divelab/Sys2Bench huggingface dataset:
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs.3432 , then what was the price of the article initially?
Options:
A)Rs.2000
B)Rs.4000
C)Rs.3000
D)Rs.5000
E)Rs.6000
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 3432
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (3432 * 100)/114.4 = 30 * 100 = Rs.3000.
Answer:C
Answer: C
Question: If 4% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is
Options:
A)250
B)231
C)200
D)288
E)111
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 4% of x = 350 - 340 = 10
x/25 = 10 => x = 250
Answer: A
Answer: A
Question: Calculate Tony''s average score in an exam if he obtained the following marks 53, 87, 89, 80 and 78 out of 100 in different subjects.
Options:
A)73.4
B)74.4
C)75.4
D)76.4
E)77.4
Rationale: Explanation:
(53+87+89+80+78)/5=77.4
Answer: Option E
Answer: E
Question: In a police selections, the weight of Arun is marked as 64 kg instead of 48 kg. Find the percentage of correction required.
Options:
A)30%
B)25%
C)24%
D)29%
E)34%
Rationale: Explanation :
% correction = (64-48)/64 X 100 = 25%
Answer : B
Answer: B
Question: Express a speed of 36 kmph in meters per second?
Options:
A)10
B)88
C)66
D)81
E)121
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: A
Question: If 375*s is a perfect square then s can be which of the following numbers?
Options:
A)21
B)35
C)54
D)15
E)150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 375 are 5*5 *5 * 3
1) 21 = 3 * 7
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 15 = 3 * 5
5) 150 = 2 * 3 * 5 * 5
So only answer choice D completes the pairing of 3, 5 . It adds a3, a5, and a7to the prime factors of 375 (3*5*5*5) and makes it a perfect square.D
Answer: D
Question: What is the are of an equilateral triangle of side 2 cm?
Options:
A)√3
B)64√9
C)64√4
D)64√3
E)64√2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 2, Area of triangle = √3/4 * 2 * 2 = √3 cm2;
Answer: A
Answer: A
Question: The average age of 20 students of a class is 20 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 20th student is
Options:
A)186
B)120
C)152
D)220
E)220
Rationale: Explanation:
Age of the 20th student = [20 * 20 - (14 * 5 + 16 * 9)] = (400-214) = 186 years.
Answer: A
Answer: A
Question: The probability that A can solve the problem is 2/3 and B can solve it is 3/4. If both of them attemp the problem, then what is the probability that the problem get solved ?
Options:
A)9/12
B)10/12
C)11/12
D)1
E)2
Rationale: Explanation :
The event is defined as:
A solves the problem AND B does not solve the problem
OR
A doesn't solve the problem AND B solves the problem
OR
A solves the problem AND B solves the problem
Numerically this is equivalent to:
(2/3) x (1/4) + (1/3) x (3/4) + (2/3) x (3/4) = 11/12
Answer : C
Answer: C
Question: The sum of four consecutive even numbers is 84. What would be the smallest number?
Options:
A)33
B)88
C)70
D)123
E)18
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 84 => x =11
Smallest number is: 2(x - 2) = 18.
Answer: E
Answer: E
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $15000 left with him. find salary..
Options:
A)$150000
B)$18000
C)$180000
D)$1800
E)None
Rationale: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $15000, = [1-9/10] * Total salary = $15000, Total salary = $15000*10 = $150000, correct answer (A)
Answer: A
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
Options:
A)33 1/3%
B)68 1/3%
C)28 1/3%
D)18 1/3%
E)11 1/3%
Rationale: Explanation:
Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%
Answer: A
Answer: A
Question: A thief steals at a car at 3.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)1 p.m
B)3 p.m
C)4 p.m
D)5 p.m
E)6 p.m
Rationale: E
6 p.m
Suppose the thief is overtaken x hrs after 3.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 6 p.m.
Answer: E
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
Options:
A)80.33%
B)82.33%
C)83.33%
D)73.33%
E)93.33%
Rationale: B
83.33%
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Answer: B
Question: Zam leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Zam, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Zam is 30 km\hr, find the speed of his son.
Options:
A)15km/hr
B)6 km/hr
C)4.28 km/hr
D)9 km/hr
E)4.12 km/hr
Rationale: Zam leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Zam, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Zam is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here, Zam would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
Answer: C
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 154 per Kg , the price of the third variety per Kg will be?
Options:
A)Rs. 147.50
B)Rs. 785.50
C)Rs. 176.50
D)Rs. 258.50
E)None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 154)
/ \
xâˆ’154 22.50
=>xâˆ’(154/22.50)=1.
=>xâˆ’154=22.50.
=>x= 176.50 Rs.
Answer : C
Answer: C
Question: Which is the following is divisible by 11
Options:
A)A)4305
B)B)4825
C)C)1635
D)D)4805
E)E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 5(5 + 1)//2 = 5 x 3 = 15
Sum of first 99 natural numbers = 55(55 + 1)//2 = 55 x 30 = 1650
1650 - 15 = 1635
Answer: Option C
Answer: C
Question: If one third of one fourth of number is 15, then three tenth of number is
Options:
A)34
B)44
C)54
D)64
E)74
Rationale: Explanation:
Let the number is x,
1/3of1/4∗x=15
=>x=15×12=180
=>so3/10×x=3/10×180=54
Option C
Answer: C
Question: A bank pays interest to its customers on the last day of the year. The interest paid to a customer
is calculated as 10% of the average monthly balance maintained by the customer. John is a
customer at the bank. On the last day, when the interest was accumulated into his account, his bank balance doubled to $2840. What is the average monthly balance maintained by John in his account during the year?
Options:
A)2840
B)5680
C)6840
D)7540
E)14200
Rationale: Soln:-
Bank balance is doubled with accumulation of interest to 2840..
this means INTEREST is 2840/2=1420 for entire year..
although since interest is 10% of avg MONthly balance, it becomes 14200..
ANSWER:E
Answer: E
Question: 9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
Options:
A)90.5%
B)87.5%
C)80.5%
D)77.5%
E)70.5%
Rationale: Within 1 standard deviation of the mean- means in the range {mean-1*sd; mean+1*sd} = {10-1*0.212; 10+0.3} = {9.788; 10.212}.
From the 8 listed numbers, 7 are within this range so 6/8=87.5%.
Answer: B.
Answer: B
Question: If 100<x<199 and 9<y<100, then the product xy CANNOT be equal to:
Options:
A)19,104
B)19,303
C)19,956.732
D)19,502
E)19,809
Rationale: Correct Answer: (C)
Determine the range of xy by multiplying the two extremes of each individual range together. The smallest value of xy must be greater than 100 * 9. The largest value must be less than 199 * 100. This means that 900 < xy < 19,900. (C) is outside of this range, so it is not a possible product of xy.
Answer: C
Question: What is the percentage increase in the area of a rectangle, if each of its sides is increased by
20 % ?
Options:
A)45%
B)44%
C)40%
D)42%
E)50%
Rationale: (20+20+ 20*20/100)% = 44%
AREA INCREASED BY 44%
THEN ORIGINAL AREA 10*10 =100
LENGTH IS INCRESED BY 20% NEW LENGTH = 10+2 =12
BREADTH IS INCREASED 20% NEW BREADTH = 10 + 2 -12
NEW AREA = 12 * 12 = 144
INCREASE IN AREA 144 - 100 =44
PERCENTAGE INCREASE IN AREA = INCREASE IN AREA / ORIGINAL AREA = 44/100 * 100 = 44
ANSWER B
Answer: B
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Options:
A)24
B)30
C)35
D)12
E)10
Rationale: b=188-1/2 = 1/24
=>24 days
ANSWER A
Answer: A
Question: If a = 1 and b = -2, then (2a^2 + b)(t + y) + (a + b)(t - y) =
Options:
A)0
B)2x
C)y - t
D)x - y
E)x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(t+y)=y-t => Smash C
Answer: C
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 650 resolutions?
Options:
A)794 m
B)704 m
C)454 m
D)186 m
E)915.2 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 650 resolutions.
= 650 * 2 * 22/7 * 22.4
= 91520 cm
= 915.2 m
Answer: E
Answer: E
Question: A train covers a distance of 20 km in 20 min. If it takes 9 sec to pass a telegraph post, then the length of the train is?
Options:
A)150m
B)200 m
C)120 m
D)225 m
E)160 m
Rationale: Speed = (20/20 * 60) km/hr
= (60 * 5/18) m/sec
= 50/3 m/sec.
Length of the train
= 50/3 *9
= 150 m.
Answer: A
Answer: A
Question: A and B can do a piece of work in 8 days. B and C can do it in 12 days and A and C in 16 days. Working together they will complete the work in how many days?
Options:
A)7.39 days
B)7.78 days
C)7.34 days
D)7.38 days
E)3.38 days
Rationale: A + B = 1/8
B + C = 1/12
C + A = 1/16
-------------------------------
2(A + B +C) = 1/8 + 1/12 + 1/16 = 13/48
A + B +C = 13/96
96/13 = 7.38 days
Answer: D
Answer: D
Question: An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Options:
A)112
B)180
C)288
D)278
E)292
Rationale: Explanation:
Angle traced by the hour hand in 6 hours=(360/12)*6
Answer: B) 180
Answer: B
Question: A wood maker constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?
Options:
A) 20
B) 40
C) 60
D) 80
E) 100
Rationale: A quick note on doubling. When you double a length you have 2*L1. When you double all lengths of a rectangle you have (2*L1)(2*L2) = A. An increase of 2^2 or 4. When you double all lengths of a rectangular prism you have (2*L1)(2*L2)(2*L3) = V. An increase of 2^3 or 8.
This leads to the basic relationship:
Line: 2*original size
Rectangle: 4*original size
Rectangular Prism: 8*original size answer is D
Answer: D
Question: The length of a train and that of a platform are equal. If with a speed of 144 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)1200
B)299
C)276
D)750
E)211
Rationale: Speed = [144 * 5/18] m/sec = 40 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 40 è x = 40 * 60 / 2 = 1200
Answer: A
Answer: A
Question: Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages
Options:
A)37 years
B)35 years
C)32 years
D)31 years
E)55 years
Rationale: Let A's age 10 years ago = x years.
Then, B's age 10 years ago = 2x years.
(x + 10) / (2x+ lO) = 3/4
=> x = 5.
So, the total of their present ages =(x + 10 + 2x + 10)
= (3x + 20) = 35 years.
Answer:B
Answer: B
Question: AB + CD = XXX, where AB and CD are two-digit numbers and XXX is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
Options:
A) 1
B) 3
C) 7
D) 9
E) Cannot be determined
Rationale: AB and CD are two digit integers, their sum can give us only one three digit integer of a kind of XXX it's 111.
So, A=1. 1B+CD=111
Now, C can not be less than 9, because no to digit integer with first digit 1 (mean that it's<20) can be added to two digit integer less than 90 to have the sum 111 (if CD<90 meaning C<9 CD+1B<111) --> C=9
Answer: D.
Answer: D
Question: A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations C of five marbles could be drawn?
Options:
A) 41
B) 51
C) 62
D) 72
E) 82
Rationale: there will be different cases, which we will take one by one..
1)case 1 when all five colours are different-7c5=21..
2)case 2 when three different colours and 2 of same type=6c3*2=30..
3)case 3 when two different colours and 3 of same type=6c2=15..
4)case 4 when one different colours and 2 of two different colors=5c1*4!/2!2!=15...
5)case 4 when 3 of one type and 2 of other colour=1...
total C-82 ans E
Answer: E
Question: -88*49+100=?
Options:
A)-4212
B)4601
C)-4801
D)-3471
E)None of these
Rationale: => -88*(50-1)+100;
=> -(88*50)+88+100;
=> -4400+188=-4212.
Correct Option: A
Answer: A
Question: A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 860 in 4 years. The
rate on interest per annum is.
Options:
A)4.5%
B)5%
C)6%
D)7.5%
E)8%
Rationale: Explanation:
S.I. on Rs 800 for 1 year = 60
Rate = (100*60)/(800*1) = 7.5%
Answer: D
Answer: D
Question: In an intercollegiate competition that lasted for 3 days, 157 students took part on day 1, 111 on day 2 and 98 on day 3. If 89 took part on day 1 and day 2 and 56 took part on day 2 and day 3 and 32 took part on all three days, how many students took part only on day 1?
Options:
A)40
B)44
C)35
D)49
E)38
Rationale: Day 1&2 = 89; Only Day 1&2 (89-32) = 57,
Day 2&3 = 56; Only Day 2&3 (56-32) = 24,
Only Day 1 = 157 - (57+24+32) = 44
Answer:B
Answer: B
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
Options:
A)30, 40
B)25, 30
C)50, 60
D)20, 40
E)30, 20
Rationale: Explanation:
Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40.
ANSWER IS A
Answer: A
Question: Dacid obtained 72, 45, 72, 77 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)67
B)68
C)87
D)26
E)75
Rationale: Average
= (72+ 45+ 72+ 77+75)/5
= 341/5 = 68.
Answer: B
Answer: B
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 15 meters of cloth?
Options:
A)114
B)115
C)116
D)117
E)118
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.128 : 15 :: 1 : x
=>0.128*x=15
=>x=15/0.128
=>x=117
ANSWER:D
Answer: D
Question: Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 2.8%.
Options:
A)237
B)270
C)398.8
D)166
E)111
Rationale: Explanation:
Cost of each share = (20 + 2.8% of 20) = Rs.20.56
Therefore, number of shares = 8200/20.56 = 398.8
ANSWER:C
Answer: C
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.2000, then what is the income of P1?
Options:
A)s.5000
B)s.2400
C)s.4000
D)s.3200
E)s.4200
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 2000 …(i) and 4x – 2y = 2000 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 2000 -> x = 1000
P1’s income = Rs 5*1000 = Rs.5000
ANSWER:A
Answer: A
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.9 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
Options:
A)1/6
B)1/2
C)5/8
D)5/6
E)15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.9(X) + 0.5(1-X) = 0.75
0.4X = 0.75 - 0.5
X = 0.25/0.4
X = 5/8
Therefore the answer is C: 5/8.
Answer: C
Question: At 12:30, the hour hand and the minute hand of a clock form an angle of
Options:
A)120°
B)135°
C)125°
D)150°
E)180°
Rationale: answer : 180 Degree
ANSWER :E
Answer: E
Question: How many times in a day, the hands of a clock are straight?
Options:
A)12
B)24
C)44
D)56
E)None
Rationale: Sol.
In 12 hours, the hands coincide or are in opposite direction 22 times.
∴ In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer C
Answer: C
Question: 0, 0, 1, 2, 2, 4, 3, 6, 4, _
Can you find out which number will complete the above series?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Solution:
Actually, there are two series in the question. If you separate the alternate places, you will find that the first series is:
0, 1, 2, 3, 4
Where the digits are multiple of 1.
The second series is:
0, 2, 4, 6, __
Here, the digits are progressing with the multiples of 2.
Therefore, the next digit will be 8.
Answer A
Answer: A
Question: A florist has 2 azaleas, 3 buttercups, and 7 petunias. The florist puts two flowers together at random in a bouquet. However, the customer calls and says that she does not want two of the same flower. What is the probability that the florist does not have to change the bouquet?
Options:
A)7/11
B)17/22
C)25/33
D)41/66
E)87/132
Rationale: The probability that two of the same flowers were chosen:
P(AA) = 2/12 * 1/11 = 2/132
P(BB) = 3/12 * 2/11 = 6/132
P(PP) = 7/12 * 6/11 = 42/132
The sum of these probabilities is 25/66
P(two flowers are different) = 1 - 25/66 = 41/66
The answer is D.
Answer: D
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.2 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend?
Options:
A)20%
B)65%
C)30%
D)33%
E)40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .2(1-a) = .33
.4a + .2 - .2a = .33
a= .65
therefore: .65/1 ounce = 65%. Therefore, the answer should be B
Answer: B
Question: If one of the followings is the product of the two 3-digit integers 8K5 and 6L5 (K and L denote the tens digit of the respective integers), then that product must be
Options:
A) 478,823
B) 511,913
C) 531,875
D) 538,424
E) 569,114
Rationale: To know the unit digit you can multiply both digit number: 5 x 5 = 25
This eliminates A, B, D, and E, because the number must end with a 5
So the answer is C
Answer: C
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different f colors patterns can be floor be parqueted?
Options:
A) 104
B) 213
C) 3^5
D) 705
E) 726
Rationale: Total number of squares we need to fill = 6
Number of colors we have f= 3
Therefore, total number of patterns = 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: E
Question: A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)177 m
B)176 m
C)270 m
D)187 m
E)186 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 38 = 15
x + 300 = 570
x = 270 m.
Answer: C
Answer: C
Question: In the 4 digits 1,2,3,4 how many 4 digested numbers are possible which are divisible by 4? Repetitions are allowed
Options:
A)61
B)62
C)63
D)64
E)65
Rationale: To be divisible by 4 the number has to be even.
When number ends in 2, options are xx12, xx32, with x representing any number.
When number ends in 4, options are xx24, xx44.
Each of these 4 options produce 16 possible numbers. Total = 16+16+16+16=64
ANSWER:D
Answer: D
Question: What is the greatest positive integer W such that 3^W is a factor of 9^10?
Options:
A)5
B)W=9
C)W=10
D)W=20
E)W=30
Rationale: What is the greatest positive integer W such that 3^W is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Answer: D
Question: At 3:00 pm, a car has driven 40 miles east. It will continue to drive east at 0.8 minutes per mile and then turn around and drive at 0.8 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
Options:
A)a) 10
B)b) 5
C)c) 12
D)d) 13
E)e) 14
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.8 = 10/8 = 1.25 miles/minute
Distance covered in 40 minutes = 1.25 * 40 = 12.5 * 4 = 50 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
40 + x = 50 - x
2x = 10
x = 5
Answer: B
Answer: B
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Options:
A)Rs. 10,000
B)Rs. 12,000
C)Rs. 14,000
D)Rs. 15,000
E)Rs. 16,000
Rationale: Principal =Rs. (100x5400)/(12x3)= Rs.15000
answer :D
Answer: D
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 10000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)12%
B)16%
C)18%
D)24.8%
E)23%
Rationale: Total CP = Rs. 42000 + Rs. 10000 = Rs. 52000 and SP
= Rs. 64900
Profit(%) = (64900 - 52000)/52000 * 100
= 24.8%
Answer:D
Answer: D