mathewhe/aqua_rat huggingface dataset:
Question: A fair gold coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
(A) A)37/256
(B) B)56/256
(C) C)65/256
(D) D)70/256
(E) E)81/256
Rationale: Landing on tails more than 5 times means tails has to hit 6, 7 or 8 times.
8!/6!2! = 7*4 = 28
8!/7!1! = 8
8!/8! = 1
28 + 8 + 1 = 37/256
ans:A
Answer: (A) A)37/256
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a black cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
(A) 90
(B) 180
(C) 360
(D) 540
(E) 720
Rationale: # ways to distribute Blue marbles(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbles(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbles(1) is :
3 ways
total number of ways = 10*6 *3 = 180 ANS:B
Answer: (B) 180
Question: A train running at the speed of 52 km/hr crosses a pole in 18 seconds. What is the length of the train?
(A) 120 metres
(B) 180 metres
(C) 260 metres
(D) 150 metres
(E) 100 meters
Rationale: Speed=52 x5/18m/sec=130/9	m/sec.
Length of the train = (Speed x Time).
Length of the train =	130/9 x 18m = 260 m.
ANSWER:C
Answer: (C) 260 metres
Question: When a train travels at a speed of 60kmph,it reaches the destination on time.when the same train travels at a speed of 50kmph,it reaches its destination 15min late.what is the length of journey?
(A) 75km
(B) 50km
(C) 60km
(D) 85km
(E) 95km
Rationale: Let x be the time reached with the speed 60km/h
50km/h ----> x+15
Distance is equal so
60(km/h)× xhr = 50(km/h) × (x+15) hr
So
60 x = 50x + 750
So the would be in km
And x = 75
So
75km
ANSWER:A
Answer: (A) 75km
Question: A jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 37 sec
(C) 36 sec
(D) 72 sec
(E) None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (250 + 120) m = 370 m.
∴ Time taken = (370⁄10) sec = 37 sec.
Answer B
Answer: (B) 37 sec
Question: What is the next number of the following sequence
7776,625,64,9,2
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 7776,625,64,9,2, x
7796 --> 6^5
625 --> 5^4
64 --> 4^3
9 --> 3^2
2 --> 2^1
x --> 1^0 ==> 1
ANSWER:A
Answer: (A) 1
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in
(A) 144 mins
(B) 140 mins
(C) 136 mins
(D) 132 minw
(E) None of these
Rationale: Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/35
=>4/x=1/35
x=35∗4=140 mins
Option B
Answer: (B) 140 mins
Question: In a division sum,the divisor is 10 times the quotient and 5 times the remainder.If the remainder is 46,what is the dividend ?
(A) 5336
(B) 5242
(C) 6524
(D) 3526
(E) 4526
Rationale: Divisor=(5*46)=230
10*quotient =230
quotient =230/10=23.
dividend =(divisor*quotient)+remainder
=(230*23)+46=(5290+46)=5336.
Answer is A
Answer: (A) 5336
Question: If in a cricket one day match, there were no wide balls, no wides, no extras and no overthrows.
What is the maximum number of runs that a batsman can score in 30 overs in an ideal case scenario?
(A) 1020
(B) 993
(C) 985
(D) 996
(E) None
Rationale: Solution:
993
Explanation:
For an ideal case, the batsman will hit a six on each ball. But if he hits six on the last ball of the over, the strike will change in the next over. Thus, the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over. Thus the total runs that he can score in each over:
6 * 5 + 3 = 33
But this will have to go like it only till the 29th over. In the 30th over, he can hit a six in the last ball as well as that will be the last ball of his destination.
Thus runs for the 30th over will be 6 * 6 = 36.
Hence the maximum runs = 33 * 29 + 36 = 993
Answer B
Answer: (B) 993
Question: 3.5 can be expressed in terms of percentage as?
(A) 0.35%
(B) 3.5%
(C) 35%
(D) 350%
(E) 0.0035%
Rationale: Answer: Option D
3.5 = 35/10 = (35/10 * 100) = 350%
Answer: (D) 350%
Question: If X = Z*Y/Y, -10 < Z < 0 and 5 < Y, which of the following is correct?
(A) X > 9.
(B) 0 < X <9.
(C) -9 < X < 0
(D) X < -10.
(E) X>-10
Rationale: Y is +ve & Z is -ve
Eliminate A & B
For min. value max. numerator and minimize denominator
take Y=5.1 & Z=-9.9
X=(-9.9*5.1)/5.1
X=-50.49/5.1
X>-10
Ans E
Answer: (E) X>-10
Question: Dacid obtained 70, 63, 80, 63 and 65 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 67
(B) 26
(C) 87
(D) 26
(E) 68
Rationale: Average
= (70+ 63+ 80+ 63+ 65)/5
= 341/5 = 68.2.
Answer: E
Answer: (E) 68
Question: What is the median from the below series
101, 105, 103, 109, 107, 110, 115, 113, and 114
(A) 105
(B) 107
(C) 101
(D) 113
(E) 109
Rationale: Ordering the data from least to greatest, we get:
101, 103, 105, 107, 109, 110, 113, 114, 115
The median number was 109. (Four numbers were higher than 109 and four were lower.)
E
Answer: (E) 109
Question: In what time a debt of Rs.7920 due may be cleared by immediate cash down
payment of Rs.3600 at 1/2% per month
(A) 10years
(B) 20years
(C) 30years
(D) 40years
(E) 50years
Rationale: Explanation:
PW=100x Amount/100+(RxT)
Answer: B
Answer: (B) 20years
Question: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 5 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 7 percent grade, what is x in terms of y and z?
(A) -1y - 2z
(B) (y +z) / 4
(C) 2y + 3z
(D) 3y + z
(E) 3y + 4.5z
Rationale: Based on the given information, the following equation could be dervied: 1% * x + 5% * y + 3% * z = 7% * (x+y+z)
Then use algebra to figure out 6%*x = -2%*y - 4%*z. Thus, 3x = -1y - 2z.
A
Answer: (A) -1y - 2z
Question: A tank is filled by 3 pipes A,B,C in 6 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
(A) 25hr
(B) 42hr
(C) 40hr
(D) 20hr
(E) 50hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/6
7/x = 1/6
x = 42 hours
Answer is B
Answer: (B) 42hr
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train?
(A) 270
(B) 277
(C) 200
(D) 257
(E) 271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 20 * 10 = 200 m.
The length of the faster train = 200 m.
Answer: C
Answer: (C) 200
Question: If you roll one fair six-sided die, what is the probability that the number is even or less than 5?
(A) 3/4
(B) 5/6
(C) 1/2
(D) 2/3
(E) 1/6
Rationale: The numbers which satisfy the conditions are 1, 2, 3, 4, and 6.
The probability is 5/6
The answer is B.
Answer: (B) 5/6
Question: A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
(A) 160
(B) 170
(C) 180
(D) 200
(E) 220
Rationale: 25 + 25 = 50
25% ------ 50
100% ----- ? => 200
ANSWER:D
Answer: (D) 200
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 26
(B) 28
(C) 23
(D) 28
(E) 21
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.Answer: C
Answer: (C) 23
Question: Present ages of Sameer and Anand are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Anand's present age in years?
(A) 24 years
(B) 28 years
(C) 27 years
(D) 16 years
(E) 09 years
Rationale: Let the present ages of Sameer and Anand be 5x and 4x years respectively.
Then, (5x + 3)/(4x + 3) = 11/9
9(5x + 3) = 11(4x + 3) => x = 6
Anand's present age = 4x = 24 years.
Answer:A
Answer: (A) 24 years
Question: The ratio of the earnings of P and Q is 9 : 10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
(A) 3/6
(B) 3/2
(C) 3/9
(D) 3/1
(E) 3/5
Rationale: Let the earnings of P and Q be Rs. 9x and Rs. 10x respectively.
New ration = [9x + 1/4(9x)]/[10x - 1/4(10x)]
=> [9x(1 + 1/4)]/[10x(1 - 1/4)] = 9/10 * (5/4)/(3/4)
=> 3/2.
Answer: B
Answer: (B) 3/2
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 210 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 88
(B) 45
(C) 36
(D) 80
(E) 12
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 210 = 450 m.
Time taken = 450/10 = 45 sec.
Answer: B
Answer: (B) 45
Question: Given that 100.48 = x, 100.70 = y and xz = y², then the value of z is close to
(A) 1.2
(B) 1.45
(C) 2.2
(D) 2.9
(E) NOne
Rationale: Sol.
xz = y² ⇔ (10 0.48 )z(100.70)2 (10 0.48z) = 10(2×0.70) = 101.40
⇔ 0.48z = 1.40 ⇔ z= 140/48 = 35/12 = 2.9 (approx).
Answer D
Answer: (D) 2.9
Question: The probability that A speaks truth is 1/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 13/35
(B) 18/38
(C) 18/36
(D) 18/16
(E) 18/31
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability
= 1/5 * 4/7 + 4/5 * 3/7
= 1/35 + 12/35
= 13/35
Answer: A
Answer: (A) 13/35
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 50 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour?
(A)  7
(B)  5
(C)  12
(D)  13
(E)  15
Rationale: Rate of H = 5 acres/hr
Remaining land to be harvested = 100 - 50 = 50
Rate of H and K = 50/5 = 10 acres/hr
Rate of K = 10 - 5 =5
Answer: B
Answer: (B)  5
Question: The average of ten numbers is 8. If each number is multiplied by 8, then what is the average of the new set of numbers?
(A) 8
(B) 16
(C) 64
(D) 80
(E) 88
Rationale: The sum of the ten numbers is 8*10 = 80
If each number is multiplied by 8, the new sum is 8*(80).
The average is then 8*8 = 64
The answer is C.
Answer: (C) 64
Question: If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {7,8,9}, what`s the probability that xy will be even?
(A) 2/3
(B) 1/3
(C) 1/2
(D) 1/6
(E) 5/6
Rationale: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: A.
Answer: (A) 2/3
Question: Find the solution set of the equation x2+x+2=0 in roster form
(A) {1,-2}
(C) {1,1}
(D) {1}
(E) none
Rationale: (x+2)(x-1)=0
x=-2 or 1
ANSWER:A
Answer: (A) {1,-2}
Question: If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: For n(n+1) to be a multiple of 3, either n or n+1 has to be a multiple of 3.
Thus n must be of the form 3k or 3k-1, but not 3k+1.
The probability is 2/3.
The answer is D.
Answer: (D) 2/3
Question: Find the compound interest on $ 56,000 at 20% per annum for 9 months, compounded quarterly
(A) 2532
(B) 2552
(C) 6524
(D) 8827
(E) 9512
Rationale: Principal = $ 56000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [56000 x (1+(5/100))^3] = $ 64827.
CI. = $ (64827 - 56000) = $ 8827.
Answer D.
Answer: (D) 8827
Question: A train overtakes two girls who are walking in the opposite direction in which the train is going at the rate of 3 km/h and 6km/h and passes them completely in 36 seconds and 30 seconds respectively. The length of the train is:
(A) 120m
(B) 150m
(C) 125m
(D) None of these
(E) Cannot be determined
Rationale: Explanation:
Let the length of the train e x meter, and let the speed of train be y km/h, then
x = (y + 3)5/18 × 36 .........(1)
and x = (y + 6)5/18 × 30 .....(2)
From eq (1) and (2), we get
(y + 3) × 36 = (y + 6) × 30
y = 12 km/h
x = (y + 3) × 5/18 × 36
x = 150 m
Answer: B
Answer: (B) 150m
Question: A set of data consists of the following 8 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 4 and 4 , results in a value that would change the SD to the least. Hence B
Answer: (B) 4 and 4
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked six 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 480
(D) 350
(E) 400
Rationale: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 6 days -> 80*6=480.
This matches answer choice C.
Answer: (C) 480
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 24,000 is made?
(A) 1,20,003
(B) 1,20,000
(C) 1,20,001
(D) 1,20,027
(E) 1,20,004
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,20,000
Answer:B1,20,000
Answer: (B) 1,20,000
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
(A) 18/35
(B) 12/35
(C) 17/35
(D) 19/35
(E) None of these
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
ANSWER:A
Answer: (A) 18/35
Question: What is the square root of 239,121?
(A) 476
(B) 489
(C) 497
(D) 511
(E) 524
Rationale: According to divisibility rules, 239,121 is divisible by 9.
2+3+9+1+2+1=18
This means, that the answer choice must be divisible by 3
A) 4+7+6= 17 NO
B) 4+8+9= 21 YES
C) 4+9+7= 20 NO
D) 5+1+1= 7 NO
E) 5+2+4= 11 NO
B is the only answer
Answer: (B) 489
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 94 percent in some time period, which of the following could be the final mass of that element?
(A) 27 grams
(B) 28 grams
(C) 29 grams
(D) 31 grams
(E) 32 grams
Rationale: Final mass/0.06 = Original mass
Original mass is a whole number. Only 27 is divisible by 0.06 or 2700/6 is a whole number.
Answer: A
Answer: (A) 27 grams
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?
(A) Rs.400
(B) Rs.450
(C) Rs.500
(D) Rs.550
(E) Rs.600
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: (C) Rs.500
Question: What is the smallest number which when increased by 3 is divisible by 27, 35, 25, & 21 ?
(A) 4722
(B) 4725
(C) 4728
(D) 4731
(E) 4733
Rationale: Here smallest number means LCM
Hence LCM of 27,35,25,21 = 3^3 x 5^2 x 7
= 4725
Therefore required number is 4725 - 3 =4722
Ans - A
Answer: (A) 4722
Question: A pipe can empty 2/3rd of a cistern in 12 mins. In 8 mins, what part of the cistern will be empty?
(A) 2/3
(B) 2/5
(C) 4/9
(D) 5/7
(E) 4/11
Rationale: 2/3 ---- 12
? ----- 8 ==> 4/9
C
Answer: (C) 4/9
Question: If 2^k + 2^k = (2^9)^(2^9) - 2^k, then k = ?
(A)  11/3
(B)  11/2
(C) 2^11 - 1
(D)  3^10
(E)  3^11 - 1
Rationale: 2^k + 2^k = (2^9)^2^9 - 2^k
2*(2^k) = 2 ^ (4 * 3^9 ) = 2^(2^2 * 2^9) = 2^(2^11)
2^k+1 = 2^(2^11)
So k+1 = 2^11
So k = 2^11 -1
Answer is C
Answer: (C) 2^11 - 1
Question: In a group of 10 doctors, 3 doctors are only pediatricians; the others are surgeons or general practitioners - but not both. A team of 3 doctors is to be chosen which must have at least 1 pediatrician, how many different teams can be chosen?
(A) 85
(B) 140
(C) 60
(D) 80
(E) 75
Rationale: The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 10
r = 3
So, total teams is 10C3 = 10!/(3!(10 - 3)!) = 120, and
n = 10 - 3 = 7
r = 3
for teams without a pediatrician is 7C3 = 7!/(3!(7 - 3)!) = 35,
so, teams with at least 1 pediatrician = 120 - 35 = 85
Answer: A
Answer: (A) 85
Question: Excluding stoppages, the speed of a bus is 54 km/hr and including stoppages, it is 45 km/hr. For how many minutes does the bus stop per hour?
(A) 22
(B) 10
(C) 99
(D) 77
(E) 29
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = 9/54 * 60 = 10 min.
Answer:B
Answer: (B) 10
Question: Nicole cycles at a constant rate of 12 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) x/3
(B) x/2
(C) x
(D) 3x/2
(E) 2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 12 = x/24 hours = 5x/2 minutes
Jessica needs to wait 5x/2 - x = 3x/2 minutes.
The answer is D.
Answer: (D) 3x/2
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre.
(A) Rs. 15,000
(B) Rs. 8,250
(C) Rs. 15,600
(D) Rs. 16,500
(E) None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (400 x 20.625)
= Rs.8,250.
Answer B
Answer: (B) Rs. 8,250
Question: If x, y, and a are positive numbers such that 10*x/(x+y)+ 20*y/(x+y)=a and if x is less than y, which of the following could be the value of a?
(A) 10
(B) 12
(C) 15
(D) 18
(E) 30
Rationale: Answer choice C: a= 15
(10x + 20y)/(x+y) = 15
10x + 20y = 15x + 15y
5y = 5x
y = x
Doesn't work because the problem states that x<y.
We need y to be larger, so let's try answer choice D: a=18
10x + 20y = 18x + 18y
2y = 8x
y/x = 8/2
Success! x<y.
The correct answer is D.
Answer: (D) 18
Question: With out any halt a train travels a certain distance with an average speed of 66 km ph , and with halts it covers the same distance at an average speed of 33 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
(A) 48 min.
(B) 12min.
(C) 60min.
(D) 18min.
(E) 19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 66/33= 2/1 = 120 minutes
:. 60 minutes is the halting time per hour
ANSWER:C
Answer: (C) 60min.
Question: After 76 liters of petrol were poured into the tank, it was still 5% empty. How much petrol must be poured into the tank in order to fill it?
(A) 7 liters
(B) 4 liters
(C) 3 liters
(D) 2 liters
(E) 6 liters
Rationale: 95% ----------- 76
5% ------------ ?
=> 4 liters
Answer: B
Answer: (B) 4 liters
Question: A part-time employee’s hourly wage was increased by 15%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
(A) 13%
(B) 15%
(C) 25%
(D) 50%
(E) 100%
Rationale: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 15% wage increase, the employee makes $1.15/hour
We want the employee's income to remain at $100/week.
So, we want ($1.15/hour)(new # of hours) = $100
Divide both sides by 1.15 to get:
new # of hours = 100/1.15
≈ 87 hours
So, the number of hours decreases from 100 hours to (approximately) 87 hours.
This represents a 13% decrease (approximately) .
Answer : A
Answer: (A) 13%
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
(A) 2000
(B) 2088
(C) 2799
(D) 2098
(E) 2798
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: (A) 2000
Question: If the curve represented by y = x^2 – 5x + t intersects with the x-axis at two points and one of the points is (–1, 0), what is the other point?
(A) (1, 0)
(B) (–2, 0)
(C) (5, 0)
(D) (6, 0)
(E) (3, 0)
Rationale: Curve represented by y = x^2 – 5x + t intersects with the x-axis at points where y = 0.
One of the points is (-1,0) Plugging in the equation => 0 = 1 + 5 + t => t = -6
Plugging t back to the equation now we have y = x^2 – 5x - 6, where y = 0.
This equation gives 2 solution x= -1 and 6.
We already know about the point (-1,0) so the other point is (6,0).
Hence D.
Answer: (D) (6, 0)
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 11,000?
(A) 50,000
(B) 2,750,000,000
(C) 850,000
(D) 7,500,000
(E) 750,000,000
Rationale: number of cars sold = x=800000-50y
y=11000
x=800000-550000=250000
revenue from 250000 cars=11000*250000=2750000000 B
Answer: (B) 2,750,000,000
Question: 850 - (1500 ÷ ?) × 8/15 = 770
(A) A)31
(B) B)10
(C) C)15
(D) D)26
(E) E)17
Rationale: Explanation:
=> 850 - (1500 ÷ ?) × 8/15 = 770
=> 850 - 770 = (1500 ÷ ?) × 8/15
=> 80 = (1500 ÷ ?) × 8/15
=> 80 × 15/8 = (1500 ÷ ?) = 150
=> 1/? = 150/1500 = 1/10
=> ? = 10
Answer: Option B
Answer: (B) B)10
Question: Two pipes can fill a tank in 10 minutes and 15 minutes. An outlet pipe can empty the tank in 30 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 7.0
(B) 7.5
(C) 8.0
(D) 8.5
(E) 9.0
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/10 + V/15 - V/30 = 2V/15 per minute
The tank will be filled in 15/2 = 7.5 minutes.
The answer is B.
Answer: (B) 7.5
Question: Find the odd man out.
41, 43, 47, 53, 61, 71, 73, 81
(A) 22
(B) 88
(C) 27
(D) 81
(E) 01
Rationale: Explanation:
Each of the numbers except 81 is a prime number.
Answer: D) 81
Answer: (D) 81