RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: How many cubes of 3cm edge can be cut out of a cube of 18cm edge
A.36
B.232
C.216
D.484
Answer: C.216
Explanation: Explanation:
number of cubes=(18 x 18 x 18) / (3 x 3 x 3) = 216
Answer: C
Question: A division of a company consists of four men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
A.2/9
B.3/11
C.4/15
D.5/18
Answer: D.5/18
Explanation: Total number of ways to select 2 members = 9C2 = 36
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/36 = 5/18
The answer is D.
Question: 8+8
A.5
B.17
C.16
D.23
Answer: C.16
Explanation: C
Question: Which of the following is/are terminating decimal(s)?
I 299/(32^123)
II 189/(49^99)
III 127/(25^37)
A.I only
B.I and III
C.II and III
D.II only
Answer: B.I and III
Explanation: The fraction will have terminating decimal if and only if the denominator of the fraction is of the form (2^n)(5^m).
If you look at the denominators:
1) (32^123) => (2^(5*123))(5^0) => Terminating Decimal
2) (49^99) => Can't be expressed as (2^n)(5^m) => Non terminating Decimal
3) (25^37) => (2^0)(5^(2*37)) => Terminating Decimal
Hence 1 and 3 are terminating decimals => Choice [B]
Question: Which of the following can be a perimeter w of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
A.I only
B.III only
C.II and III only
D.I, II, and III
Answer: D.I, II, and III
Explanation: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: w>0.
Answer is D.
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.22
B.30
C.48
D.99
Answer: B.30
Explanation: Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
Answer: B
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
A.6:8
B.6:4
C.6:2
D.6:5
Answer: D.6:5
Explanation: 5M + 12B ----- 4 days
7M + 6B ------- 5 days
20M + 48B = 35M + 30B
18B = 15M => 5M = 6B
M: B = 6:5
Answer: D
Question: What percent of a day is seven hours?
A.20.83%
B.16x1/2%
C.29.16%
D.22x1/2%
Answer: C.29.16%
Explanation: Explanation :
Required percentage = (7/24100)%
= 29.16%.
Answer : C
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 10 minutes, what part of the cistern will be emptied?
A.4/9
B.4/3
C.4/2
D.5/9
Answer: D.5/9
Explanation: 2/3 ---- 12
? ----- 10 ==> 5/9
Answer: D
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
A.299
B.375
C.27878
D.288
Answer: B.375
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
75 ----- ? => 375.Answer: B
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned?
A.Rs.19,828.89
B.Rs.19,828.80
C.Rs.19,828.92
D.Rs.19,822.00
Answer: B.Rs.19,828.80
Explanation: Let the sum be Rs.P
P{ [ 1 + 8/100]2 - 1 } = 2828.80
P(8/100)(2 + 8/100) = 2828.80 [a2 - b2
= (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08
= 17000 Principal + Interest = Rs. 19828.80
Answer:B
Question: if 20% of a number is added to second no.,then it increase by 50%.calculate the ratio of these no.
A.3:2
B.2:3
C.5:2
D.can't be calculated
Answer: C.5:2
Explanation: Answer:	let no. be A and B.
(20%of A)+B=150% of B
A/5=3B/2-B=B/2;A/B=5/2,
A:B=5:2
answer C
Question: A and B starts a business with Rs.8000 each, and after 6 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
A.3:2
B.12:5
C.18:10
D.18:14
Answer: A.3:2
Explanation: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 6 months and then withdraws Rs.4000. So, the investment of B for remaining 12 months is Rs.4000 only.
A : B
8000*18 : (8000*6) + (4000*12)
14400 : 96000
A:B = 3:2
Answer: A
Question: 8 x 1.6 - 3 x 1.4/1.3 = ?
A.21.5
B.22
C.15.8
D.12.8
Answer: A.21.5
Explanation: Given Expression
= (12.8 -4.2)/0.4
= 8.6/0.4
= 8.6/0.4
= 21.5
Answer is A.
Question: Two employees M and N are paid a total of $616 per week by their employer. If M is paid 120 percent of the salary paid to N, how much is N paid per week?
A.$270
B.$280
C.$290
D.$300
Answer: B.$280
Explanation: 1.2N + N = 616
2.2N = 616
N = 280
The answer is B.
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?
A.338
B.279
C.125
D.776
Answer: C.125
Explanation: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 1/2 = Rs.125
Answer:C
Question: If (4x + 7)(x + 2) = 8x^2 + x, what is a possible value of x?
A. 12
B. -7
C. 7
D. -1
Answer: D. -1
Explanation: Rearranging the given expression:
(4x + 7)(x + 2) = 8x^2 + x
i.e. 8x^2 + 15x + 14 = 8x^2 + x
i.e. 14x = -14
i.e. x = -14/14 = -1
Answer: Option D
Had it been a difficult expression to solve further, then we could have used options to check which on esatisfies the expression after solving it as further as possible
Question: If a and b are positive integers, and a=3b+12, the greatest common divisor of a and b CANNOT be
A.1
B.3
C.2
D.5
Answer: D.5
Explanation: If b is 1, 2, 3, or 4, then GCD of a and b is 1, 2, 3, and 4 respectively. So, by POE the answer must be D.
Still: if b is a multiple of 5, then a is 12 greater than a multiple of 5, so not a multiple of 5, so both of them cannot be divisive by 5.
Answer: D.
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,00,000 as total savings, how much has he saved in Public Provident Fund ?
A.Rs. 40,000
B.Rs. 50,000
C.Rs. 60,000
D.Rs. 90,000
Answer: A.Rs. 40,000
Explanation: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (100000 – x) respectively. Then,
1/3x=1/2(100000-x)
=> x/3 + x/2 = 50000
=> 5x/6 = 50000
=> x= 50000 x 6 /5= 60000
Savings in Public Provident Fund = Rs. (100000 – 60000) = Rs. 40000
Answer A
Question: Calculate the sum of first 19 natural numbers.
A.190
B.120
C.150
D.199
Answer: A.190
Explanation: Solution
We know that(1+2+3+.....+19)	= n(n+1)/2
Therefore (1+2+3+....+19)	=(19×20 / 2)
= 190.
Answer A
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 60 per cent. The two reductions together are equal to a single reduction of
A.45%
B.70%
C.35%
D.32.5%
Answer: B.70%
Explanation: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 60percent is reduced which means the new price is merely 40percent of 3/4P
==> (3/4)x(2/5)P = 6/20P is the new price after both deduction which is 30percent of the original value P. This implies this entire series of deduction is worth having discounted 70% of P. So answer is B = 70%
Question: A store sells chairs and tables. If the price of 2 chairs and 1 table is 60% of the price of 1 chair and 2 tables, and the price of 1 table and 1 chair is $96, what is the price, in dollars, of 1 table? (Assume that every chair has the same price and every table has the same price.)
A.81
B.84
C.85
D.88
Answer: B.84
Explanation: LET C= CHAIR ; T =TABLE
2C+1T = 0.6 (1C + 2T) OR C( 2-0.6) = 1.2T -1T OR 1.4C = 0.2 T THEREFORE C= 0.2/1.4 T = 1/7 T
IC +1T =96 OR 1/7T + 1T =96 THEREFORE T= 96*7/8 = 84
B
Question: 5/8th of a job is completed in 10 days. If a person works at the same pace, how many days will he take to complete the job?
A.8
B.9
C.6
D.2
Answer: C.6
Explanation: Explanation:
Solution: It is given that 5/8th of the work is completed in 10 days.
=> Remaining work = 3/8th of total
Applying unitary method:
Total work will be completed in 10 * 8 / 5 days
=> It takes 16 days to complete total work
=> Hence, remaining work days = 16 - 10 = 6 days
ANSWER:C
Question: Which is the least number that must be subtracted from 1828 so that the remainder when divided by 8, 12, 16 is 4?
A.0
B.4
C.8
D.6
Answer: A.0
Explanation: First we need to figure out what numbers are exactly divisible by 8,12,16. This will be the set {LCM,LCMx2,LCMx3,...}
LCM(8,12,16) = 48 = 48
number is to be subtracted is 0
The largest such number less than or equal to 1828 is 48*38+4
A
Question: Find the quadratic equations whose roots are the reciprocals of the roots of 2x2 + 5y + 3 = 0?
A.+ 5y - 2 = 0
B.+ 5y + 2 = 0
C.- 5y + 2 = 0
D.- 5y - 2 = 0
Answer: B.+ 5y + 2 = 0
Explanation: The quadratic equation whose roots are reciprocal of 2x2 + 5y + 3 = 0 can be obtained by replacing y by 1/y.
Hence, 2(1/y)2 + 5(1/y) + 3 = 0
=> 3x2 + 5y + 2 = 0
ANSWER:B
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 60. No two digits of h are identical. How many different numbers are possible values of h?
A.20
B.22
C.24
D.30
Answer: C.24
Explanation: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 60
a,b,c,d can be 1,2,3,10
Number of ways = 4*3*2 = 24
Question: Average age of total 80 students from three classes, V, VI and VII, is 13 years. Average age of 30 students of class V is 11 1/2 years. If average age of another 30 students of class VI is 12 1/2 years, what is the average aage of rest of 20 students of class VIII ?
A.13 1/2 years
B.14 1/2 years
C.15 years
D.16 years
Answer: D.16 years
Explanation: Explanation :
Sum of ages of 80 students = 80 x 13 = 1040
Sum of ages of 30 students of class V = 30 x 11.5 = 345
Sum of ages of 30 students of class VI = 30 x 12.5 = 375
∴ Total age of 20 students of class VII = 1040 - 345 - 375 = 320
∴ Average age = 320/20 = 16 years.
Answer : Option D
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 19 seconds. What is the length of the platform in meters?
A.220 meters
B.360 meters
C.420 meters
D.600 meters
Answer: A.220 meters
Explanation: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 19 * 20 = 380 = Length of train
Length of platform = 600 - 380 = 220
Answer: A
Question: If W is the set of all the integers between 35 and 64, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
A.18
B.19
C.61
D.31
Answer: B.19
Explanation: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 63, the smallest is 36): 63 - 36 = 27
Step 2. Divide by 3: 27 / 3 = 9
Step 3. Add 1: 9 + 1 = 10.
So there are 10 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 64, the smallest is 36): 64 - 36 = 28
Step 2. Divide by 2: 28 / 2 = 14
Step 3. Add 1: 14 + 1 = 15.
So there are 15 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 10 multiples of 3 and the 15 multiples of 2: 10+15=25.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 10+15=25. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 60 - 30 = 30
Step 2. Divide by 6: 30 / 6 = 5
Step 3. Add 1: 5 + 1 = 6.
So there are 6 multiples of 6 within the range: we counted 6 numbers twice.
Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:
= 10+15 - 6
= 25 - 6
= 19
Therefore, the final number of multiples of 2, 3 or 6 is 19.
Hence, this is the correct answer. (B)
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40 meters. How many times did the ball bounce?
A.2
B.6
C.7
D.8
Answer: A.2
Explanation: Division of total distance travelled will be 16+16+8
Ans:2
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
A.3 hr
B.2 hr
C.1 hr
D.4 hr
Answer: C.1 hr
Explanation: 600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
ANSWER C
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
A.14
B.16
C.21
D.25
Answer: C.21
Explanation: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
A.5
B.4
C.8
D.12
Answer: A.5
Explanation: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 32 + 40 + 10 - (12) - 2x
x = 5
So, answer will be A
Question: Ratio of two numbers x and y is 1:2. If x is increased by 20% and y is increased by 4 then the new ratio becomes 1:5. What is the ratio 2y:x
A.1:3
B.3:1
C.2:3
D.4:1
Answer: D.4:1
Explanation: Let:
x = 1n
y = 2n
1.2n/(2n+4) = 1/5
6n = 2n+4
n = 1
So, x =1; y=2
2y/x = 4/1 = 4:1
Answer = D
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.
Answer C
Question: A warning notice is to be prepared for a building demolition in which the 'warning' is written in 8 differnent languages, including english, french and german. The authority requires you to put french after english and german after french. In how many different order of languages can you prepare the notice?
A.4!
B.5!
C.6!
D.7!
Answer: C.6!
Explanation: The problem requires you to find the total number of arrangements in which 8 object can be arranged paying attention to the given constraints. The constrain is that English, French and German mus follow the order E>F>G. Since there is only one way to arrange E,F and G, we can consider EFG as one object. Therefore 6 object is to be arranged and we can do this in 6! Ways. So the correct option is C. 6!.
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many E hours does it currently take Anne to clean the house on her own?
A.6
B.7
C.8
D.12
Answer: D.12
Explanation: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in E=3 hours)
Solving these 2 equations we can find B as 12
So, D
Question: If 45-[28-{37-(15-*)}]= 56, then * is equal to:
A.-29
B.-19
C.17
D.29
Answer: C.17
Explanation: 45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56
45-[28-37+15-*]=56 => 45[43-37-*]=56
45-[6-*]=56 => 45-6+*=56
39+*=56 => *=56-39
= 17
ANSWER:C
Question: If a trader bought 9 balls per rupee and sells at the rate of 8 balls per rupee, what is the percentage profit or loss?
A.12.5 %
B.11.5 %
C.23.5 %
D.23.5 %x
Answer: A.12.5 %
Explanation: Let he total number of oranges bought by the shopkeeper be 12.
If he buys 9 a rupee, his CP = 8
He selling at 8 a rupee, his SP = 9
Profit = SP - CP = 9 - 8 = 1
Profit Percent = 1/8 * 100 = 12.5 %
Answer: A
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $900 was the net sum to be paid for the entire work, what was the average daily wage of B?
A.$144
B.$90
C.$60
D.$54
Answer: C.$60
Explanation: The correct answer is C.
Question: In how many ways can the letters of the word ABEIX be arranged in a row so that the vowels appear in alphabetic order?
A.20
B.30
C.40
D.50
Answer: A.20
Explanation: three letters can be arranged in 3! ways.
only one combination AEI is required.
5 letters can be arranged in 5! ways.
thus 5!/ 3! * 1 = 20.
A
Question: A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec.
A.10th
B.15th
C.20th
D.25th
Answer: C.20th
Explanation: After 1st second, it moves 1 + (23/11)r = 1 + 1 = 2, So 25th position
After 2nd second, it moves 1 + 25/11 = 1 + 3 = 4, So 29th position = 0
After 3rd second, it moves 1 + 0/11 = 1 + 0 = 1, So 1st position
After 4th second, it moves 1 + 1 = 3rd position
after 5th, 1 + 3/11 = 4 So 7th
After 6th, 1 + 7/11 = 8 so 15th
After 7th, 1 + 15/11 = 5 so 20th
After 8th, 1 + 20/11 = 10th, So 30th = 1st
So it is on 1st after every 3 + 5n seconds. So it is on 1st position after 2008 seconds (3 + 5 x 401) So on 20th after 2012 position.
ANSWER:C
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 235 true?
A.1
B.2
C.5
D.7
Answer: B.2
Explanation: Answer B
(a+b)(a-b)=235
2cases For (a+b), (a-b)
235, 1
47, 5
Answer B
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. 31150. What percentage of profit did he make?
A.22
B.27
C.40
D.26
Answer: C.40
Explanation: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%.Answer:C
Question: Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in?
A.18
B.8
C.12
D.6
Answer: A.18
Explanation: The part of the tank filled by three pipes in one hour
= 1/12
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/12 = 1/18.
The tank can be filled in 18 hours.
Answer:A
Question: A certain jeans in a shop was marked down 30% the first week and another 20% the next week. What percent of the regular price was the final cost of the jeans after the two markdowns?
A.30%
B.36%
C.40%
D.56%
Answer: D.56%
Explanation: If the price of the jeans is 100, and it is marked down by 30% and 20% respectively or charged 70% of the price first and 80% of the price of reduced price, the final price is :-
100*70*80/10000= 56
56% is the final price of old price.
D is the answer
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 20, 60, and what number?
A.25
B.30
C.35
D.40
Answer: A.25
Explanation: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -80 = 25
A
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.12 days
B.15 days
C.16 days
D.18 days
Answer: B.15 days
Explanation: A's 2 day's work = (1/20 × 2) = 1/10	.
(A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 1/10.
Work done in 3 days = (1/10 + 1/10) = 1/5.
Now,	1/5	work is done in 3 days.
Therefore, Whole work will be done in (3 x 5) = 15 days.
CORRECT ANSWER: "B".
Question: The number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is ?
A.43280
B.43280
C.35280
D.32786
Answer: C.35280
Explanation: x Not younger
The last ball can be thrown by any of the remaining 8 players. The first 6 players can throw the ball in 7P7 ways.
The required number of ways = 7(7!)
= 35280
Answer:C
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
A.$198
B.$216
C.$220
D.$230
Answer: B.$216
Explanation: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 10
Employee paid = .9 * 240 = 216 $
Answer B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, the how old is B?
A.7
B.9
C.8
D.14
Answer: D.14
Explanation: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
⇒ 5x = 35
⇒ x = 7.
Hence, B's age = 2x = 14 years.
Answer: D
Question: The mean of 40 observations was 100. It was found later that an observation 50 was wrongly taken as 75 The corrected new mean is
A.125.8
B.102.8
C.99.375
D.100.52
Answer: C.99.375
Explanation: Explanation:
Correct Sum = (100 * 40 + 50 - 75) = 3975.
Correct mean = = 3975/40 = 99.375
Answer: C
Question: A and B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit, what is their total profit?
A.27000
B.25000
C.29000
D.28000
Answer: D.28000
Explanation: Suppose B's investment =x.
Then A's investment =3x
Suppose B's period of investment =y
then A's period of investment =2y
A : B =3x×2y:xy=6:1
Total profit ×1/7=4000
=> Total profit =4000×7
=28000
Answer is D.
Question: Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed?
A.110
B.1100
C.9900
D.10000
Answer: C.9900
Explanation: We know that P,Q, R can only lie on a grid 10x11
Let's start by fixing P' x-coordinate: we have 10 possible places for it
Then we choose x-coordinate for R: since PR || x-axis, R's x-coordinate can not coincide with P's x-coord, so we have only 9 possible choices left.
Then, we fix P's (and R's too) y-coordinate: 11 possible choices.
Finally, after we fixed P and R, Q's x-coordinate must be the same as P's (because P is the right angle and PR || x-axis), so the only choice is for y-coordinate, and we have 10 possible choices left.
So, total number of different triangles: 10*9*11*10=9,900
ANSWER:C