mathewhe/aqua_rat huggingface dataset:
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 2887 sq m
(B) 6866 sq m
(C) 4312 sq m
(D) 9277 sq m
(E) 2678 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7)
= 4312 sq m
Answer: C
Answer: (C) 4312 sq m
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) 3 1/2 sec
(B) 3 5/2 sec
(C) 3 7/2 sec
(D) 8 1/2 sec
(E) 3 1/8 sec
Rationale: D = 170
S = 72 * 5/18 = 20 mps
T = 170/20 = 8 1/2 sec
Answer: D
Answer: (D) 8 1/2 sec
Question: (2^x) (30^3) = (2^3) (3^3) (4^3) (5^3)
In the above equation, what is the value of x?
(A) 9
(B) 7
(C) 8
(D) 6
(E) 4
Rationale: D
6
(2^x)(30^3) = (2^3) (3^3) (4^3) (5^3)
(2^x)(30^3) = (120^3)
(2^x) = (120^3)/ (30^3)
(2^x) = (4^3)
(2^x) = 64
ln(2^x) = ln(64)
x ln(2) = ln(64)
x = ln(64)/ln(2)
x = 6
Thus x = 6.
Answer: (D) 6
Question: How much water should be added to 13 liters of a 20%-solution of alcohol to reduce the concentration of alcohol in the solution by 75% ?
(A) 25 liters
(B) 27 liters
(C) 30 liters
(D) 32 liters
(E) 35 liters
Rationale: Let x ltr water to be added
2ltr alcohol to be represented as (20(1-3/4(new soln.=13+x)))
2=5%*(13+x)-------->x=27
Ans B
Answer: (B) 27 liters
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) 299
(B) 100
(C) 270
(D) 278
(E) 213
Rationale: (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640.Answer: B
Answer: (B) 100
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/7
(B) 11 1/4
(C) 11 1/3
(D) 11 1/2
(E) 11 1/1
Rationale: 3/12 + x/15 = 1
x= 11 1/4.Answer: B
Answer: (B) 11 1/4
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6 min
(B) 4 min
(C) 2 min
(D) 5 min
(E) 8 min
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min.
Answer:A
Answer: (A) 6 min
Question: by what least number 675 be multiplied to obtain a number which is a perfect cube ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Solution
675 = 5 * 5 * 3 * 3 *3 .
to make it a perfect cube, it must be multiplied by 5.
Answer A
Answer: (A) 5
Question: A store owner estimates that the average price of type A products will increase by 30% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,980
(B) $15,325
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.30 * 4500 = 5850
cost of type B products next year = 1.1 * 8300 = 9130
total 5850 + 9130 = 14980 option A
Answer: (A) $14,980
Question: A 4-letter code word consists of letters O, U, AND P. If the code includes all the three letters, how many such codes are possible?
(A) 72
(B) 48
(C) 4
(D) 84
(E) 36
Rationale: Note that the correct answer to this question is 36, not 72.
O-OUP can be arranged in 4!/2!=12 ways;
U-OUP can be arranged in 4!/2!=12 ways;
P-OUP can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: E
Answer: (E) 36
Question: Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding c boxes. What is the price charged per magnet, in cents, if Magnabulk charges m dollars for each crate?
(A) 100cd/m
(B) cd/(100m)
(C) 100m/(cd)
(D) m/(cd)
(E) cd/m
Rationale: crate has = cd magnates
C crate cost = m dollars = 100 m cents
each magnate cost for each crate = 100 m / cd
Ans; C
Answer: (C) 100m/(cd)
Question: A train passes a station platform in 36 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?
(A) 176 m
(B) 240 m
(C) 267 m
(D) 602 m
(E) 267 m
Rationale: Speed = (54 * 5/18) m/sec
= 15 m/sec. Length of the train
= (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15
==> x + 300 = 540 ==> x
= 240 m
Answer: B
Answer: (B) 240 m
Question: A, Band C start a business each investing Rs. 20,000. After 5 months A withdrew Rs.6000 B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.
(A) 19500;22500;24500
(B) 18400;21900;23100
(C) 20500;21200;28200
(D) 22300;19850;20600
(E) None of them
Rationale: Ratio of the capitals of A, Band C
= 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7
= 205000:212000 : 282000 = 205 : 212 : 282.
A’s share = Rs. 69900 x (205/699) = Rs. 20500	I
B's share = Rs. 69900 x (212/699) = Rs. 21200;
C's share = Rs. 69900 x (282/699) = Rs. 28200.
Answer is C.
Answer: (C) 20500;21200;28200
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 450 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 370
(B) 365
(C) 360
(D) 380
(E) 350
Rationale: C
450 * T = 1 km => T = 1/450 km/h
V*(T+2/3600) = 1
V (1/450 + 2/3600) = 1 => V = 360 km/h
Answer: (C) 360
Question: Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 84 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?
(A) 15%
(B) 20%
(C) 25%
(D) 33 1/3%
(E) 40%
Rationale: 0.4*75 + 0.6x = 84
30 + 0.6x=84
0.6x = 54
x= 90
90/75= 1.2
Ans:B
Answer: (B) 20%
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 30 km/hr. For how many minutes does the bus stop per hour?
(A) 22
(B) 30
(C) 77
(D) 20
(E) 99
Rationale: In 1hr, the bus covers 60 km without stoppages and 30 km with stoppages.
Stoppage time = time take to travel (60 - 30) km i.e 30 km at 60 km/hr.
stoppage time = 30/60 hrs = 30 min.
Answer: B
Answer: (B) 30
Question: In a stack of boards at a lumber yard, the 41th board counting from the top of the stack is immediately below the 23th board counting from the bottom of the stack. how many boards are in the stack?
(A) 68
(B) 62
(C) 65
(D) 64
(E) 36
Rationale: 1 2 3 ... 14 15 16 ...................
..............41 40 ................. 1
So the number of boards = 41+21 =62
Option: B
Answer: (B) 62
Question: A, B and C can do a work in 6, 8 and 12 days respectively doing the work together and get a payment of Rs.1800. What is B’s share?
(A) 600
(B) 278
(C) 298
(D) 267
(E) 127
Rationale: WC = 1/6:1/8:1/12 => 4:3:2
3/9 * 1800 = 600
Answer:A
Answer: (A) 600
Question: What decimal of an hour is a second ?
(A) 0.0027
(B) 0.00027
(C) 0.027
(D) 0.00072
(E) None of them
Rationale: Required decimal = 1/60x60 = 1/3600 = .00027
Answer is B.
Answer: (B) 0.00027
Question: The food in a camp lasts for 40 men for 45 days. If fifteen more men join, how many days will the food last?
(A) 80 days
(B) 33 days
(C) 35 days
(D) 16 days
(E) 15 days
Rationale: one man can consume the same food in 40*45 = 1800 days.
15 more men join, the total number of men = 55
The number of days the food will last = 1800/55
= 33 days.
Answer:B
Answer: (B) 33 days
Question: A sum of Rs 1162.00 is divided among A, B and C such that 4 times A’s share is equal to 5 times B’s share and 7 times C’s share. What is the share of C?
(A) 280
(B) 285
(C) 270
(D) 295
(E) 255
Rationale: given 4x=5y=7z
so x:y=5:4
y:z=7:5
x:y:z=35:28:20
c share=20*1162/(35+28+20) =280.
ANSWER:A
Answer: (A) 280
Question: A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?
(A) $8.75
(B) $12
(C) $13.40
(D) $17.40
(E) $24.40
Rationale: Discount = 40% of spending
We want to maximise discount so we will need to maximise spending. We do that by assuming that 60 calls were made of 1 min each because the first minute is the most expensive.
Max discount = (40/100)* 60 * 1.6 = (40/100)*96
This would be slightly less than 40. About 38 to 39.
Saving = (Slightly less than 40) - 25 = Slightly less than 15
Answer (C)
Answer: (C) $13.40
Question: At what angle the hands of a clock are inclined at 15 minutes past 5 ?
(A) 72 1⁄2°
(B) 64°
(C) 58 1⁄2°
(D) 67 1⁄2°
(E) None of these
Rationale: At 15 minutes past 5, the minute hand is at 3 and hour hand slightly advanced from 5. Angle between their 3rd and 5th position.
Angle through which hour hand shifts in 15 minutes is
(15 &times 1⁄2)° = 7 1⁄2°
∴ Required angle = (60 + 71⁄2) = 67 1⁄2°
Answer D
Answer: (D) 67 1⁄2°
Question: The sum and the product of two numbers are 20 and 64 respectively, the difference of the number is?
(A) 1
(B) 6
(C) 7
(D) 8
(E) 12
Rationale: Explanation:
x + y = 20
xy = 64
(x- y)2 = (x + y)2 - 4xy
(x- y)2 = 400 - 256 => (x - y) = 12
Answer: E
Answer: (E) 12
Question: For the bake sale, 5 people brought cookies, 2 people brought pies, 6 brought brownies, and 5 people brought cakes. If each person only brought one item, how many people brought items in all?
(A) 14
(B) 18
(C) 22
(D) 23
(E) 25
Rationale: As each person only brought one item, you can simply add the number of items brought: 5+2+6+5=18. As such, the correct answer is B: 18.
Answer: (B) 18
Question: In a race of length L metres, Johnson beats Lewis by U metres and Greene by V metres, By how many metres does Lewis beat Greene in the same race ? (U<V)
(A) L(L-V) / L-U
(B) L(V-U) / L-U
(C) L-V
(D) U-V
(E) U+V
Rationale: As the time is constant, the ratio of distances will be the same as the ratio of speeds.
If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then
Sj/Sl = L/(L-U)
and Sj/Sg = L/(L-V)
=> Sg/Sl = (L-V)/(L-U)
Therefore the speeds of Lewis and Greene are in the ratio (L-U)/(L-V)
When Lewis finishes the race, the time run by him and Greene are same
=> The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.
=> Distance run by Greene when Lewis finishes the race = (L-V)/(L-U) * L
=> Lewis beats Greene by L - L*(L-V)/(L-U) = L [ 1 - (L-V)/(L-U)] = L (V-U) / (L-U)
Option (B) is therefore correct.
Answer: (B) L(V-U) / L-U
Question: What will be the compound interest on a sum of Rs. 28,000 after 3 years at the rate of 12% p.a.?
(A) s.10123.77
(B) s.10123.21
(C) s.10123.20
(D) s.10123.28
(E) s.11337.98
Rationale: Amount = [28000 * (1 + 12/100)3]
= 28000 * 28/25 * 28/25 * 28/25
= Rs. 39337.984
C.I. = (39337.984 - 28000)
= Rs. 11337.98
Answer:E
Answer: (E) s.11337.98
Question: There are 24 girls in hostel whose average age is decreased by 2 months, when one girl 18 yrs is replaced by a new boy.Find the age of new girl.
(A) 1 year
(B) 1 years 2 months
(C) 2 years 5 months
(D) 4 years
(E) None
Rationale: Total decrease = 24 * 2 = 48 months
= 4 years
D
Answer: (D) 4 years
Question: A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?
(A) 9
(B) 7
(C) 6
(D) 1
(E) 5
Rationale: Explanation:
Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.
or 137 + x = 144 or x = 144 - 137 = 7.
Answer: B
Answer: (B) 7
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $56. If $2,000 is the total amount invested, how much is invested at 8 percent?
(A) $280
(B) $800
(C) $892
(D) $1,108
(E) $1,200
Rationale: (A) $280 (B) $800 (C) $892 (D) $1,108 (E) $1,200
y = 2000 - x
.1x - .08(2000-x) = 56
.-160+.18x = 56
x = 1200 and y = 800
ANSWER:B
Answer: (B) $800
Question: In a certain book club, the members are voting between two books – a comic novel and a biography – to decide which book the group will read next. There are 3 times as many votes for the comic novel as there are votes for the biography. The ratio of biography votes to the comic votes is
(A) 1 to 2
(B) 1 to 3
(C) 1 to 4
(D) 2 to 3
(E) 3 to 4
Rationale: IMO : Answer B 1 to 3
Answer: (B) 1 to 3
Question: A man rows his boat 120 km downstream and 60 km upstream, taking 2 hours each time. Find the speed of the stream?
(A) 6
(B) 15
(C) 17
(D) 18
(E) 2
Rationale: Speed downstream = d/t = 120/(2 ) = 60 kmph
Speed upstream = d/t = 60/(2) = 30 kmph
The speed of the stream = (60 - 30)/2 = 15 kmph
Answer:B
Answer: (B) 15
Question: What is the sum of all possible solutions to the equation √2x^2−x−9 = x+1 ?
(A) -2
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: First of all notice that since LHS is the square root of a number, it must be non-negative (the square root function cannot give negative result), then the RHS must also be non-negative: x+1≥0 --> x≥−1
Square the equation: 2x^2−x−9=x^2+2x+1 --> x^2−3x−10=0 --> x=-2 or x=5. Discard x=-2 because it's not >=-1. We are left with only one root: 5.
Answer: D
Answer: (D) 5
Question: Jayes can eat 25 marshmallows is 20 minutes. Dylan can eat 25 in one hour. In how much time will the two eat 150 marshmallows?
(A) 40 minutes.
(B) 1 hour and 30 minutes.
(C) 1 hour.
(D) 1 hour and 40 minutes.
(E) 2 hours and 15 minutes.
Rationale: Rate =Output/Time
Jayes Rate=25/20=5/4
Dylan Rate=25/60=5/12
Combined rate = 5/4+5/12= 20/12
CombinedRate*CombinedTime= CombinedOutput
20/12*t=150
t=90 mins => 1 hr 30 min
Answer: (C) 1 hour.
Question: What positive number, when squared, is equal to the cube of the positive square root of 14?
(A) 64
(B) 32
(C) 8
(D) 4
(E) 2
Rationale: Let the positive number be x
x^2 = ((16)^(1/2))^3
=>x^2 = 4^3 = 4
=> x =4
Answer D
Answer: (D) 4
Question: A money lender lends Rs.1500 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) 1978
(C) 1653.75
(D) 2827
(E) 2781
Rationale: A = 1500(21/20)2
= 1653.75
Answer: C
Answer: (C) 1653.75
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 2x5 meter sheets of metal that can be cut, how many metal sheets will be required for this order? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 60
(D) 78
(E) 75
Rationale: The question say:A welder received an order to make a 1 million liter cube-shaped tank. (1 cubic meter = 1,000 liters)
In other words, the tank is going to have a volume of 1000 cubic meters. That would equal 1 million liters.
A cube with a volume of 1000 cubic meters must be (10 meters) x (10 meters) x (10 meters).
The question doesn't specify whether this tank should have a closed top or an open top. (The real GMAT is good about specifying things like that.) Here, we are going to assume a closed top, only because if the top is open, we don't use enough metal --- we get an answer smaller than any of the answer choices. A closed-top cube, a full cube, has 6 sides, each of which is (10 meters) x (10 meters). That's a total surface area of 600 sq m.
The question tells us:he has only 2x5 meter sheets of metal that can be cut.
Each sheet has an area of 10 sq m. How many of these need to fill up 600 sq m? 600/10 = 60. He needs 60 sheets.
Answer =C
Answer: (C) 60
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
(A) 6.9 km/hr
(B) 7 km/hr
(C) 7.2 km/hr
(D) 8.9 km/hr
(E) 9 km/hr
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Answer: (C) 7.2 km/hr
Question: Find the area of trapezium whose parallel sides are 12 cm and 16 cm long, and the distance between them is 14 cm?
(A) 288 cm2
(B) 277 cm2
(C) 285 cm2
(D) 196 cm2
(E) 287 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (12 + 16) * (14)
= 196 cm2
Answer: D
Answer: (D) 196 cm2
Question: 10, 15, 22.5, 33.75, 50.62, (...)
(A) 60
(B) 60.75
(C) 75.93
(D) 76.33
(E) 70.1
Rationale: 10
(10Ã—3)Ã· 2 = 15
(15Ã—3)Ã· 2 = 22.5
(22.5Ã—3)Ã· 2 = 33.75
(33.75Ã—3)Ã· 2 = 50.62
(50.62Ã—3)Ã· 2 = 75.93
Answer is C
Answer: (C) 75.93
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 15 days before completion of project, then in how many days the project will be completed?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 15 days before completion of the project..
Thus,B alone does the remaining job in 15 days.
So,In 15 days ,B can do 1/2 w ..
Thus,(A+B) have worked (1-1/2)=1/2 w..
(A+B)can do 1/12 work in 1 day...
They did 1/2 w in 6 days.
Total days=(6+15) = 21
ANSWER:D
Answer: (D) 21
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 920 grams per kg, what is his percent?
(A) 22%
(B) 25%
(C) 77%
(D) 99%
(E) 8.7%
Rationale: 920 --- 80
100 --- ? => 8.7%
Answer: E
Answer: (E) 8.7%
Question: Find the next number in the series
3,3,5,4,4,3,5,5,4,3,...
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: (3, 3, 5), (4 ,4 ,3), (5, 5, 4), (3, x, y)
In first group , middle digit = 3
In 2nd group , middle digit = 4
In 3rd group , middle digit = 5
In 4th group , middle digit should be 6
ANSWER:D
Answer: (D) 6
Question: On a certain farm the ratio of horses to cows is 4:1. If the farm were to sell 15 horses and buy 15 cows, the ratio of horses to cows would then be 7:3. After the transaction, how many more horses than cows would the farm own?
(A) 20
(B) 40
(C) 50
(D) 60
(E) 80
Rationale: Originally, there were 4k horses and k cows.
3(4k-15) = 7(k+15)
12k-7k = 105+45
5k = 150
k = 30
The difference between horses and cows is (4k-15)-(k+15) = 3k-30 = 60
The answer is D.
Answer: (D) 60
Question: Two people stand back to back next to the rails in a small railway station. As the head of the express train that passes the station reaches them, they start to walk parallel to the rails. As the tail of the train reaches each of them, they stop, having walked 30m and 40m respectively.
If they both walked with identical, constant speed and the train kept its speed as well, can you tell how long the train was?
(A) 140m
(B) 240m
(C) 340m
(D) 440m
(E) 540m
Rationale: Let d be the length of the train, and
let t1 be the time it took for the tail of the train to reach
the first person, and
let t2 be the time it took for the tail of the train to reach
the second person.
By time t1, the head of the train is d-30 meters beyond the point where it passed the two people.
By time t2, the head was d+40 meters beyond where it passed the two people. The ratio of these distances,
d-30 : d+40
is equal to the ratio of t1:t2, because the train is moving at a constant speed.
Since both people walk at the same constant rate, this ratio is 3:4.
d-30 : d+40 = 3:4
The product of the means equals the product of the extremes, so
3(d+40) = 4(d-30)
3d + 120 = 4d - 120
240 = d
Answer B
Answer: (B) 240m
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 3 : 3?
(A) 16
(B) 48
(C) 277
(D) 92
(E) 11
Rationale: Let the distances between city A to B and B to C be 3x km and 3x km respectively.
Total time taken to cover from A to C
= (3x)/40 + (3x)/60 = (9x + 6x)/120 = 15x/120 = x/8 Average speed = (3x + 3x)/(x/8) = 48 kmph.
Answer:B
Answer: (B) 48
Question: What will be the difference between simple and compound interest at 12% per annum on a sum of Rs. 1000 after 4 years?
(A) 94.19
(B) 94.12
(C) 93.5
(D) 64.1
(E) 64.11
Rationale: S.I. = (1000 * 12 * 4)/100 = Rs. 480
C.I. = [1000 * (1 + 12/100)4 - 1000] = Rs. 573.5 Difference = (573.5 - 480) = Rs. 93.5
Answer: C
Answer: (C) 93.5
Question: There are three departments having students 66,58,24 .In an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only (No mixing of departments). Find the minimum number of rooms required?
(A) 73
(B) 74
(C) 75
(D) 76
(E) 77
Rationale: WE NEED TO TAKE GCD WHICH IS 2
THUS ALL THE ROOMS WILL HAVE 2 STUDENTS OF THE SAME DEPT
1) 66/2 = 33
2) 58/2 = 29
3) 24/2 = 12
TOTAL NO. OF MIN ROOMS REQD = 33+12+29 = 74
ANSWER:B
Answer: (B) 74
Question: Every student in a certain classroom was given a lollypop. 1/3 of the students were given a green lollypop, 1/4 of the students were given a yellow lollypop, and all of the other students were given a red lollypop. After lunch, 1/4 of the students who had green lollypops and 2/3 of the students who had yellow lollypops left the classroom; the other students did not leave. What fraction of all students have either a green or yellow lollypop?
(A) 5/9
(B) 4/9
(C) 2/3
(D) 4/7
(E) 3/5
Rationale: Lets pick smart numbers. Total number of students in the classroom: 12
Green lollypop (1/3): 4
Yellow lollypop (1/4): 3
Red lollypop (5/12): 5
After lunch
Green lollypop: 3
Yellow lollypop: 1
Red lollypop: 5
New Total number of students in the classroom: 9
Green and yellow lollypops: 4
Answer 4/9 or B
Answer: (B) 4/9
Question: What is the sum of all the composite numbers up to 12?
(A) 228
(B) 28
(C) 60
(D) 49
(E) 50
Rationale: Explanation:
4 + 6 + 8 + 9 + 10 + 12 = 49
Answer: D
Answer: (D) 49
Question: If 10^(v-1)< 0.000125 <10^v, what is the value of an integer v?
(A) -4
(B) -3
(C) -2
(D) 3
(E) 4
Rationale: -> Multiply 10^6- > (10^6){10^(v-1)}<125<(10^6)(10^v) -> 125 is bigger than 100
-> (10^6)(10^(v-1))=100 -> 10^(6+v-1)=10^2, v+5=2 -> v=-3
Thus, the answer is B
Answer: (B) -3
Question: Total ages of p,q,r be 27.P is two years elder than Q. Who is twice as old as R. Then how old is Q?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: p+q+r=27.........(1)
p= q+2
q= 2r
so,r=q/2
(1)........ is
q+2+q+q/2= 27
or,2q+q/2=25
5q=50
so,q =10
ANSWER:A
Answer: (A) 10
Question: A person crosses a 1080 m long street in 14 minutes. What is his speed in km per hour?
(A) 4.1
(B) 4.5
(C) 4.6
(D) 5.4
(E) 5.5
Rationale: Speed = 1080/(12x60) m/sec
= 1.3 m/sec.
Converting m/sec to km/hr =1.3 x(18/5) km/hr
= 4.6 km/hr.
ANSWER :C
Answer: (C) 4.6
Question: A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 3/7
(C) 2/7
(D) 11/7
(E) 8/7
Rationale: Let number of balls = (6 + 8) = 14.
Number of white balls = 8.
P (drawing a white ball) = 8/14
= 4/7
Answer should be A
Answer: (A) 4/7
Question: The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
(A) 155
(B) 158
(C) 161
(D) 165
(E) 172
Rationale: Classic combination problem
At least 1 boy = Total - all girls
All girls = C(4,3) = 4
Total combination = C(11,3) = 165
Ans = 165-4 = 161
ANS:C
Answer: (C) 161