divelab/Sys2Bench huggingface dataset:
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
Options:
A)200
B)230
C)364
D)354
E)365
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: C
Question: There are 300 seniors at Morse High School, and 40% of them have cars. Of the remaining grades (freshmen, sophomores, and juniors), only 10% of them have cars. If 15% of all the students at Morse have cars, how many students are in those other three lower grades?
Options:
A)600
B)900
C)1200
D)1350
E)1500
Rationale: Let the total no of students be n.
The no of seniors having cars is 40% of 300 i.e. 120.
The rest of the students with other three grades who have cars is 10% of (n-300).
The total no of students with cars is 15% of n.
Thus, 0.15n= 120+0.1(n-300)
On solving this, we get n=1800.
Hence, the no of students with other three grades is 1800-300, i.e. 1500 (E).
Answer: E
Question: Calculate the circumference of a circular field whose radius is 2 centimeters.
Options:
A)2
B)4
C)6
D)8
E)10
Rationale: Circumference C is given by
C = 2Ï€r = 2Ï€*2 = 4 Ï€ cm
correct answer B
Answer: B
Question: Two trains, each 100 m long are moving in opposite directions. They cross each other in 8 seconds. If one is moving twice as fast the other, the speed of the faster train is
Options:
A)75 km/hr
B)60 km/hr
C)35 km/hr
D)70 km/hr
E)80 km/hr
Rationale: Total distance covered = 100+100 = 200 m
Time = 8 s
let speed of slower train is v . Then the speed of the faster train is 2v
(Since one is moving twice as fast the other)
Relative speed = v + 2v = 3v
3v = 200/8 m/s = 25 m/s
=> v = 25/3 m/s
Speed of the faster train = 2v = 50/3 m/s = (50/3)×(36/10) km/hr
= 5×36/3 = 5×12
= 60 km/hr
ANSWER:B
Answer: B
Question: A car crosses a 600 m long bridge in 5 minutes. Whatis the speed of car in km per hour?
Options:
A)1 m/sec
B)7.2 km/hr
C)3 m/sec
D)4 m/sec
E)5 m/sec
Rationale: Speed = 600 m/sec.
5 x 60
= 2 m/sec.
Converting m/sec to km/hr (see important formulas section)
= 2 x 18 km/hr
5
= 7.2 km/hr
B
Answer: B
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)82.1 sec.
B)12.1 sec
C)19.1 sec.
D)17.1 sec.
E)42.1 sec.
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Answer: B
Question: When the positive integer x is divided by 9,the remainder is 5.What is the remainder when 4x is divided by 9?
Options:
A)0
B)1
C)2
D)4
E)6
Rationale: i tried plugging in numbers
x = 9q+5
x = 14
4x = 56
4x/9 = 9*6+2
remainder is 2.
Answer is C
Answer: C
Question: In how many ways can 16 different gifts be divided among four children such that each child receives exactly four gifts?
Options:
A)16^4
B)(4!)^4
C)16!/(4!)^4
D)16!/4!
E)4^16
Rationale: Total 16 different Gifts, and 4 children.
Thus any one child gets 16C4 gifts,
then the other child gets 12C4 gifts(16 total - 4 already given),
then the third one gets 8C4 gifts,
and the last child gets 4C4 gifts.
Since order in which each child gets the gift is not imp, thus, ans :
16C4 * 12C4 * 8C4 * 4C4 = 16! / (4!)^4
Ans : C.
Answer: C
Question: Consider below info to be a table:
AMOUNT OF BACTERIA
TIME - AMOUNT
1PM - 10gms
4PM - x gms
7PM - 19.6 gms
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same factor during each of the two 3-hour periods shown, how many grams of bacteria were present at 4PM ?
Options:
A)12.0
B)13.0
C)12.2
D)12.3
E)12.4
Rationale: let say the factor is x, the at 7PM quantity = 10 (i.e. quantity @1PM)* x^2 =19.6 => x^2 =1.96 or x = 1.3 => @4PM quantity = 10x =10*1.3 =13.
Answer B
Answer: B
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.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)288
B)200
C)999
D)277
E)271
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 = 999
Answer:C
Answer: C
Question: Find the numbers which are in the ratio 3:2:2 such that the sum of the first and the second added to the difference of the third and the second is 20?
Options:
A)12,8,8
B)4,4,22
C)9,3,32
D)9,6,12
E)9,2,23
Rationale: Let the numbers be a, b and c.
a:b:c = 3:2:2
Given, (a + b) + (c - b) = 20
=> a + c = 20
=> 3x + 2x = 20 => x =4
a, b, c are 3x, 2x, 2x
a, b, c are 12, 8, 8.
Answer:A
Answer: A
Question: There is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall. There is one each bird sitting on top of both the towers. They fly at a constant speed and time to reach a grain in b/w the towers at the same time. At what distance from the church is the grain?
Options:
A)170 meters
B)160 meters
C)150 meters
D)140 meters
E)130 meters
Rationale: If x ft is the distance of grain from 200 ft tall tower, then
150^2 +(350-x)^2= 200^2 + x^2
then
x= 150 meters
ANSWER:C
Answer: C
Question: How many 3-digit numbers are completely divisible 6 ?
Options:
A)149
B)150
C)151
D)166
E)172
Rationale: Explanation:
3-digit number divisible by 6 are: 102, 108, 114,... , 996
This is an A.P. in which a = 102, d = 6 and l = 996
Let the number of terms be n. Then tn = 996.
a + (n - 1)d = 996
102 + (n - 1) x 6 = 996
6 x (n - 1) = 894
(n - 1) = 149
n = 150
Number of terms = 150.
ANSWER IS B
Answer: B
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 2, 1, (1/2), (1/4), ... What number should come next?
Options:
A)1/8
B)1/4
C)2/5
D)2/7
E)1/1
Rationale: A
1/8
This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result.
4/2 = 2
2/2 = 1
1/2 = 1/2
(1/2)/2 = 1/4
(1/4)/2 = 1/8 and so on.
Answer: A
Question: A train running at 1/3 of its own speed reached a place in 9 hours. How much time could be saved if the train would have run at its own speed?
Options:
A)8hrs
B)10hrs
C)12hrs
D)15hrs
E)6hrs
Rationale: time taken if run its own speed = 1/3*9 =3 hrs
Time saved = 9 - 3 = 6 hrs
Answer : E
Answer: E
Question: The ratio of two numbers is 1:3 and the sum of their cubes is 945. The difference of number is?
Options:
A)5.23
B)1.23
C)3.93
D)3.23
E)4.23
Rationale: 1x 3x
1x cube + 27x cube = 945
28x cube = 945
x cube = 33.75 => x = 3.23
ANSWER:D
Answer: D
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/9%
B)16 3/3%
C)16 2/2%
D)13 2/3%
E)16 2/9%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: If ‘DELHI’ is coded as ‘EFMIJ’, then ‘PUNE’ is coded as
Options:
A)QVOF
B)TGFR
C)RFDE
D)QVOO
E)YHGT
Rationale: D= 4 = 4+1 = 5 = E
E = 5 =5+1 =6 = F
SIMILARLY,
P = 16 = 16+1 = 17 = Q
U = 21 = 21+1 = 22 = V
N = 14 = 14+1 = 15 = O
E = 4 = 4 +1 = 5 = F
SO ANS IS
QVOF
Answer: A
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is:
Options:
A)12
B)15
C)18
D)20
E)22
Rationale: Explanation:
Dividend on Rs. 20 = Rs. (9/100) x 20 = Rs.9/5.
Rs. 12 is an income on Rs. 100.
Rs.9/5 is an income on Rs.[ (100/12) x (9/5)] = Rs. 15.
Answer: B
Answer: B
Question: In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
Options:
A)75 cu. m
B)750 cu. m
C)7500 cu. m
D)75000 cu. m
E)7.50 cu. m
Rationale: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.05*1.5*10000 = 75*10 cu, mtr = 750 cub mtr .
ANSWER:B
Answer: B
Question: The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Options:
A)6.06%
B)6.07%
C)6.08%
D)6.09%
E)6.10%
Rationale: Explanation:
Amount of Rs. 100 for 1 year = Rs.[100 x (1 + 3/100)2]=Rs. 106.09
when compounded half-yearly
Effective rate = (106.09 - 100)% = 6.09%
ANSWER IS D
Answer: D
Question: The compound interest earned on a sum for the second and the third years are $1400 and $1540 respectively. What is the rate of interest?
Options:
A)2%
B)4%
C)6%
D)8%
E)10%
Rationale: 1540 - 1400 = 140 is the rate of interest on $1400 for one year.
The rate of interest = (100 * 140) / (1400) = 10%
The answer is E.
Answer: E
Question: For how many integers pair (x,y) satisfies the result
(1/x)+((1/y)=1/19
Options:
A)a)22
B)b) 6
C)c) 10
D)d) 16
E)e) 32
Rationale: It seems that the accepted answer is wrong, according to WolframAlpha. The answer should be 32, which isn't even listed as a selectable answer.
A
Answer: A
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 30 days to complete the same work. then Q alone can do it in
Options:
A)10
B)22
C)25
D)27
E)30
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/30
Work done by P, Q and R in 1 day = 1/10 + 1/30 = 4/30
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 4/30
=> Work done by P in 1 day = 4/60
=> Work done by Q and R in 1 day = 4/60
Hence work done by Q in 1 day = 4/60 â€“ 1/30 =2/60 = 1/30
So Q alone can do the work in 30 days
Answer is E.
Answer: E
Question: 53, 53, 40, 40, 27, 27, ?
Options:
A)14
B)12
C)16
D)18
E)20
Rationale: First, each number is repeated, then 13 is subtracted to arrive at the next number.
Answer : A.
Answer: A
Question: what is the smallest integer that is multiple of 3,7 and 20
Options:
A)141
B)180
C)130
D)122
E)420
Rationale: Correct Answer :E
It is the lcm of 3,7 and 20 which is 420
Answer: E
Question: If a: b :: 3 : 7, then what is (5a+6b): (a-4b)?
Options:
A)57:11
B)-57:11
C)11 : 10
D)-57 : 25
E)-1 : 10
Rationale: a/b= 3/7
Dividing numerator & denominator of ' (5a+6b)/(a-2b) 'by b,
[5(a/b)+6]/[(a/b)-4]= [5*(3/7)+6]/[(3/7)-4]= -57/25
ANSWER:D
Answer: D
Question: The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places).
Options:
A)178.27
B)178.29
C)178.21
D)178.19
E)178.55
Rationale: Calculated average height of 35 boys = 180 cm.
Wrong total height of 35 boys = 180 * 35 cm. This was as a result of an actual height of 106 cm being wrongly written as 166 cm. Correct total height of 35 boys = 180 * 35 cm - 166 cm + 106 cm
= 180 * 35 cm - 166 cm + 106 cm/35 = 180 cm - 60 /35 cm
= 180 cm - 1.71 cm = 178.29 cm.Answer:B
Answer: B
Question: If it takes a hrs for x to repair 1 machine and b hrs for y to repair 1 machine then how many hrs will they take to repair 750 machines if they work together?
Options:
A)750 × ab/(a+b)
B)750 (a+b)/ab
C)750 ab
D)750/(a+b)
E)None of these
Rationale: Explanation:
x repair machine in a hrs he work 1/a for 1 hr
y repairs machine in b hrs he works 1/b for 1 hr
(x+y) work per 1 hr = 1/a+1/b= (a+b)/ab
time = ab/(a+b)
for 750 machines time = 750 × ab/(a+b)
Answer: Option A
Answer: A
Question: In a box of 11 pens, a total of 3 are defective. If a customer buys 2 pens selected at random from the box, what is the probability that neither pen will be defective?
Options:
A)5/11
B)16/33
C)28/55
D)38/77
E)45/88
Rationale: # defective pens = 3
# good pens = 8
Probability of the 1st pen being good = 8/11
Probability of the 2nd pen being good = 7/10
Total probability = 8/11 * 7/10 = 28/55
The answer is C.
Answer: C
Question: After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
Options:
A)2338
B)2298
C)5000
D)2871
E)1171
Rationale: Explanation:
Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15) = Rs. 8000
If SP = Rs. 8000, profit = 60%
CP = [SP(100)]/(100 + 60) = (8000 * 100)/160 = Rs. 5000
Answer:C
Answer: C
Question: A tradesman by means of his false balance defrauds to the extent of 30%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)60%
B)70%
C)69%
D)71%
E)68%
Rationale: g% = 30 + 30 + (30*30)/100
= 69%
ANSWER:C
Answer: C
Question: If A earns 99/3% more than B,how much percent does B earn less then A ?
Options:
A)42%
B)14%
C)25%
D)15%
E)35%
Rationale: Required Percentage = [((100/3)*100)/[100+(100/3)]]%
=[(100/400)*100]%=25%
Answer is C.
Answer: C
Question: The sum of the present ages of a son and his father is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, what will be son's age?
Options:
A)100
B)40
C)80
D)20
E)10
Rationale: Let the present age of the son =x
Then, present age of the father =(60−x)
Six years ago father's age was 5 times the age of the son
(60-X)-6=5(X-6)
84=6X
X=84/6=14
Son's age after 6 years
=X+6=14+6=20
answer is D.
Answer: D
Question: From the word 'HEARTLESS', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
Options:
A)5
B)8
C)3
D)2
E)9
Rationale: Explanation:
The words formed are
HE, ART, LESS, HEART and EAR
Answer: A) 5
Answer: A
Question: By the how much is two-fifth of 150 greater than three -fifths of 25?
Options:
A)15
B)3
C)45
D)30
E)None of these
Rationale: Reqd no. = 2â„5 Ã— 150 - 3â„5 Ã— 25
= 60 - 15 = 45
Answer C
Answer: C
Question: A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 4 rows or 5 rows or 6 rows, then no tree will be left. Find the least number of trees required
Options:
A)22
B)60
C)28
D)76
E)21
Rationale: Explanation:
The least number of trees that are required = LCM(4, 5, 6) = 60.
Answer: B
Answer: B
Question: Baker Adam is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
Options:
A)330
B)300
C)252
D)225
E)210
Rationale: Baker Adam is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.
Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
Answer: E
Question: During the second quarter of 1984, a total of 3,976,000 domestic cars were sold. If this was 32% greater than the number sold during the first quarter of 1984, how many were sold during the first quarter ?
Options:
A)714,240
B)2,261,760
C)2,400,000
D)3,012,121
E)3,915,790
Rationale: Let number of cars sold in 1st quarter = x
Number of cars sold in 2nd quarter = 32% greater than the number sold during the first quarter = (1 + 32/100)x = 1.32 x
1.32 x = 3,976,000
=> x = 3,012,121
So, answer will be D
Answer: D
Question: What is the difference between the place value and face value of 3 in the numeral 1375?
Options:
A)287
B)290
C)297
D)390
E)398
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
C
Answer: C
Question: A certain sum of money doubles itself in 12 years in how much many years will it trible itself at the same rate?
Options:
A)20 years
B)76 years
C)24 years
D)44 years
E)11 years
Rationale: 100 ---- 100 --- 12
100 --- 12
--------------------
300 ---- 24 years
Answer: C
Answer: C
Question: Jerry, an electrician, worked 6 months out of the year. What percent
of the year did he work? (round answer to the nearest hundredth)
What percent 12 is 6? 12 months = 1 year
Options:
A)58.33%
B)68.33%
C)78.33%
D)50.00%
E)98.33%
Rationale: 1. Multiply the opposites
6 x 100 = 600
100=6/12
50% (rounded to hundredth)
correct answer D
Answer: D
Question: A textile manufacturing firm employees 70 looms. It makes fabrics for a branded company. The aggregate sales value of the output of the 70 looms is Rs 5,00,000 and the monthly manufacturing expenses is Rs 1,50,000. Assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms. Monthly establishment charges are Rs 75000. If one loom breaks down and remains idle for one month, the decrease in profit is:
Options:
A)13000
B)7000
C)10000
D)5000
E)None of these
Rationale: Explanation :
Profit = 5,00,000âˆ’(1,50,000+75,000) =Rs. 2,75,000.
Since, such loom contributes equally to sales and manufacturing expenses.
But the monthly charges are fixed at Rs 75,000.
If one loan breaks down sales and expenses will decrease.
New profit :-
=>500000Ã—(69/70)âˆ’150000Ã—(69/70)âˆ’75000.
=>Rs 2,70,000.
Decrease in profit
=>2,75,000âˆ’2,70,000
=>Rs. 5,000.
Answer : D
Answer: D
Question: Jeya invested an amount of Rs. 9,500 at the rate of 13% p.a simple interest and another amount at the rate of 15% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Options:
A)15550
B)18450
C)13450
D)14450
E)14650
Rationale: Let the second amount be Rs. x. Then,
(9500 * 13 * 1)/100 + (x * 15 * 1)/100 = [(12000 + x) * 14 * 1] / 100
12350+ 15x= 16800 + 14x
x = 4450
Total investment = 10000 + 4450 = Rs. 14450 .Answer: D
Answer: D
Question: In a classroom, 12 students brought apples and 8 students brought bananas. If exactly 10 students brought only one of the two types of fruits, how many students brought both types of fruits?
Options:
A)5
B)6
C)7
D)12
E)14
Rationale: Say x students brought both fruits.
(12 - x) + (8 - x) = 10 --> x = 5.
Answer: A.
Answer: A
Question: Helen went to the stationers and bought things worth Euro 45, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)Euro 15
B)Euro 15.7
C)Euro 19.7
D)Euro 39.7
E)None
Rationale: Explanation: Let the amount taxable purchases be Euro x.
Then, 6% of x = 30/100
x = (30/100 x 100/6) = 5.
Cost of tax free items = Euro [45 - (5 + 0.30)] = Euro 39.70
Answer: Option D
Answer: D
Question: Find the value of 72519 x 9999 = m?
Options:
A)434539873
B)355797990
C)435453490
D)m=725117481
E)873430134
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: At a certain university, 69% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
Options:
A)25
B)37.5
C)50
D)52.5
E)75
Rationale: answer is 75%
total women = 69%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured =21%
but question wants to know the percent of men that are tenured
21%/40% = 52.5%
D
Answer: D
Question: Two trains of equal lengths take 12 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)22
B)13
C)77
D)99
E)21
Rationale: Speed of the first train = 120/12 = 10 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 10 + 8 = 18 m/sec.
Required time = (120 + 120)/18 = 13 sec.
Answer: B
Answer: B
Question: It's Valentine's day and Alan has promised to cook his girlfriend Alana her favorite meal: fish fingers and custard. Alana will be arriving in one hour exactly. Alan only has a microwave. The fish fingers take 13 minutes to defrost in the microwave and 6 minutes to cook in the microwave. The custard must be prepared after the fish fingers and takes 24 minutes to cook in the microwave and then 6 minutes to cool sufficiently so as not to burn someone's tongue. It will take Alan 1 minute to plate the food. However, Alan is on his Xbox and really wants to play one more game of his football video game before Alana arrives. What is the maximum length of each half of the match that Alan can play to ensure the meal is ready for Alana's arrival?
Options:
A)5 min
B)6 minutes
C)7 minutes
D)8 minutes
E)10 minutes
Rationale: Alana will arrive in 60 minutes.
The total meal preparation time is 13 (fish finger defrost) + 6 (fish finger cook) + 24 (custard cook) + 6 (custard cool) + 1 (plate time) = 50 minutes.
Alan therefore has 10 minutes (60-50 = 10) to play his football video game.
As football matches have two halves, Alan have select 5 minute halves (10/2 = 5)
ANSWER: A
Answer: A
Question: If X-Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?
Options:
A)-4.5.
B)-2.
C)-1.7.
D)-0.667.
E)2.5.
Rationale: X-Y = 2X-2Z
Y= -X+2Z---------- 1
X-2Y = 4Z
X-4Z= 2Y--------- 2
Adding equation 1 from equation 2
-2Z= 3Y
Y/Z= -0.667
D is the answer
Answer: D
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 400. Find the average mark scored by all the three boys?
Options:
A)384
B)192
C)207
D)269
E)208
Rationale: Average mark scored by all the three boys =
[64/100 (400) + 36/100 (400) + 44/100 (400)] / 3
= 192
Answer: B
Answer: B
Question: A man buys an song for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:
Options:
A)<25
B)<10
C)>20
D)>30
E)<30
Rationale: C
>20
Let the song be worth $x.
C.P. 90% of $x = $9x/10
S.P. = 110% of $x = $11x/10
Gain = (11x/10 - 9x/10) = $x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: C
Question: An empty bucket being filled with paint at a constant rate takes 6 minutes to be filled to 7/10 of its capacity. How much more time B will it take to fill the bucket to full capacity?
Options:
A)7/18
B)9/18
C)2
D)18/7
E)18/5
Rationale: Solution -
Work and Time are directly proportional. W1/W2=T1/T2
7/10 work in 6 mins
1 work in T mins
(7/10)/1 = 6/T -> T = 60/7 mins.
Remaining minutes to fill the tank B= 60/7 - 6 = 18/7 mins. ANS D.
Answer: D
Question: The probability that a number selected at random from the first 100 natural numbers is a composite number is ?
Options:
A)2/3
B)3/5
C)3/4
D)3/2
E)5/2
Rationale: Explanation:
The number of exhaustive events = 100 C₁ = 100.
We have 25 primes from 1 to 100.
Number of favourable cases are 75.
Required probability = 75/50 = 3/2.
Answer is D
Answer: D
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
Options:
A)17 years
B)19 years
C)29 years
D)10 years
E)12 years
Rationale: Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.
Answer: D
Answer: D
Question: If N = 2^0.20 and N^b = 16, b must equal
Options:
A)3/80
B)3/5
C)20
D)5/3
E)80/3
Rationale: 20/100 = 1/5
N = 2 ^ 1/5
N^b = 2^4
(2^1/5)^b = 2^4
b = 20
Answer: C
Answer: C
Question: A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options:
A)27
B)29
C)40
D)89
E)22
Rationale: 1/8 - 1/x = 1/10
x = 40
Answer: C
Answer: C
Question: Cole drove from home to work at an average speed of 30 kmh. He then returned home at an average speed of 90 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)75
E)90
Rationale: Let the distance one way be x
Time from home to work = x/30
Time from work to home = x/90
Total time = 2 hrs
(x/30) + (x/90)= 2
Solving for x, we get x = 45
Time from home to work in minutes= (45)*60/30= 90 minutes
Ans= E
Answer: E
Question: Five years ago, John’s age was half of the age he will be in 6 years. How old is he now?
Options:
A)14years
B)15years
C)16years
D)17years
E)18years
Rationale: Let John=j,j-5=(j+6)/2,then j=16years
ANSWER:C
Answer: C