RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is -
A.1/35
B.1/36
C.1/37
D.1/31
Answer: B.1/36
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Question: If an article is sold at 12% profit instead of 16% profit, then the profit would be Rs. 105 less. What is the cost price?
A.Rs. 3000
B.Rs.4000
C.Rs. 3500
D.Rs.4500
Answer: B.Rs.4000
Explanation: Explanation:
Let the cost price of an article be Rs. x.
(16% of x) - (12% of x) = 105
16x/100 - 12x/100 = 105 => 4x = 160 * 100
=> x = 1500
Cost price = Rs. 4000
Answer:B
Question: The average age of an adult class is 40years. 10 new students with an avg age of 32years join the class. Therefore
decreasing the average by 4year. Find what was the original strength of class?
A.10
B.12
C.16
D.20
Answer: A.10
Explanation: Let original strength = y
Then , 40y + 10 x 32 = ( y + 10) x 36
â‡’ 40y + 320 = 36y + 360
â‡’ 4y = 40
âˆ´ y = 10
A
Question: A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 550 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A.550 * sqrt 2
B.550 * sqrt (2^7)
C.550 * sqrt (2^12)
D.550 * the twelfth root of (2^7)
Answer: A.550 * sqrt 2
Explanation: Let the constant be k.
F1 = 550
F2 = 550k
F3 = 550 k * k = 550 * k^2
F13= 550 * k^12
we know F13 = 2 *F1 = 2 * 550 = 1100
1100/550 = k^12
k = twelfth root of 2
for F7...
F7 = 550 * k^6 ( as we wrote for F2 and F3)
F7 = 550 * (twelfth root of 2) ^ 6
F7 = 550 * sqrt (2)
The answer is A.
Question: Two cars are driving towards one another. The first car is traveling at a speed of 120 Km/h, which is 28% faster than the second car. If the distance between the cars is 855 Km, how long will it takes the cars to meet (in hours)?
A.2.5.
B.3.
C.3.5
D.4.
Answer: D.4.
Explanation: Let S be the speed of the slower car.
Then the speed of the faster is 1.28S
1.28S = 120
S = 120/1.28
Cumulative speed/rate = S + 1.28S = 2.28S
Time taken to meet = 855/2.28S =855/213.75 = 4hrs
ANSWER:D
Question: Three friends had dinner at a restaurant. When the bill was received, Akshitha paid 1/3 as much as Veena paid and Veena paid 1/2 as much as Lasya paid. What fraction of the bill did Veena pay ?
A.3/19
B.3/12
C.3/11
D.3/10
Answer: D.3/10
Explanation: Let Veena paid x,
so Akshitha paid x/3 , and Lasya paid 2x,
So total bill paid is given by
x+(x/3) +2x = 1, we get
i.e. x = 3/10
Answer: D
Question: A man goes downstream at 15 kmph, and upstream8 kmph. The speed of the stream is
A.0kmph
B.3.5kmph
C.16kmph
D.2.5kmph
Answer: B.3.5kmph
Explanation: Speed of the stream = 1/2(15-8)kmph
=3.5kmph.
correct option :B
Question: Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 302 m, then its area is?? We have: (l - b) = 15 and 2(l + b) = 302 or (l + b) = 151?
A.5446 m^2
B.5464 m^2
C.5644 m^2
D.5434 m^2
Answer: C.5644 m^2
Explanation: Solving the two equations, we get: l = 83 and b = 68.
Area = (l x b) = (83 x 68) m2 = 5644 m^2
C
Question: What is the perimeter of a square with area 9p^2/64 ?
A.3p/2
B.3p^2/4
C.3p
D.3p^2
Answer: A.3p/2
Explanation: Area of square, (side)^2 = (3p/8)^2
Therefore side of the square = 3p/8
Perimeter of square = 4*side = 4* (3p/8) = 3p/2
Answer is A.
Question: Which number is the odd one out?
9654 4832 5945 7642 7963 8216 3649
A.4549
B.6549
C.3729
D.3649
Answer: D.3649
Explanation: D
3649
In all the others multiply the first two digits together to produce the number formed by the last two digits.
Question: A train passes a station platform in 40 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.180 m
B.200 m
C.240 m
D.300 m
Answer: D.300 m
Explanation: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 40 = 15 ⇔ x + 300 = 600 ⇔ x = 300 m.
Answer D
Question: How many integers between 3000 and 4000 that have distinct digits and increase from left to right ?
A.20
B.48
C.60
D.120
Answer: A.20
Explanation: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
345_ --> 4
346_ --> 3
347_ --> 2
348_ --> 1
356_ --> 3
357_ --> 2
358_ --> 1
367_ --> 2
368_ --> 1
378_ --> 1
Number of integers =20
So the answer is A.
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 37380
. What percentage of profit did he make?
A.80%
B.68%
C.40%
D.70%
Answer: B.68%
Explanation: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 31150
Profit(%) = (37380 - 22250)/22250 * 100
= 68%
Answer:B
Question: The least number by which 72 must be multiplied in order to produce a multiple of 112, is
A.6
B.12
C.14
D.18
Answer: C.14
Explanation: Solution
Required numbers is divisible by 72 as well as by 112, if it is divisible by their LCM, which is 1008.
Now, 1008 when divided by 72, gives quotient	= 14.
Required number	= 14.
Answer C
Question: If n is a natural number, then(6n^2+6n) is always divisible by?
A.6 only
B.6 and 12 both
C.12 only
D.by 18 only
Answer: B.6 and 12 both
Explanation: (6n^2+6n)=6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Correct Option: B
Question: Running at their respective constant rate, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 5w widgets.
A.4
B.6
C.8
D.30
Answer: D.30
Explanation: I am getting 12. E. Hope havent done any calculation errors..
approach..
let y=no. of days taken by Y to do w widgets. Then X will take y+2 days.
1/(y+2) +1/y = 5/12(5/12 is because (5/4)w widgets are done in 3 days. So, x widgets will be done in 12/5 days or 5/12 th of a widget in a day)
Solving, we have y = 4
=>X takes 6 days to doing x widgets. So, he will take 30 days to doing 5w widgets.
Answer : D
Question: In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
A.24,000
B.36,000 votes
C.168,000
D.240,000
Answer: B.36,000 votes
Explanation: D + R = 100 ---- (1)
D - R = 12 ---- (2)
Solving (1) and (2) D = 56% and R = 44%
44% of Total = 132000
Total = 300000
D = 168000
Difference = 168000 - 132000 = 36000
Answer: B
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 40% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
A.45%
B.40%
C.25%
D.28%
Answer: B.40%
Explanation: I year
Best is to give a number to his income, say 100..
and let saving be x..
so expenditure = 100-x
next year-
Income = 140
savings = 2x
expenditure = 140-2x..
Now 140-2x+100-x = 2(100-x)...
240-3x = 200-2x ................x = 40...
saving % = 40/100 * 100 = 40%
ANSWER:B
Question: If x is the median of the set {8/2, 11/3, 27/9, 21/5, x}, x could be
A.4
B.17/5
C.16/5
D.30/7
Answer: A.4
Explanation: The median is the middle number once all the numbers are arranged in increasing/decreasing order.
We see that
11/3 = 3.something,
28/9 = 3.something
21/5 = 4.something
9/2 = 4.something
So x should greater than the smallest two numbers and smaller than the greatest two numbers. We can see that x = 4 is possible. (First look at the simplest option or the middle option since options are usually arranged in increasing/decreasing order)
Answer (A)
Question: If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?
A.25/36
B.125/216
C.91/216
D.11/36
Answer: C.91/216
Explanation: Thus, the probability of at least 1 roll = 1- Probability of NO 3s = 1- (5/6)(5/6)(5/6) = 1-125/216 = 91/216.
5/6 is the probability of NOT getting a 3 in any 1 roll with 5 allowed numbers (=1,2,4,5,6) out of a total of 6 possibilities.
answer:C
Question: Murali travelled from city A to city B at a speed of 60 kmph and from city B to city C at 40 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 2 : 3?
A.kmph
B.kmph
C.kmph
D.kmph
Answer: B.kmph
Explanation: Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/60 + (3x)/40
= (4x + 9x)/120 = 13x/120
= (2x + 3x)/(13x/120) = 46.2 kmph.
Answer: B
Question: Evaluate permutation
3P3
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: Explanation:
nPn=n!
3P3=3∗2∗1=6
Option A
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
A.12.9
B.18.9
C.12.5
D.12.2
Answer: C.12.5
Explanation: :
1000*15 = 1200*x
x = 12.5
Answer: C
Question: A certain auto manufacturer sold 6% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
A.63,000
B.1,980,000
C.2,030,000
D.2,040,000
Answer: B.1,980,000
Explanation: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-6/100(X)
If sales in 2006,X= 2.1 million find X-6/100(X)
(2.1 x 10^6)-6/100(2.1 x 10^6)
2100000-126000=1,974,000-----> 1,980,000(approx)
ANSWER:B
Question: If r is a positive integer and r^2 is divisible by 12, then the largest positive integer that must divide r ^3 is
A. 2^3
B. 2^6
C. 3^3
D. 6^3
Answer: D. 6^3
Explanation: Since r is an integer so r cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making r^2 as a multiple of 12))
r^2 is divisible by 12 (12 = 2*2*3), So, r should have at least one 2 and one 3 so that r^2 has a 2^2 and two 3
So, r will have a 2 and a 3. Or r will be a multiple of 6
So, largest possible integer than should divide r^3 is 6^3
So, Answer will be D
Question: If z is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of z?
A.51
B.162
C.72
D.54
Answer: B.162
Explanation: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: B.
Question: If 10 litres of an oil of Rs.54 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
A.Rs.49.17
B.Rs.58
C.Rs.54.17
D.Rs.55.33
Answer: B.Rs.58
Explanation: 54*10 = 540
66*5 = 330
870/15 = 58
ANSWER:B
Question: If 6x^2 + x - 12 = (ax + w)(cx + d), then |a| + |w| + |c| + |d| =
For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
A. 10
B. 12
C. 15
D. 18
Answer: B. 12
Explanation: 6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (ax+w)(cx+d)
Hence a=2, w=c=3, d=-4
So, 2+3+3+ |-4| = 2+3+3+4 = 12
Answer B.
Question: The average age 20 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
A.18
B.99
C.77
D.40
Answer: D.40
Explanation: 20 * 2 = 40 years
Answer: D
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
A.45
B.60
C.75
D.90
Answer: D.90
Explanation: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: Option D
Question: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?
A.3
B.5
C.6
D.8
Answer: C.6
Explanation: Work done by X in 1 day = 1/18
Work done by Y in 1 day = 1/15
Work done by Y in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which X can finish the remaining work = (1/3) / (1/18) = 6
C
Question: In traveling from a dormitory to a certain city, a student went 1/3 of the way by foot, 3/5 of the way by bus, and the remaining 2 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
A.30
B.45
C.60
D.90
Answer: A.30
Explanation: Whole trip = distance by foot + distance by bus + distance by car
x = 1/3x + 3/5x + 2
x - 1/3x - 3/5x = 2
x = 30km
Option: A
Question: The number of new words that can be formed by rearranging the letters of the word 'goat' is?
A.24
B.25
C.4
D.23
Answer: D.23
Explanation: Number of words which can be formed
= 4! - 1 = 24 - 1
= 23.
Answer:D
Question: The product of two numbers is 168 and the sum of their squares is 289. The sum of the number is?
A.A)23
B.B)25
C.C)27
D.D)31
Answer: B.B)25
Explanation: Let the numbers be x and y.
Then, xy = 168 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 168) = 625
x + y = 25.
Option B
Question: In an exam, Amar scored 64 percent, Bhavan scored 36 percent and Chetan 44 percent. The maximum score awarded in the exam is 800. Find the average mark scored by all the three boys?
A.384
B.656
C.443
D.324
Answer: A.384
Explanation: Average mark scored by all the three boys =
[64/100 (800) + 36/100 (800) + 44/100 (800)] / 3 = 384
Answer:A
Question: In Solution P, the proportion of water to alcohol is 5:2. In Solution Q, the proportion of water to alcohol is 3:2. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?
A.25%
B.28%
C.31%
D.34%
Answer: D.34%
Explanation: Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (2/7)*V/2=(1/7)*V
The amount of alcohol added from Solution Q is (2/5)*V/2=(1/5)*V
The total amount of alcohol in the new solution is (1/7+1/5)*V=(12/35)*V
The alcohol concentration is 12/35=34% (approximately)
The answer is D.
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 38 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 42 km/h. If the distance between City P and City Q is 378 km, at what time will the truck and the car meet each other?
A.5:30
B.5:45
C.6:00
D.6:15
Answer: D.6:15
Explanation: At 2:00 pm, the truck and the car are 340 km apart.
The truck and the car complete a distance of 80 km each hour.
The time it takes to meet is 340/80 = 4.25 hours.
They will meet at 6:15 pm.
The answer is D.
Question: If 5a= 3125, then the value of 5(a-3) is
A.25
B.50
C.250
D.300
Answer: A.25
Explanation: Sol.
5a = 3125 = 5a = 55
a = 5.
5(1-3) = 5(5-3) = 5(2) = 25.
Answer A
Question: Find the ratio in which rice at Rs. 7.00 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg
A.6:7
B.2:3
C.2:1
D.2:2
Answer: A.6:7
Explanation: By the rule of alligation:
Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind
Required ratio = 60 : 70 = 6 : 7
Answer: A
Question: How many numbers greater than a thousand can be made using the following digits without repetition: 1, 0, 3, 4, and 5:
A.96^2
B.96*2 IS ANSWER
C.576
D.24^2
Answer: B.96*2 IS ANSWER
Explanation: We have 5 digits: {0, 1, 3, 4, 5}
We can have 4-digit OR 5-digit numbers greater than 1,000.
# of 4-digit numbers greater than 1,000 = 4*4*3*2 = 96. The first digit can take 4 values: 1, 3, 4, or 5. So, any value but 0, since in this case a number will no longer be a 4-digit and becomes 3-digit. The second digit can take 4 values (5 values minus 1 we already used for the first digit), ...
# of 5-digit numbers greater than 1,000 = 4*4*3*2*1 = 96.
Total: 96+96=2*96.
Answer: B.
Question: Which of the following equations represents a line that is perpendicular to y=1/3*x+2?
A.y−2x=8
B.2x+4y=10
C.3y+6x=12
D.4y−8x=16
Answer: D.4y−8x=16
Explanation: For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: D
Question: What is the remainder when 2676 * 1487 * 4459 is divided by 12
A.3
B.8
C.12
D.9
Answer: A.3
Explanation: 2679/12==> Remainder=3
1487/12==> Remainder=11
4459/12==> Remainder=7
=3*11*7=231/12==> Remainder=3
Answer: A
Question: Walking at 4/5 of his usual speed a man is 10 mins too late. find his usual time.
A.81 mins
B.64 mins
C.52 mins
D.40 mins
Answer: D.40 mins
Explanation: speed=s,time=t,
4/5s*(t+10)=st
t=40
ANSWER:D
Question: If P represents the product of the first 12 positive integers, which of the following must be true?
I. P is an odd number
II. P is a multiple of 26
III. P is a multiple of 17
A.I only
B.II only
C.III only
D.None of the above
Answer: B.II only
Explanation: Answer = B) II only
Question: There are 7 stores in town that had a total of 21 visitors on a particular day. However, only 11 people went shopping that day; some people visited more than one store. If 7 people visited exactly two stores each, and everyone visited at least one store, what is the largest number of stores anyone could have visited?
A.6
B.8
C.4
D.9
Answer: C.4
Explanation: 7 people visited 2 stores each for 14 visits.
To maximize the number of stores that one person visited, let's assume that 3 people visited 1 store each. The number of remaining visits is 21 - 14 - 3 = 4, which is the maximum that one person could have visited.
The answer is C.
Question: A certain sum becomes Rs. 20720 in four years and 24080 in six years at simple interest. Find sum and rate of interest?
A.28%
B.12%
C.72%
D.82%
Answer: B.12%
Explanation: Let the interest for one year be x.
As amount = Principal + Interest, we have
P + 4x = 20720 --- (1) ; P + 6x = 24080 --- (2)
Solving the equations (1) and (2), we can get
P = Rs. 14000 and x = Rs. 1680
Interest for one year on Rs. 14000 is Rs. 1680
So, R = (100 * 1680)/(14000 * 1) = 12% p.a.
Answer:B
Question: The ratio of two quantities is 5 to 6. If each of the quantities is increased by 2, what is the ratio of these two new quantities?
A.It cannot be determined from the information given.
B.5/14
C.6/15
D.7/16
Answer: A.It cannot be determined from the information given.
Explanation: let the actual ratio be 5k/6k, increase numerator and denominator by 2=> 5k+2/6k+2
Until the value of k is unknown we can not determine the actual ratio.
OR
let the actual be 3/4. After increasing 2 => 5/6
let the actual be 6/8. After increasing 2 => 8/10
Therefore without actual quantities we cannot determine the actual ratio.
Answer : A
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
A.22
B.28
C.40
D.27
Answer: C.40
Explanation: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds.
Answer: C:
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.2312 sq m
B.2871 sq m
C.4312 sq m
D.1566 sq m
Answer: C.4312 sq m
Explanation: 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
Question: A company D has 30 percent of the employees are secretaries and 45 percent are salespeople. If there are 50 other employees of Company D, how many employees does Company D have?
A.200
B.162
C.180
D.152
Answer: A.200
Explanation: Let the total number of employees in the company be x
% of secretaries = 30%
% of salespeople = 45%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 50
so 25% of x = 50
x = 200
Therefore there a total of 200 employees in the company D
Correct answer - A
Question: Which of the following numbers has only one prime factor?
A.16
B.19
C.22
D.30
Answer: B.19
Explanation: 16=2^4
19=19
22=2*11
30=2*3*5
32=2^5
19 has 1 distinct prime factor
Answer B
Question: The average (arithmetic mean) of seven numbers is 12.2
If the sum of four of these numbers is 42.8, what is the average of the other 3 numbers?
A.(a) 12.4
B.(b) 14.2
C.(c) 16.8
D.(d) 18.6
Answer: B.(b) 14.2
Explanation: We're told that the average of 7 numbers is 12.2
(Sum of numbers)/7 = 12.2
Sum of numbers = (12.2)(7) = 85.4
Next, we're told that the sum of 4 (of the 7) numbers is 42.8
From this information, we can calculate the sum of the OTHER 3 numbers:
85.4 - 42.8 = 42.6
The question asks for the AVERAGE of the OTHER 3 numbers....
42.6/3 = 14.2
B
Question: The average of ten numbers is 7. If each number is multiplied by 12 ,then the average of new set of numbers is :
A.22
B.29
C.27
D.84
Answer: D.84
Explanation: The avg will be = 12×7= 84
Answer:	D
Question: The prices of tea and coffee per kg were the same in May. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
A.50
B.45
C.40
D.32
Answer: A.50
Explanation: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.8x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.8x(1/2) = 50
=> x =50
A
Question: How many prime factors in 25^10 * 36^10 * 20^10 ?
A.90
B.80
C.70
D.60
Answer: A.90
Explanation: 25^10 * 36^10 * 20^10
=(5*5)^10 * (2*2*3*3)^10 * (2*2*5)^10
=(5^10 * 5^10) * (2^10 * 2^10 * 3^10 * 3^10) * (2^10 * 2^10 * 5^10)
=5^30 * 2^40 * 3^20
number of distinct prime factors = 3
number of prime factors = 30+40+20 = 90 ANSWER:A
Question: The greatest common factor of two positive integers is F. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
A.FY⁄Z
B.XZ + YZ
C.X⁄Z + Y
D.X + Y⁄Z
Answer: A.FY⁄Z
Explanation: Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
F*Y = W*Z
So W= FY/Z
Answer A
Question: Two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph. In what time will they cross each other completely?
A.7.8 sec
B.8.1 sec
C.8.3 sec
D.8.2 sec
Answer: B.8.1 sec
Explanation: D = 180m + 180m = 360m * 1/1000 = 0.36 kms
RS = 80 + 80 = 160 kmph
T = (0.36/160) * 3600 = 8.1 sec
ANSWER:B
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 20 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
A.$222
B.$209
C.$211
D.$220
Answer: A.$222
Explanation: Final price = (1+20/100) * Original Price
= 1.20 * Original Price
From options given only 222 is divisible by 1.20 as it is stated OP is whole dollar amount.
Hence A
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
A.66 3/3%
B.16 2/3%
C.16 4/3%
D.76 2/3%
Answer: C.16 4/3%
Explanation: Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Question: Dean Winchester has got a long wooden stock of size 60 feet, he need to cut small stock of size 1 feet long using his axe.
He takes 5 minutes to cut one small stock (1 feet), how long will he take to make 60 such small stocks?
A.296 minutes.
B.297 minutes.
C.295 minutes.
D.294 minutes.
Answer: C.295 minutes.
Explanation: Solution:
295 minutes.
When he cut 59 stocks, the 60th stock will remain.
59 * 5 = 295 minutes.
Answer C
Question: If each edge of cube increased by 20%, the percentage increase in
A.42
B.44
C.48
D.45
Answer: B.44
Explanation: 100 × (120)/100 × (120)/100 = 144 => 44%
Answer is B.