% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
Options:
A)967532
B)977522
C)984424
D)997454
E)1225250
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 30/100)(1 - 35/100)(1 + 45/100)
= 1225250
E
Answer: E
Question: When a student Joe, weighing 42 kg, joins a group of students whose average weight is 30 kg, the average weight goes up by 1 kg. Subsequently, if two students, excluding Joe, leave the group the average weight comes back to 30 kg. What is the difference between the average weight of the two students who left and the weight of Joe?
Options:
A)5.5 kg
B)6 kg
C)30 kg
D)36.5 kg
E)71 kg
Rationale: After two persons leave the group the average remains the same. That means the weight of the two persons = 42+30 = 72
So, the average the two persons = 36
That gives the answer 42-36 = 6
Answer B
Answer: B
Question: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?
Options:
A)6 days
B)7 days
C)8 days
D)5 days
E)2 days
Rationale: 4/10 + 9/x = 1 => x = 15
1/10 + 1/15 = 1/6 => 6 days
\Answer:A
Answer: A
Question: A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
Options:
A)24
B)66
C)88
D)92
E)22
Rationale: 10/40 + 10/30 + 10/x = 1
x = 24 days
Answer:A
Answer: A
Question: What is the rate percent when the simple interest on Rs.800 amount to Rs.160 in 4 Years?
Options:
A)5
B)6
C)7
D)1
E)2
Rationale: 160 = (180*4*R)/100
R = 5%
Answer: A
Answer: A
Question: 25 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)8 days
B)6 days
C)7 days
D)9 days
E)10 days
Rationale: 1 women's 1 day work = 1/175
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/175 + 10/140) = 1/10
5 women and 10 children will complete the work in 10 days.
Answer: E
Answer: E
Question: The speed of a boat in still water is 30kmph and the speed of the current is 15kmph. Find the speed downstream and upstream?
Options:
A)76,20 kmph
B)40,10 kmph
C)29 ,10,kmph
D)26,20 kmph
E)45,15 kmph
Rationale: Speed downstream = 30 + 15
= 45 kmph
Speed upstream = 30 - 15
= 15 kmph
Answer: E
Answer: E
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.
Options:
A)33.25
B)33.5
C)34.25
D)35
E)None
Rationale: Solution:
Total sum of last 4 matches,
= (10 * 38.9) – (6 * 42)
= 389 – 252 = 137.
Average = 137 /4 = 34.25
Answer: Option C
Answer: C
Question: Find the value for m?
19(m + n) + 17 = 19(-m + n) - 135
Options:
A)0
B)-1
C)1
D)2
E)-4
Rationale: 19m + 19n + 17 = -19m + 19n - 135
38m= -152 => m = -4
E
Answer: E
Question: How many multiples of 8 are there between 100 and 200 (both are inclusive)?
Options:
A)27
B)4
C)6
D)13.5
E)8
Rationale: the answer is (200-100)/8+1=13.5
Answer is D
Answer: D
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 90 km/hr, what is the length of the platform?
Options:
A)338
B)240
C)287
D)400
E)191
Rationale: Speed = (90 * 5/18) m/sec = 25 m/sec. Length of the train = (25 x 20)m = 500 m. Let the length of the platform be x meters. Then, (x + 500)/36 = 25 ==> x + 500 = 900 ==> x = 400 m.
Answer: D
Answer: D
Question: The S.I. on a certain sum of money for 3 years at 8% per annum is half the C.I. on Rs. 4000 for 2 years at 10% per annum. The sum placed on S.I. is?
Options:
A)Rs. 1550
B)Rs. 1650
C)Rs. 1750
D)Rs. 2000
E)Rs. 2500
Rationale: Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750
ANSWER IS C
Answer: C
Question: If 50% of a number is equal to one-third of another number, what is the ratio of first number to the second number?
Options:
A)2:5
B)1:4
C)3:7
D)6:11
E)2:3
Rationale: Let 50% of A = 1/3 B
then 50A/100 = 1B/3
A/2 = B/3
A/B = 2/3
A:B = 2:3
Answer is E
Answer: E
Question: Two horses begin running on an oval course at the same time. One runs each lap in 9 minutes; the other takes 15 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
Options:
A)36
B)12
C)9
D)45/2
E)3
Rationale: The rate of the faster horse is 1/9 lap/minute;
The rate of the slower horse is 1/15 lap/minute;
Their relative rate is 1/9-1/15=2/45 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(2/45)=45/2 minutes.
Answer: D.
Answer: D
Question: In ten years, David will be four times as old as Aaron. Twenty years ago, David was twice as old as Ellen. If David is eleven years older than Ellen, how old is Aaron?
Options:
A)1–5
B)3–5
C)11–15
D)16–20
E)21–25
Rationale: Let David's present age be 'd', Aaron's present age be 'a' and Ellen's present age be 'e'
In ten years, David will be four times as old as Aaron --> d+10 = 4(a+10)
Twenty years ago, David was twice as old as Ellen --> d-20 = 2(e-20)
David is seven years older than Ellen --> d = e + 11
e+11-20 = 2e-40
e-9 = 2e-40
e = 31
d = 42
52 = 4a + 40
a = 3
Answer: B
Answer: B
Question: A student worked for 20 days. For each of the amounts shown in the first row of the table, the second row gives the number of days that the student earned that amount. What is the amount of money that the student earned per day for the 16th day?
Amounts earned per day : $96 $84 $80 $70 $48
Number of days : 4 7 4 3 2
Options:
A)(1) $96
B)(2) $84
C)(3) $80
D)(4) $70
E)(5) $48
Rationale: 4+7+4+3+2 = 20
The series is as follows. Arrange the terms in increasing order of amounts earned and cumulatively add up the number of days of each amount.
1st to 2nd term = 48 (2 days)
3rd to 5th term = 70 (3 days)
6th to 9th term = 80 (4 days)
10th to 16th term = 84 (7 days)
Pick B
Answer: B
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/4 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
Options:
A)0
B)1/15
C)2/15
D)1/8
E)2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/4) = L
CX = 4L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 4L
= 1/8
Answer will be D
Answer: D