mathewhe/aqua_rat huggingface dataset:
Question: If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 4, and 5, what is the greatest number of four-digit extensions that the company can have?
(A) 4
(B) 6
(C) 12
(D) 16
(E) 24
Rationale: Since the phone number must be even, the unit's digit can be either 2 or 4.
When the unit's digit is 2 --> number of possibilities is 3! = 6
When the unit's digit is 4 --> number of possibilities is 3! = 6
Largest number of extensions = 6 + 6 =12
Answer:C
Answer: (C) 12
Question: Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?
(A) 30000 B = 40000 C = 48000
(B) 30060 B = 40800 C = 49000
(C) 33000 B = 40000 C = 48600
(D) 30000 B = 40000 C = 48000
(E) 30000 B = 43000 C = 48060
Rationale: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000
Answer:A
Answer: (A) 30000 B = 40000 C = 48000
Question: If (n+2)!/n!=156, n=?
(A) 2/131
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: (n+2)!/n!= 156
Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132
Cancel out terms: (n+2)(n+1) = 156
From here, we might just TEST the answer choices.
Since (13)(12) = 156, we can see that n = 11
D
Answer: (D) 11
Question: What is the length of a bridge (in meters), which a train 156 meters long and travelling at 45 km/h can cross in 30 seconds?
(A) 203
(B) 211
(C) 219
(D) 227
(E) 235
Rationale: speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 156 = 219 meters
The answer is C.
Answer: (C) 219
Question: There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?
(A) 12
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: There are 18 balls in a jar. You take out 3 blue balls without putting
3 blue balls + 15 / 5 =6
Answer:E
Answer: (E) 6
Question: In how many ways can six different rings be worn on four fingers of one hand?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Required number of ways = ways of selecting 4 objects out of 6 given objects
= 6C4 = 6x 5/2= 15
Answer C
Answer: (C) 15
Question: How long does a train 110 metres long running at the speed of 72 km / hr take to cross a bridge 132 metres in length?
(A) 9.8 sec
(B) 12.1 sec
(C) 12.42 sec
(D) 14.3 sec
(E) None
Rationale: Solution
Speed	= (72 x 5/18 )m/sec
= 20 m/ sec
Total Distance covered	= (110 + 132) m
= 242 m
Required time	= (242 / 60) sec
= 12.1 sec
Answer B
Answer: (B) 12.1 sec
Question: Each student is given a four-character identification code. The first character is a number from 0 to 9 inclusive, and the last three characters are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?
(A) 175,760
(B) 163,120
(C) 152,340
(D) 143,590
(E) 132,670
Rationale: The number of possible codes is 10*26*26*26=175,760.
The answer is A.
Answer: (A) 175,760
Question: If a and b are prime numbers and one the value of them is 2, which of the following CANNOT be the value of ab?
(A) 9
(B) 14
(C) 21
(D) 24
(E) 25
Rationale: Here one the prime number is 2,so the answer should be the double of a prime number,which is14=7/2..
ans B
Answer: (B) 14
Question: Solve:-
222 x 222 x 222 + 555 x 555 x 555 = ?(222 x 222 - 222 x 555 + 555 x 555)
(A) 888
(B) 333
(C) 555
(D) 988
(E) 777
Rationale: Given Exp. = (a3 + b3) = (a + b) = (222 + 555) = 777(a2 - ab + b2)
Answer E
Answer: (E) 777
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?
(A) 0
(B) 200
(C) 440
(D) 668
(E) 762
Rationale: Simplifying the question into easier words we just need to find which of the numbers is not divisible by 4
clearly the answer is 762 because if we divide 762 by 4 we get a remainder of 2
Correct answer - E
Answer: (E) 762
Question: If m and n are positive integers, and m=2n and k=m, then -
(A) m/2 is a factor of k.
(B) 2m is a factor of k.
(C) 3m is a factor of k/2.
(D) k is a factor of m.
(E) k is a factor of m/2.
Rationale: m=2n --> m is even.
k=m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: A.
Answer: (A) m/2 is a factor of k.
Question: Rodrick mixes a martini that has a volume of 'n' ounces having 35% Vermouth and 60% Gin by volume. He wants to change it so that the martini is 25% Vermouth by volume. How many ounces of Gin must he add?
(A) n/6
(B) n/3
(C) 2n/5
(D) 5n/6
(E) 8n/5
Rationale: total V G
1 ounce 0.35 0.6
n ounce 0.35n 0.6n -------------initial expression
lets say g ounces of gin is added to this mixture
n+g 0.35n 0.6n+g --------------final expression
given that after adding g ounces of gin , V should become 25% of the total volume.
=>Volume of V/total volume = 25/100
=> 0.35n /n+g = 1/4
=> 1.4n = n+g
=> g = 2n/5
Answer is C.
Note that after we add pure Gin, the volume of Vermouth will remain the same. Based on this set the equation:
0.35n=0.25(n+g) --> g=2n/5
Answer: C.
Answer: (C) 2n/5
Question: A boat moves upstream at the rate of 1 km in 20 minutes and down stream 1 km in 15 minutes. Then the speed of the current is :
(A) 1 kmph
(B) 0.5 kmph
(C) 3 kmph
(D) 2.5 kmph
(E) 3.5 kmph
Rationale: Rate upstream = (1/20 *60) = 3 kmph
Rate down stream = 1/15 * 60 = 4 kmph
Rate of the current = ½ (4-3) = 0.5 kmph
ANSWER:B
Answer: (B) 0.5 kmph
Question: The cost of.275 kgs. of sugar is Rs.26. What is the cost of 6 kgs. of sugar?
(A) Rs.68
(B) Rs.67
(C) Rs.572
(D) Rs.567.275
(E) Rs.75
Rationale: Explanation:
The cost of 6 kgs. of sugar = 26X6/0.275 = Rs.567.275
Answer: Option :D
Answer: (D) Rs.567.275
Question: Ms. Samantha sold two properties, X and Y, for $45,500 each. She sold property X for 30 % more than she paid for it and sold property Y for 30% less than she paid for it. If expenses are disregarded , what was her total net gain or loss, if any, on the two properties ?
(A) $9500
(B) $9000
(C) $9600
(D) $9700
(E) $9800
Rationale: There is a property to solve such questions withCommon Selling PriceandCommon %gain and loss. such cases always result in a loss and...
Total %Loss = (Common Gain% or Loss%/10)^2
Hence Here Loss% = (30/10)^2 = 9%
which means he recovered only 91% of his investment which amount to a total revenue = 45500 + 45500 = 91000
i.e. 91% of cost = 91000
therefore, 9% of cost (Loss) = $9000
Answer: B
Answer: (B) $9000
Question: A motorcyclist made 3 roundtrips to the park until he ran out of gas back at home. Te park is 1500 meters away from his home. His speedometer was broke and he wanted to calculate his speed. It took him two and half hours to complete the journey. How fast was the motorcyclist traveling?
(A) 25
(B) 60
(C) 36
(D) 45
(E) 32
Rationale: The distance from the park to the motorcyclist home was 15000 meters.
He made the trip 3 times in total with each trip being 30000 meters.
multiply 3 by 30000 to get 90000 meters or 90km in total.
D= ST
90000/2.5 = T which comes to 36000 meters or 36 km per hour
Correct answer = 36
Answer: (C) 36
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability W that the worker is under 25 years old?
(A)  0.30
(B)  0.25
(C)  0.45
(D)  0.70
(E)  0.90
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old W= .7
Answer D
Answer: (D)  0.70
Question: Jayant opened a shop investing Rs. 30,000. Madhu joined him 2 months later, investing Rs. 45,000. They earned a profit of Rs. 60,000 after completion of one year. What will be Madhu's share of profit?
(A) Rs. 27,000
(B) Rs. 24,000
(C) Rs. 30,000
(D) Rs. 36,000
(E) None of these
Rationale: 30,000 *12=45,000*8
1:1
Madhu's share=1/2*60,000
i.e. Rs. 30,000
ANSWER:C
Answer: (C) Rs. 30,000
Question: A table is bought for Rs.900/- and sold at Rs.810/- find the loss percentage
(A) 5%
(B) 10%
(C) 15%
(D) 20%
(E) 22%
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (810 ~ 900)/900 = 10% Loss
B
Answer: (B) 10%
Question: The average of 5 numbers is 6.8. If one of the numbers is multiplied by a factor of 3, the average of the numbers increases to 12.8. What number is multiplied by 3?
(A)  15.0
(B)  13.0
(C)  13.9
(D)  10.0
(E)  6.0
Rationale: The average of 5 numbers is 6.8
The sum of 5 numbers will be 6.8 x 5 = 34
The average of 5 number after one of the number is multiplied by 3 is 12.8
The sum of the numbers will now be 12.8 x 5 = 64
So the sum has increased by 64-34 = 30
Let the number multiplied by 3 be n
Then,
3n = n+30
or 2n = 30
or n = 15
Answer:- A
Answer: (A)  15.0
Question: Some of the workers at a hedge fund are analysts; the others are not analysts. There are a total of 2x/3 analysts at the hedge fund. A total of x hedge fund workers have an MBA. Furthermore, x/3 analysts have an MBA, y/4 of the hedge fund workers are neither analysts nor have an MBA, and 60 workers are not analysts. If there are y total workers at the hedge fund, x is equal to which of the following?
(A) 45
(B) 54
(C) 60
(D) 75
(E) 80
Rationale: AnalystsNot AnalystsTotal
MBAx/32x/3x
No MBAy/4
Total2x/350y
We are asked for the value of x.
From the table: 2x/3 = y - 60
y - 60 + (y/4) = 60
5y/4 = 120
y = 96
2x/3 = 96 - 60 = 36
x = 108/2 = 54
Answer: B
Answer: (B) 54
Question: In how many ways, a committee of 5 members can be selected from 8 men and 5 ladies, consisting of 3 men and 2 ladies?
(A) 75
(B) 152
(C) 175
(D) 560
(E) 612
Rationale: (3 men out 8) and (2 ladies out of 5) are to be chosen
Required number of ways = (8C3 * 5C2) = 560
Answer is D
Answer: (D) 560
Question: The dimensions of a rectangular solid are 4 inches, 5 inches, and 9 inches. If a cube, a side of which is equal to one of the dimensions of the rectangular solid, is placed entirely within thespherejust large enough to hold the cube, what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube?
(A)  2:5
(B)  5:9
(C)  5:16
(D)  25:7
(E)  32:25
Rationale: Answer: B.
Answer: (B)  5:9
Question: Two trains are moving in the same direction at 108 kmph and 36 kmph. The faster train crosses the slower train in 17 seconds. Find the length of the faster train in meters.
(A) 270 m
(B) 340 m
(C) 310 m
(D) 350 m
(E) 327 m
Rationale: Relative speed = (108 - 36) * 5/18 = 4 * 5 = 20 mps.
Distance covered in 17 sec = 17 * 20 = 340 m.
The length of the faster train = 340 m.
Answer:B
Answer: (B) 340 m
Question: Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
(A) 10
(B) 9
(C) 11
(D) 10.4
(E) 20
Rationale: Explanation :
Here's is the solution :
S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
Therefore True Discount on Rs. 260 = Rs. (10 / 250) * 260
= Rs. 10.40
Hence (D) is the correct answer.
Answer : D
Answer: (D) 10.4
Question: A train of 25 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 1.0 km long?
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 150 sec
(D) 164 sec
(E) 2 mins 44 sec
Rationale: D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 sec
ANSWER:C
Answer: (C) 150 sec
Question: Two cyclist start from the same places in opposite directions. One is going towards north at 10kmph and the other is going towards south 15kmph. What time will they take to be 50km apart?
(A) 1hr
(B) 2hrs
(C) 3hrs
(D) 5hrs
(E) 6hrs
Rationale: To be (10+15) km apart, they take 1 hour
To be 50 km apart, they take 1/25 *50 = 2 hrs
Answer is B
Answer: (B) 2hrs
Question: If 2/z = 2/(z + 1) + 2/(z + 36) which of these integers could be the value of z?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 6
Rationale: Solving for z algebraically in this problem would not be easy. Instead, we can follow the hint in the question (“which of these integers…”) and test each answer choice:
A. 2/0 = 2/1 +2/36 INCORRECT (Division by zero)
B. 2/1 = 2/2 +2/37 INCORRECT
C. 2/2 = 2/3 +2/38 INCORRECT
D. 2/3 = 2/4 +2/39 INCORRECT
E. 2/4 = 2/5 +2/40 CORRECT
The correct answer is E, because it contains the only value that makes the equation work. Notice how quickly this strategy worked in this case
Answer: (E) 6
Question: Square ABCD is the base of the cube while square EFGH is the cube's top face such that point E is above point A, point F is above point B etc. What is the distance between the midpoint of edge AB and the midpoint of edge EH if the area of square ABCD is 2?
(A) 1/sqrt2
(B) 1
(C) sqrt2
(D) sqrt3
(E) 2sqrt3
Rationale: distance from mid point of AB to AD = sqrt [(1/sqrt2)^2+(1/sqrt2)^2] = 1
the distance between the midpoint of edge AB and the midpoint of edge EH = sqrt [1^2+(sqrt2)^2] = sqrt3.
ANSWER:D
Answer: (D) sqrt3
Question: A boy has nine trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
(A) 88
(B) 98
(C) 126
(D) 108
(E) 111
Rationale: Explanation:
The boy can select one trouser in nine ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 14 = 126 ways
C)
Answer: (C) 126
Question: If f is a function defined for all k by f(k) = k^(2/3)/16, what is f(64 k) in terms of f(k)?
(A) 1/8 f(k)
(B) 5/8 f(k)
(C) 2 f(k)
(D) 16 f(k)
(E) 32 f(k)
Rationale: f(k) = k^(2/3)/16
f(64 k) = (64k)^(2/3)/16 = 16 * k^(2/3)/16 = 16 * (k^(2/3)/16) = 16 f(k).
So answer is D.
Answer: (D) 16 f(k)
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each. The radius of the sphere is
(A) 3 cm
(B) 5 cm
(C) 6 cm
(D) 8 cm
(E) None
Rationale: Solution
4Î R2	= 2Î 5x10
â‡’ R2 = (5x10/2)
â‡’ 25
â‡’ R = 5 cm.
Answer B
Answer: (B) 5 cm
Question: A train passes a man standing on the platform. If the train is 170 meters long and its speed is 72 kmph, how much time it took in doing so?
(A) 6 ½ sec
(B) 4 ½ sec
(C) 9 ½ sec
(D) 8 ½ sec
(E) 2 ½ sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 ½ sec
Answer: D
Answer: (D) 8 ½ sec
Question: How much time will a train of length 300 m moving at a speed of 72 kmph take to cross another train of length 500 m, moving at 36 kmph in the same direction?
(A) 50
(B) 80
(C) 88
(D) 76
(E) 12
Rationale: The distance to be covered = Sum of their lengths = 300 + 500 = 800 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 800/10 = 80 sec.
Answer:B
Answer: (B) 80
Question: If the cost price of 50 articles is equal to the selling price of 40 articles, then the gain or loss percent is?
(A) 20% loss
(B) 20% profit
(C) 10% profit
(D) 25% loss
(E) None of these
Rationale: Given that, cost price of 50 article is equal to selling price of 40 articles.
Let cost price of one article = Rs. 1
Selling price of 40 articles = Rs. 50
But Cost price of 40 articles = Rs. 40
Therefore, the trader made profit.\Percentage of profit = 10/40 * 100 = 25%
ANSWER:E
Answer: (E) None of these
Question: In a recent election, James received 0.5 percent of the 2,000 votes cast. To win the election, a candidate needed to receive more than 50 percent of the vote. How many additional votes would James have needed to win the election?
(A) 901
(B) 989
(C) 990
(D) 991
(E) 1,001
Rationale: James = (0.5/100)*2000 = 10
Votes to win = (50/100)*Total Votes +1 = (50/100)*2000 +1 = 1001
Remaining Voted needed to win election = 1001 - 10 = 991
Answer: option D
Answer: (D) 991
Question: If 2x-y=4 then 6x-3y=?
(A) 15
(B) 12
(C) 18
(D) 10
(E) 14
Rationale: 6x-3y=3*(2x-y)
=3*4
=12
ANSWER:B
Answer: (B) 12
Question: An assembly line produces 20 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: The time to produce the first 60 cogs is 60/20 = 3 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / 4 hours = 30 cogs per hour.
The answer is B.
Answer: (B) 30
Question: A dual sink has a right side and left side. Working alone, the right side can fill up in 5 hours. Working alone, the left side can empty in 15 hours. If it is desired that the sink should be filled, from empty, exactly 6 hours after the right side is turned on at 9:30am, then at what time should the left side also be turned on?
(A) 10:00am
(B) 10:45am
(C) 12:00pm
(D) 12:30pm
(E) 1:30pm
Rationale: In 6 hours the right side will fill up with water equal to 6*1/5 = 6/5 of the sink. So, 1/5 more than necessary, which should be compensated by the left side of the sink. To pump out 1/5 of the water the left side needs 15/5 = 3 hours.
Therefore, the left side of the sink should be turned on at 9:30am + 6 hours - 3 hours = 12:30pm.
Answer: D.
Answer: (D) 12:30pm
Question: Some persons can do a piece of work in 8 days. Two times the number of these people will do half of that work in?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 8/ (2 * 2) = 2 days
Answer:A
Answer: (A) 2
Question: A number when divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is:
(A) 214
(B) 476
(C) 954
(D) 1908
(E) 1910
Rationale: Z= 6*1 +4= 10.
Y= 5z+3= 53
X= 4y+2= 214.
ANSWER:A
Answer: (A) 214
Question: After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
(A) 27
(B) 28
(C) 20
(D) 24
(E) 12
Rationale: 1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30
2/3 ----? => 20 days
Answer:C
Answer: (C) 20
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Ans.(D)
Sol. Number of choices to go by ship = 8 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 8 x 5 = 40 ways
Answer: (D) 40
Question: At what rate p.a a sum of Rs. 2400 will become Rs. 3600/- in 5 years.
(A) 10%
(B) 15%
(C) 20%
(D) 12%
(E) 22%
Rationale: Explanation:
principal P = 2400/-
Rate of interest R = ?
Time T = 5 years
Accumulated Amount A = Rs.10400/-
A = P + I
A = P + PTR/100
A = P(1+ TR/100)
2400[ 1 + (5 x R)/100] = 3600
2[(20 + R)/20] = 3
20 + R = 30
R = 10%
Answer: Option A
Answer: (A) 10%
Question: Two-third of a positive number and 16/216 of its reciprocal are equal. Find the positive number.
(A) 4 /12
(B) 4 /17
(C) 4 /15
(D) 4 /11
(E) 4 /03
Rationale: Explanation:
Let the positive number be x.
Then, 2/3 x = 16/216 * 1/x
x2 = 16/216 * 3/2
= 16/144
x = √16/144 =4 /12.
ANSWER:A
Answer: (A) 4 /12
Question: A and B can finish a work together in 12 days, and B and C together in 16 days. If A alone works for 5 days and then B alone continues for 7 days, then remaining work is done by C in 13 days. In how many days can C alone finish the complete work?
(A) 24
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: As A and B can finish the work in 12 days time, hence
(A + B)’s one day’s work = 1/12;
similarly
(B + C)’s one day’s work = 1/16
Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1
A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1
Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1
i.e. 5/12 + 2/16 + C’s 11 days’ work = 1
or C’s 11 days’ work = 1 - (5/12 + 2/16)
or C’s 11 days’ work = 1 - 13/24
or C’s 11 days’ work = 11/24
or C’s 1 day’s work = 11/24 x 1/11 = 1/24
Therefore, C alone can finish the complete work in 24 days.
ANSWER:A
Answer: (A) 24
Question: A, B and C completed a piece of work, A worked for 16 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
(A) Rs.80
(B) Rs.120
(C) Rs.71.15
(D) Rs.51.15
(E) Rs.180
Rationale: 3x 4x 5x
16 9 4
48x + 36x + 20x = 1480
104x = 1480 => x = 14.23
5x = 71.15 Rs.
ANSWER:C
Answer: (C) Rs.71.15
Question: A 340-liter solution of Kola is made from 64% water, 9% concentrated Kola and the rest is made from sugar. If 3.2 liters of sugar, 8 liter of water and 6.8 liters of concentrated Kola were added to the solution, what percent of the solution is made from sugar?
(A) 6%.
(B) 7.5%.
(C) 9.2%.
(D) 10.5%.
(E) 26.5%.
Rationale: Denominator:
340+8+3.2+6.8=358
Numerator:
340(1-.64-.09)+3.2
340(0.27)+3.2
91.8+3.2
95
Ratio:
95/358=0.265
Answer: E
Answer: (E) 26.5%.
Question: In the rectangular coordinate system Point O has coordinates (0,0) and Point B has coordinates (5,5) and if point A is equidistant from points O and B and the area of the triangle OAB is 16, which of the following are the possible coordinates of point A.
(A) (-2,6)
(B) (0,4)
(C) (2,-6)
(D) (2,6)
(E) (4,0)
Rationale: Area.pngSince A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB).
(2,-6) and (2,6) are not on that line. If A is at (0,5) or (5,0), then the area is 1/2*5*5=25/2. Thus A must be at (2,6).
Answer: D.
Answer: (D) (2,6)
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 87
(B) 27
(C) 90
(D) 26
(E) 29
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Answer: (C) 90
Question: Which of the following CANNOT be the median R of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
(A) (w+x)/2 - 1
(B) (w+z)/2
(C) (x+y)/2
(D) (y+z)/2 -1
(E) (w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median R.
Answer (A)
Answer: (A) (w+x)/2 - 1
Question: A money lender lends Rs.1800 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 1984.5
(C) 2834
(D) 2827
(E) 2781
Rationale: A = 1800(21/20)2
= 1984.5
Answer: B
Answer: (B) 1984.5
Question: John has $1,600 at the beginning of his trip, after spending money, he still has exactly $800 less than he spent on the trip. How much money does John still have?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $1,200
Rationale: let the money spent be x
money he is left with after spending = x-800
total money --> x+(x-800) = 1600
solving for x will give x = 1200,
therefore the money he is left with = x-800
= 1200 - 800
= 400
ANSWER:B
Answer: (B) $400