mathewhe/aqua_rat huggingface dataset:
Question: There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?
(A) 16
(B) 15
(C) 12
(D) 87
(E) 16
Rationale: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.
a2 = 784 = (4)(196) = (22).(142)
a = (2)(14) = 28
a = 2l, l = a/2 = 14
l = (7/3)s
Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s
= 12∏ cm.
Answer:C
Answer: (C) 12
Question: A train running at the speed of 90 km/hr crosses a pole in 6 seconds. What is the length of the train?
(A) 150
(B) 2766
(C) 187
(D) 267
(E) 191
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.
Answer: A
Answer: (A) 150
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:47
(B) 32:49
(C) 32:45
(D) 32:46
(E) 32:41
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45
Answer: C
Answer: (C) 32:45
Question: In a graduate physics course, 60 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the female students is single?
(A) 2/7
(B) 17/30
(C) 1/2
(D) 27/40
(E) 5/7
Rationale: let assume there are 100 students of which 60 are male and 40 are females
if 30 are married then 70 will be single.
now its given that two-sevenths of the male students are married that means 2/7 of 60 = 17 males are married
if 30 is the total number of students who are married and out of that 17 are males then the remaining 13 will be females who are married.
total females = 40
married females = 13
then single females = 40-13 = 27
we need to find the fraction of female students who are single i.e single female students / total female student
= 27/40 [D]
Answer: (D) 27/40
Question: In how many ways, a committee of 5 members can be selected from 7 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 75
(B) 152
(C) 175
(D) 350
(E) 412
Rationale: (3 men out 7) and (2 ladies out of 5) are to be chosen
Required number of ways = (7C3 * 5C2) = 350
Answer is D
Answer: (D) 350
Question: Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 300 grams of compound X?
(A) 54
(B) 162
(C) 250
(D) 270
(E) 322
Rationale: total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 300 gms of X have 300*10/12=250 gms of B
and 300-250=50 gms of A.
cross check:- A/B = 50/250 =2/10 (as given)
Ans C
Answer: (C) 250
Question: The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 7 years hence?
(A) 58
(B) 74
(C) 62
(D) 70
(E) 74
Rationale: Explanation:
A + B = 60, A = 2B
2B + B = 60 => B = 20 then A = 40.
7 years, their ages will be 47 and 27.
Sum of their ages = 47 + 27 = 74.
B)
Answer: (B) 74
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 10%
(B) 11%
(C) 12%
(D) 15%
(E) 13%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
ANSWER:C
Answer: (C) 12%
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 3 hours. How long would it take for both hoses to fill up two-thirds of the pool?
(A) 5/12 hours
(B) 5/8 hours
(C) 4/3 hours
(D) 12/7 hours
(E) 12/5 hours
Rationale: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 3 hours
i.e. 1 Hour work of Hose 2 = 1/3
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/3) = (1/2)
i.e. (1/2) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(2)*(2/3) = 4/3 hour
Answer: Option C
Answer: (C) 4/3 hours
Question: 10^185 - 10^9 = Which of the following best approximates the value of the expression above?
(A) 10^170
(B) 10^180
(C) 10^(185)
(D) 10^160
(E) 10^179
Rationale: 10^185 - 10^9 =
Which of the following best approximates the value of the expression above?
Yes, answer 10^185 is correct. Note that we need approximate value of the given expression and as 10^(185) is much larger number than 10^(9) then 10^(9) is pretty much negligible in this case: 10^(185)-10^(9)=~10^(185).
Answer : C
Answer: (C) 10^(185)
Question: 45 pupil,out of them 12 in debate only and 22 in singing only.then how many in both?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: The intersection for two = 45 - 12 - 22 = 11 play both games.
ANSWER:C
Answer: (C) 11
Question: In the first 10 overs of a cricket game, the run rate was only 4.8. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 4.25
(B) 5.85
(C) 6.25
(D) 7
(E) 7.5
Rationale: Required run rate = 282 - (4.8 x 10) =	234
234/40= 5.85
B)
Answer: (B) 5.85
Question: A and B can do a work in 6 days, B and C in 2 days and C and A in 8 days. In how many days will the work be completed, if all three of them work together?
(A) 12/24
(B) 48/63
(C) 45/56
(D) 48/19
(E) 28/12
Rationale: One day work of A and B = 1/6
One day work of B and C = 1/2
One day work of C and A = 1/8
2(A + B + C) = 1/6 + 1/2 + 1/8
2(A + B + C) = 19/24
(A + B + C) = 19/48
Number of days required = 48/19 days.
Answer: D
Answer: (D) 48/19
Question: A series of book was published at seven years intervals when the seventh book was published the total sum of publication year was 13, 1524. first book was published in?
(A) 1911
(B) 1912
(C) 1913
(D) 1914
(E) 1915
Rationale: First of all total sum of publication years is 13524 not 131524.
Let the first year is x.
so the years are x, x+7, x+14, x+21, x+28, x+35 and x+42.
Now Sum of all years = (n/2)(2a+(n-1)d) [n=number of years, a=first year, d=difference of two years]
=(7/2)(2x+(7-1)7)
=7x+147
Again Sum of all years = 13524
So, 7x+147=13524
=> x=1911
ANSWER:A
Answer: (A) 1911
Question: Every student of a certain school must play an instrument. In last year, 1/2 of the students picked a woodwind instrument, 2/5 of the students picked a brass instrument, and all of the other students took percussion. In this year, 1/2 of the students who play woodwind and 1/4 of the students who play brass instruments left school, other students did not leave, and no fresh student come in. What fraction of all students play either a woodwind or brass instrument?
(A) 7/13
(B) 4/5
(C) 9/13
(D) 11/13
(E) 7/10
Rationale: Lets pick smart numbers. Total number of students: 20
Woodwind (1/2): 10
Brass (2/5): 8
Percussion (1/10): 2
After leaving school
Woodwind: 5
Brass: 6
Percussion: 2
New Total number of students: 13
Woodwind and Brass: 11
Answer 11/13 or D
Answer: (D) 11/13
Question: Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 6.85
(B) 7.18
(C) 7.16
(D) 7.15
(E) 7.12
Rationale: T = (111 + 165)/ (80 + 65) * 18/5
T = 6.85
Answer: A
Answer: (A) 6.85
Question: The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 6000, brokerage being 1/4%, is:
(A) 83.08
(B) 114
(C) 114.75
(D) 124
(E) 124.75
Rationale: Face Value = Rs. 6000.
Dividend = 10.5%.
Annual Income = Rs. 756.
Brokerage per Rs. 100 = Rs. 0.25.
Dividend is always paid on the face value of a share.
Face Value * Dividend / (Market Value + Brokerage per Rs. 100) = Annual income.
= 6000 * 10.5 / 756 = Market Value of Rs. 100 stock + Brokerage per Rs. 100.
= Market Value of Rs. 100 stock + Brokerage per Rs. 100 = Rs. 83.33.
= Market Value of Rs. 100 stock = Rs. 83.33 - Re. 0.25.
= Market Value of Rs. 100 stock = Rs. 83.08
answer : A
Answer: (A) 83.08
Question: A, B and C start a business each investing 20,000. After 5 months A withdrew 10000, B withdrew 15000 and C invests 5000 more. At the end of the year, a total profit of 58000 was recorded. Find the share of B.
(A) 20,000
(B) 21,200
(C) 28,200
(D) 13,500
(E) None of these
Rationale: Ratio of the capitals of A, B and C
= 20000 Ã— 5 + 10000 Ã— 7 : 20000 Ã— 5 + 5000 Ã— 7 : 20000 Ã— 5 + 25000 Ã— 7
=170000 : 135000 : 275000 = 170 : 135 : 275.
Bâ€™s share = (58000 Ã— 135â„580) = 13500
Answer D
Answer: (D) 13,500
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
(A) 1 Â½ mins
(B) 3 mins
(C) 3 Â½ mins
(D) 7 mins
(E) 5 mins
Rationale: Explanation:
D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins
ANSWER IS B
Answer: (B) 3 mins
Question: A publisher has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, what is the discount rate on mysteries book?
(A) 10%
(B) 40%
(C) 35%
(D) 30%
(E) 25%
Rationale: Let B be the discount on biographies and M be the discount on mysteries
So., B + M = 0.35 -----(1)
And
(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
--> 100(1-(1-B)) + 36(1-(1-M) = 19
100B + 36M = 19 ------(2)
Solving 12., we get M = 0.25 = 25%
E
Answer: (E) 25%
Question: In a certain country ½ of 5 = 3. Assuming the same proportion, what would be the value of 1/3 of 10 ?
(A) 3
(B) 4
(C) 8
(D) 7
(E) 9
Rationale: B
4
Answer: (B) 4
Question: Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 49?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 4?
(A) 25x^2 + 4 = y^2
(B) 75x^2 = 3y^2 - 12
(C) 25x^2 = (y + 2)(y - 2)
(D) 5x = y - 7
(E) x^2 = (y^2 - 4)/25
Rationale: 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 7
If we square both sides, we end up with....
(5X)^2 = (Y-7)^2
(5X)(5X) = (Y-7)(Y-7)
25X^2 = Y^2 - 14Y + 49
This is NOT a match for the original equation, so it's the answer that is NOT equivalent.D
Answer: (D) 5x = y - 7
Question: A certain bus driver is paid a regular rate of $14 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $976 in total compensation, how many total hours did he work that week?
(A) 54
(B) 51
(C) 59
(D) 55
(E) 52
Rationale: For 40 hrs = 40*14=560
Excess = 976-560=416
For extra hours =.75(14)=10.5+14=24.5
Number of extra hrs =416/24.5=18.82=19 approx.
Total hrs =40+19=59
Answer C 59
Answer: (C) 59
Question: 24 oz of juice P and 25 oz of juice F are mixed to make smothies X and Y . The ratio of p to F in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to F ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice F will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice F = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice V = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: (D) 20
Question: Harkamal purchased 3 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)700
(B) B)1065
(C) C)1070
(D) D)1075
(E) E)1080
Rationale: Cost of 3 kg grapes = 70 × 3 = 210.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 210 + 490 = 700
A
Answer: (A) A)700
Question: There are 76 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
(A) 28
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: Editing my solution:
Number of switches = 76
Number of switches turned on by A: 3, 6, ... 75 = 25
Number of switches turned on by B: 5, 10, ....75 = 15
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (25 - 6) + (15 - 6) = 28
Answer: A
Answer: (A) 28
Question: For positive integers n, the integer part of the nth term of sequence B equals n, while the infinite decimal part of the nth term is constructed in order out of the consecutive positive multiples of n, beginning with 2n. For instance, B_1 = 1.2345678…, while B_2 = 2.4681012… The sum of the first seven terms of sequence B is between:
(A) 28 and 29
(B) 29 and 30
(C) 30 and 31
(D) 31 and 32
(E) 32 and 33
Rationale: First, construct the first seven terms, though only out to a few decimal places, following the given pattern.
B_1 = 1.23…
B_2 = 2.46…
B_3 = 3.69…
B_4 = 4.812…
B_5 = 5.10…
B_6 = 6.12…
B_7 = 7.14…
Now, to add up the first seven terms, you should be strategic about how many decimal places to keep. You can drop the hundredths place and get a good approximation with the tenths place—and if you find the sum too close to a boundary between choices, then you can refine your answer if necessary.
1.2 + 2.4 + 3.6 + 4.8 + 5.1 + 6.1 + 7.1 = 30.3
Including more decimal places would only add a couple of tenths to the sum—not enough to tip the sum over 31.
The correct answer is C.
Answer: (C) 30 and 31
Question: A jar is filled of liquid which is 3 parts water and 5 parts alcohol. How much of this mixture should be drawn out and replaced such that this mixture may contain half
water and half alcohol?
(A) 28%
(B) 10%
(C) 20%
(D) 29%
(E) 26%
Rationale: Explanation:
Let the jar initially contain 8 litres of mixture:3 litres water and 5 litres alcohol
Let x litres of this mixture is drawn out and is replaced by x litres of water.
Amount of water now in the solution: 3-(3/8)x+x.
Amount of alcohol now in the solution: 5-(5/8)x
Desired ratio: 1/1
=>3-(3/8)x+x=5-(5/8)x
x=8/5 litres
%x=((8/5)/8)*100=20%
ANSWER: C
Answer: (C) 20%
Question: A large delicatessen purchased p pounds of cheese for c dollars per pound. If d pounds of the cheese had to be discarded due to spoilage and the delicatessen sold the rest for S dollars per pound, which of the following represents the gross profit on the sale of the purchase? (gross profitequalssales revenueminusproduct cost)
(A) (p − d)(s − c)
(B) s(p − d) − pc
(C) c(p − d) − ds
(D) S(p-d) - cp
(E) pc − ds
Rationale: Total cost price = c*p ............... (1)
Wastage = d pounds
Quantity sold = p-d
Selling price per pound = S
Total selling price = S(p-d) ........... (2)
Profit = (2) - (1)
= S(p-d) - cp
D
Answer: (D) S(p-d) - cp
Question: What is the rate percent when the simple interest on Rs.1200 amount to Rs.400 in 4 Years?
(A) 8.33%
(B) 6%
(C) 2%
(D) 95%
(E) 1%
Rationale: Interest for 4yrs = 400
Interest for 1yr = 100
Interest rate = 100/1200 x 100 = 8.33%
Answer : A
Answer: (A) 8.33%
Question: If a and b are different positive integers and b(a + b) = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer
D.
Answer: (D) I and II
Question: Ramesh can complete a work in 12 days, working 7 hours a day. Suresh can complete the same work in 8 days, working 9 hours a day. If Ramesh and Suresh work together working 7 hours a day, in how many days can they complete the work?
(A) 5 * 7 / 13
(B) 5 * 7 / 19
(C) 5 * 7 / 11
(D) 5 * 7 / 19
(E) 5 * 6 / 11
Rationale: Explanation:
Ramesh can finish the work in 12 * 7 = 84 hours
Amount of work he can complete in 1 hour = 1/84
Suresh can finish the same work in 8 * 9 = 72 hours
Amount of work he can complete in 1 hour = 1/72 hours
Work done by both of them in 1 hour =
= 1/84 + 1/72 = 13/504
Ramesh and Suresh together can complete the work in 504/13 hours.
i.e. 504/13 * 1/7 = 72/13 days
i.e. 5 * 7 / 13 days
ANSWER: A
Answer: (A) 5 * 7 / 13
Question: A train 250 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 9 sec
(C) 12 sec
(D) 15 sec
(E) 18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 250 m at 50/3 m / sec
= 250 *3/ 50 sec = 15sec
Answer : D
Answer: (D) 15 sec
Question: If x, 3, 5, 7 are there and the range and median of them are the same, what is the value of x?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 4
Rationale: Try taking the values of x as you suggested and then see if the median and the range are equal.
Once you do that, you will get the answer yourself.
Tried substituting values starting with 3, 5, 7...
only x = 5 satisfies the condition.
D
Answer: (D) 5
Question: The average of first six prime numbers which are between 40 and 80 is
(A) 35.4
(B) 50.7
(C) 45.7
(D) 57
(E) 67
Rationale: Explanation :
first six prime numbers which are between 40 and 80 = 41, 43, 47, 53, 59, 61
average = (41 + 43 + 47 + 53 + 59 + 61)/6
= 50.7
Answer : B
Answer: (B) 50.7
Question: Ravi can do a piece of work in 30 days while Prakash can do it in 40 days. In how many days will they finish it together?
(A) 17 1/7 days
(B) 17 1/8 days
(C) 17 5/7 days
(D) 17 3/7 days
(E) 13 1/7 days
Rationale: 1/30 + 1/40 = 7/120
120/7 = 17 1/7 days
Answer: A
Answer: (A) 17 1/7 days
Question: Determine the value of 62/54 divided by 62/54
(A) 0
(B) 1
(C) 2
(D) 3
(E) none
Rationale: Solution:
Each number divided by itself equals 1.
Answer B
Answer: (B) 1
Question: A train passes a station platform in 30 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 120 m
(B) 240 m
(C) 168 m
(D) 75 m
(E) 60 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/30 = 15 => x
= 60 m
Answer: E
Answer: (E) 60 m
Question: A and B are two partially filled buckets of water. If 6 liters are transferred from A to B, then A would contain one-third of the amount of water in B. Alternatively, if 6 liters are transferred from B to A, B would contain one-half of the amount of water in A. Bucket A contains how many liters of water?
(A) 66/5
(B) 13
(C) 17
(D) 21
(E) 23
Rationale: Let Bucket A be A and Bucket B be B
Scenario 1
A-6 = 1/3 (B+6) ----> 3A-18 =B+6
Scenario 2
B-6 = 1/2 (A+6) -----> 2B-12 = A+6
From Scenario 1, B = 3A-24
Substitute B with this information in Stmt 2
2 (3A-24) -12 = A+6 ------> 6A -48-12 = A+6 ------> 6A- A = 60+6 ---> 5A= 66
A= 66/5, Answer choice A
Answer: (A) 66/5
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity W of the pool?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Rationale: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: (D) 12000 cubic meters
Question: What is the smallest number which when diminished by 20, is divisible 15, 30, 45 and 60?
(A) 200
(B) 220
(C) 240
(D) 322
(E) 342
Rationale: Required Number
= (LCM of 15, 30, 45 and 60) + 20
= 180 + 20 = 200
Option A
Answer: (A) 200
Question: A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 135 m
(B) 786 m
(C) 566 m
(D) 546 m
(E) 445 m
Rationale: Speed = 54 * 5/18 = 15 m/sec
Length of the train = speed * time = 15 * 9
= 135 m
Answer: A
Answer: (A) 135 m
Question: r=2^(n+2), then in terms of r, 9^n=
(A) r^2/81
(B) r^2/16
(C) r^2
(D) r/3
(E) r
Rationale: Questions in terms of variables can be easily solved by plugging in some values: Say n = 0
r = 2^2 = 4
and you need the value of 4^n which is 4^0 = 1
So when you put r = 4 in the options, you should get 1. Only option (A) satisfies.
Answer (B)
Answer: (B) r^2/16
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.3624
(B) s.4518
(C) s.4518
(D) s.4530
(E) s.4517
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls = 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3) = 906 sq.ft.
Total cost = 906 * 4 = Rs.3624
Answer: A
Answer: (A) s.3624
Question: In a Question paper there are 6 multiple choice questions. Each question has 3 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the four answers correct?
(A) 19
(B) 85
(C) 748
(D) 624
(E) 1024
Rationale: A candidate can answer the test in 3^6 number of ways (each question has 3 choices and we have total of 6 questions). Now, out of these cases there will be only one case when the candidate answered all the six questions correct. Therefore the total number of ways in which a candidate will NOT get all the six answers correct is 3^6-1=748.
Answer: C.
Answer: (D) 624
Question: Nine children — A, B, C, D, E, F, G, H and I — are going to sit in nine chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 80640
(D) 84320
(E) 84800
Rationale: for such questions , we can treat both as one then total person=8..
these 8 can be arranged in 8! ways.. but within these 8 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =8!*2=80640
ans C
Answer: (C) 80640