RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Ashwin rented a power tool from a rental shop. The rent for the tool was $25 for the first hour and $10 for each additional hour. If Ashwin paid a total of $125, excluding sales tax, to rent the tool, for how many hours did she rent it?
A.11
B.12
C.15
D.18
Answer: A.11
Explanation: 25 + 10n = 125
n = 10
Total time = n+1 hrs = 10+1 hrs = 11 hrs
Answer : A
Question: A thief is noticed by a policeman from a distance of 220 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
A.120
B.277
C.2987
D.278
Answer: A.120
Explanation: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 220 - 100 = 120 m.
Answer: A
Question: The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
A.7
B.6
C.5
D.2
Answer: C.5
Explanation: A + B + C = 48
B + C + D = 45
A + D = 13
A – D = 3
A + D = 13
2D = 10
D = 5
Answer: C
Question: The sum of money at compound interest amounts to thrice itself in 4 years. In how many years will it be 15 times itself?
A.8 years
B.16 years
C.2 years
D.6 years
Answer: B.16 years
Explanation: 100 ---- 300 --- 4
900 --- 4
1200----4
1500---4
16 years
Answer: B
Question: A bag contains 3 red, 3 green and 3 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
A.5/7
B.11/14
C.16/21
D.19/28
Answer: C.16/21
Explanation: P(no red balls) = 6/9*5/8*4/7 = 5/21
P(at least one red ball) = 1 - 5/21 = 16/21
The answer is C.
Question: A candidate got 35% of the votes polled and he lost to his rival by 2250 votes. How many votes were cast?
A.7500
B.3600
C.8900
D.9000
Answer: A.7500
Explanation: 35%-----------L
65%-----------W
------------------
30%----------2250
100%---------? => 7500
ANSWER A
Question: John walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 12 minutes earlier. How far is the office from his house?
A.3 2/5 Km
B.3 1/5 Km
C.4 Km
D.5 1/5 Km
Answer: C.4 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 20/6
= 24/2 * 20/60
= 20/5 = 4 Km
C
Question: Ten years ago, Q was half of R's age. If the ratio of their present ages is 3:4, what will be the total of their present ages?
A.5
B.10
C.15
D.20
Answer: B.10
Explanation: Let present age of P and Q be x and 2x respectively.
Ten years ago, Q was half of R's age
⇒(x−10)=2(2x−10)
⇒x−10=4x−20
⇒3x=10
⇒x=10/3
Total of their present ages=x+2x
=>10/3 + 20/3
=>30/3
=>10
ANSWER:B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
A.227
B.240
C.987
D.178
Answer: B.240
Explanation: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:B
Question: Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?
A.Rs.160/-
B.Rs.170/-
C.Rs.180/-
D.Rs.190/-
Answer: A.Rs.160/-
Explanation: A:B:C = 3:4:5
Total parts = 12
A's share is = 3 parts
12 -----> Rs.600/-
3 -----> Rs.150/-
A's total = 150 + 10 = Rs.160/-
A)
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
A.227
B.1668
C.5400
D.1688
Answer: C.5400
Explanation: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer:C
Question: If q>0.9, which of the following options can be the value of q?
A.0.9^2
B.√(0.9)
C.0.09
D.0.9
Answer: B.√(0.9)
Explanation: Lets take a few examples
When .2 is squared it gives .04
when .5 is squared it gives .25
When .9 is squared it gives .81
So raising a fraction to its power of 2 or 3 only reduces the value of the fraction
This is because
.2 = 2/10
.2^2= 4/100
.2^3=8/1000
Since the denominator gets an extra 0 each time u increase the power , it is going to drag the value down
But if you just think about the opposite case :
Then we can see , if squaring a fraction diminish its value, then taking the square root of it will again increase its value
that is √(0.04) will give you back 0.2
so √(0.04) > 0.04
so obviously diminishing the power will appreciate the value
So q √(0.9) > 0.9
Hence Correct Answer is (B)
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.20 days
B.19 days
C.10 days
D.12 days
Answer: A.20 days
Explanation: 1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30--- 2/3 ---- 20 days
ANSWER A
Question: After deducting a commission of 5% a T.V. set costs Rs. 9595. Its gross value is ?
A.Rs. 10000
B.Rs. 10074.75
C.Rs. 10100
D.None of these
Answer: C.Rs. 10100
Explanation: Answer
∵ 95% of gross value = 9595
∴ gross value = (9595 x 100)/95 = 10100
Correct Option: C
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 105 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
A.280
B.320
C.360
D.420
Answer: A.280
Explanation: Easy 280 is the answer.
3/4 ( x/2) = 105
x = 105 * 8 /3 = 280.
Answer A
Question: A train traveling at 144 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds. What is the length of the platform in meters?
A.240 meters
B.360 meters
C.480 meters
D.600 meters
Answer: C.480 meters
Explanation: Answer
Distance covered by the train when crossing a man and when crossing a platform
When a train crosses a man standing on a platform, the distance covered by the train is equal to the length of the train.
However, when the same train crosses a platform, the distance covered by the train is equal to the length of the train plus the length of the platform.
The extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover. i.e., length of the platform.
Compute length of platform
Length of the platform = speed of train * extra time taken to cross the platform.
Length of platform = 144 kmph * 12 seconds
Convert 144 kmph into m/sec
1 kmph = 5/18 m/s (This can be easily derived. But if you can remember this conversion, it saves a good 30 seconds).
∴ 144 kmph = 5/18∗144 = 40 m/sec
Therefore, length of the platform = 40 m/s * 12 sec = 480 meters.
Choice C
Question: Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 80 m, then its area is??
A.2000 m^2
B.2340 m^2
C.375 m^2
D.2556 m^2
Answer: C.375 m^2
Explanation: We have: (l - b) = 10 and 2(l + b) = 80 or
(l + b) = 40
2 l = 50 => l = 25 & b = 15
Area = 25 * 15 = 375 m^2
Answer : C
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
A.23/35
B.23/36
C.23/18
D.23/17
Answer: A.23/35
Explanation: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (⁶C₁ * ⁹C₁)/¹⁵C₂ + ⁶C₂/¹⁵C₂
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer:A
Question: What values of 'x' will be the solution to the inequality 15x - 2/x > 1?
A.x > 0.4
B.x < 1/3
C.-1/3 < x < 0.4, x > 15/2
D.-1/3 < x < 0, x > 2/5
Answer: D.-1/3 < x < 0, x > 2/5
Explanation: Explanatory Answer
We can rewrite the above inequality as 15x - 2/x- 1 > 0
i.e., 15x2−2−x/x> 0
i.e., 15x2−6x+5x−2/x> 0
Factorize the quadratic expression: (5x−2)(3x+1)/x > 0
The above inequality will hold good if the numerator and denominator are both positive or are both negative.
Possibility 1: When (5x - 2)(3x + 1) > 0 and x > 0
This will hold true for values of 'x' that do not lie between -1/3 and 2/5 and for x > 0.
Combining all these conditions, we get x > 2/5
Possibility 2: When (5x - 2)(3x + 1) < 0 and x < 0.
This will hold true for the following values of 'x': -1/3 < x < 2/5 and x < 0.
Combining, we get -1/3< x < 0.
Therefore, the range of values of x for which the above inequality will hold true is: -1/3 < x < 0 ∪∪ x > 2/5
Choice D
Question: In case K is the only individual sewing on committee B, which among the following shouldserve on committee A?
A.V and U
B.V and T
C.U and S
D.L and M
Answer: D.L and M
Explanation: L and M should serve on A
ANSWER:D
Question: What is the sum of digits of (5!*4!*3!*2! - 144*120)/5!
A.22
B.4
C.12
D.3
Answer: D.3
Explanation: (5!*4!*3!*2! - 144*120)/5!
=(5!*4!*3!*2! - 24*6*5!)/5!
=(5!*4!*3!*2! - 4!*3!*5!)/5!
=5!*4!*3!(2!-1)/5!
=120
Sum of digits=3
Answer D
Question: Find the distance covered by a man walking for 42 min at a speed of 10km/hr?
A.7km
B.3km
C.4km
D.5km
Answer: A.7km
Explanation: Distance = 10*42/60 = 7 km
Answer is A
Question: Which expression has the greatest value?
A.1977452/1977455
B.1982466/1982469
C.1982487/1982490
D.1982456/1982459
Answer: C.1982487/1982490
Explanation: The difference between each numerator/denominator pair is three.
The largest expression (which in this case will also be the closest to one) is the expression where '3' is the smallest fraction of the numerator (or the denominator).
The largest numerator is 1982487, or C, and this will give an expression with a value closest to one.
We can also demonstrate that this approach works with some simple logic. Taking numerator/denominator pairs that differ by three...
1/4 = 0.25
2/5 = 0.4
3/6 = 0.5
...
27/30 = 0.9
...
1982487/1982490 = 0.999998486...
ANSWER:C
Question: If positive integer k is divided by 14, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
A.None
B.I
C.II
D.III
Answer: A.None
Explanation: k = 14m+2 = 2(7m+1)
I. k + m = 2(17m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
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 44.5 meters. How many times did the ball bounce?
A.4
B.6
C.7
D.8
Answer: A.4
Explanation: Division of total diatance travelled will be 16+16+8+4+0.5
Ans: 4
Question: A can do a work in 24 days and B can do it in 8 days. In how many days A and B can do the work?
A.20 days
B.10 days
C.6 days
D.8 days
Answer: C.6 days
Explanation: Explanation:
A's 1day's work = 1/24
B's 1day's work = 1/8
They work together = 1/24 + 1/8 = 6 days
Answer: Option C
Question: A gambler bought $5,000 worth of chips at a casino in denominations of $20 and $100. That evening, the gambler lost 16 chips, and then cashed in the remainder. If the number of $20 chips lost was 2 more or 2 less than the number of $100 chips lost, what is the largest amount of money that the gambler could have received back?
A.$4,040
B.$4,120
C.$1,960
D.$4,920
Answer: B.$4,120
Explanation: In order to maximize the amount of money that the gambler kept, we should maximize # of $20 chips lost and minimize # of $100 chips lost, which means that # of $20 chips lost must be 2 more than # of $100 chips lost.
So, if # of $20 chips lost is x then # of $100 chips lost should be x-2. Now, given that total # of chips lost is 16: x+x-2=16 --> x=9: 9 $20 chips were lost and 9-2=7 $100 chips were lost.
Total worth of chips lost is 9*20+7*100=$880, so the gambler kept $5,000-$880=$4,120.
Answer: B.
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A.32
B.4/7
C.6/15
D.1/26
Answer: D.1/26
Explanation: Explanation:
Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) =n(E)/n(S)=2/52=1/26
Answer: D
Question: What is the ratio whose term differ by 50 and the measure of which is 2/7?
A.A)32:23
B.B)16:56
C.C)71:85
D.D)20:70
Answer: D.D)20:70
Explanation: Let the ratio be x:(x+50)
Then, x/(x+50) = 2/7
x=20
required ratio = 20:70
Answer is D
Question: The average (arithmetic mean) of 16 students first quiz scores in a difficult English class is 62.5. When one student dropped the class, the average of the remaining scores increased to 65.0. What is the quiz score of the student who dropped the class?
A.a) 10
B.b) 25
C.c) 40
D.d) 55
Answer: B.b) 25
Explanation: Total Score of 16 students is 16*62.50 = 1000
Total Score of 15 students is 15*65 = 975
So, the score of the person who left is 25 ( 1000 - 975 )
Answer will be (B)
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.38029
B.38000
C.38028
D.38009
Answer: B.38000
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Question: If $1092 are divided between worker A and worker B in the ratio 5:8,what is the share that worker B will get?
A.60.32%
B.61.54%
C.62.21%
D.62.76%
Answer: B.61.54%
Explanation: Worker B will get 8/13 = 61.54%
The answer is B.
Question: The public library has exactly 2 floors. It has 2/3 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 1/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
A.1/4
B.9/10
C.5/9
D.9/14
Answer: B.9/10
Explanation: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (2/3)*x
no of books per shelf on 2nd floor = (1/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (2/3)*x*(1/6)*y = (1/9)*xy
fraction of library books on first floor = (xy)/(xy + (1/9)*xy)
=1 / (1+(1/9))
=9/10
So B
Question: The two lines y = x and x = -4 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length E of a cube whose surface area is equal to 6z?
A.E=16
B.E=8√2
C.E=8
D.E=2√2
Answer: D.E=2√2
Explanation: 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(4 × 4) = 8; so z = 8.
The next step requires us to find the length of a side of a cube that has a face area equal to 8. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 8. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 8. Clearly s = √8 = 2√2 , oranswer choice (D).
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
A.52.6
B.52.9
C.52.8
D.52.1
Answer: C.52.8
Explanation: 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
Question: A straight line in the xy- plane has y-intercept of 79 and slope of 6. On this line the y-coordinate of the point is 14, then what is the X-coordinate of the point?
A.11
B.-10.83
C.71
D.20.83
Answer: B.-10.83
Explanation: Eq of line = Y = MX +C
C= 79
M=6
Y=14
Substitute given:
X = (Y - C) / M = (14 - 79) / 6 = -65/6 = -10.83
correct option is B
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
A.3
B.3.2
C.3.6
D.3.8
Answer: C.3.6
Explanation: 3.6
Option 'C'
Question: A car covers a distance of 624 km in 4 hours. Find its speed?
A.104 kmph
B.126 kmph
C.156 kmph
D.174 kmph
Answer: C.156 kmph
Explanation: 624/4
=156 kmph
Answer:C
Question: 7500 + (1250 / 50)
A.7500
B.7525
C.7550
D.8000
Answer: B.7525
Explanation: Explanation:
As per BODMAS rule first we will solve the terms in the bracket then other.
= 7500 + (25) = 7525
Option B
Question: A driver paid n dollars for auto insurance for the year 1997. This annual premium was raised by p percent for the year 1998; for each of the years 1999 and 2000, the premium was decreased by 1/6 from the previous year’s figure. If the driver’s insurance premium for the year 2000 was again n dollars, what is the value of p?
A.12
B.33 1/3
C.36
D.44
Answer: D.44
Explanation: Premium in 1997 = n;
Premium in 1998 = n(1+p/100);
Premium in 1999 = 5/6*n(1+p/100);
Premium in 2000 = 5/6*5/6*n(1+p/100).
Given that premium in 2000 = 5/6*5/6*n(1+p/100)=n --> 5/6*5/6*(1+p/100)=1 --> 1+p/100=36/25 --> p/100=11/25=44/100 --> p=44.
Answer: D.
Question: Which of the following is equal to the cube of a non-integer?
A.–64
B.–1
C.8
D.9
Answer: D.9
Explanation: All except 9 is cube of non integer as it is square of 3.
A. –64 = -4*-4*-4-- OUT
B. –1 = -1*-1*-1 -- OUT
C. 8 = 2*2*2 -- OUT
D. 9 -- Left One. Hence the answer
E. 27 = 3*3*3 -- OUT
ANSWER:D
Question: Two sides of a triangle have lengths x and e and meet at a right angle. If the perimeter of the triangle is 4x, what is the ratio of x to e ?
A.a) 2 : 3
B.b) 3 : 4
C.c) 4 : 3
D.d) 3 : 2
Answer: B.b) 3 : 4
Explanation: Ahhhh....my bad. Thank you, you're correct. 8x = 6e --> x/e = 3/4.
Actually B is the right answer.
Question: Sebastian bought a meal at a restaurant
and left a 15% tip. With the tip, he paid
exactly $36.11. How much did the meal cost without the tip?
A.$28.98
B.$29.91
C.$30.40
D.$30.60
Answer: C.$30.40
Explanation: The tip is a percent increase of 15%, which is 115%. Let x equal the price before the tip.
Thus, 115% of this price equals $36.11:
1.15x = 36.11
Divide both sides by 1.15:=>x=36.11/1.15=31.40
correct answer C)$31.40
Question: A amount doubles itself in 15 years. what is the rate of interest?
A.20/3 %
B.10/3 %
C.40/3 %
D.50/3 %
Answer: A.20/3 %
Explanation: let amount be x & rate of interest be r% annual then
(2x-x)=(x*15*r)/100
=> 15r = 100
=> r=20/3 %
ANSWER:A
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 15 different models of televisions, what is the minimum number of letters that must be used to make the codes?
A.6
B.7
C.4
D.9
Answer: C.4
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≥15. The smallest n which fulfills this condition is n = 4.
Answer C
Question: The number of stamps that P and Q had were in the ratio of 7:3 respectively. After P gave Q 13 stamps, the ratio of the number of P's stamps to the number of Q's stamps was 5:4. As a result of the gift, P had how many more stamps than Q?
A.10
B.25
C.40
D.65
Answer: A.10
Explanation: P started with 7k stamps and Q started with 3k stamps.
(7k-13)/(3k+13) = 5/4
28k - 15k = 117
k = 9
P has 7(9) - 13 = 50 stamps and Q has 3(9)+13 = 40 stamps.
The answer is A.
Question: Solution Y is 30 percent liquid X and 70 percent water. If 3 kilograms of water evaporate from 8 kilograms of solution Y and 3 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
A.35%
B.37%
C.41.3%
D.42%
Answer: C.41.3%
Explanation: In 8 kilograms of solution Y there are 0.3*8=2.4 kilograms of solution X;
After 3 kilograms of water are replaced by 3 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*3=0.9 kilograms of solution X are added, so in the new solution of 8 kilograms there are 2.4+0.9=3.3 kilograms of solution X, which is 3.3/8*100=41.3% of this new solution.
Answer: C.
Question: 40% of a number is added to 120, the result is the same number. Find the number?
A.400
B.288
C.1687
D.997
Answer: A.400
Explanation: (40/100) * X + 120 = X
2X = 400
X = 200
Answer:A
Question: The average of first 22 natural numbers is?
A.11.6
B.11.5
C.12.9
D.15.4
Answer: B.11.5
Explanation: Sum of 22 natural no. = 506/2 = 253
Average = 253/22 = 11.5
Answer:B
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
A.18 years
B.20 years
C.24 years
D.32 years
Answer: A.18 years
Explanation: Explanation:
Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
ANSWER IS A
Question: Pointing to a photograph, a lady tells Pramod, "I am the only daughter of this lady and her son is your maternal uncle." How is the speaker related to Pramod's father
A.Sister-in-law
B.Wife
C.Either (a) or (b)
D.Neither (a) nor (b)
Answer: B.Wife
Explanation: Explanation:
Clearly, the speaker's brother is Pramod's maternal uncle. So, the speaker is Pramod's mother or his father's wife
Answer: B
Question: Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature E in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6
A.29
B.30
C.30.5
D.31
Answer: B.30
Explanation: to find out median===>they must be arranged in ascending order.
29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)
total days=5+11+8+6=30
therefore 30 numbers ...median E will be==>mean of 15 and 16 th place temperature===>(30+30)/2=30
hence B
Question: If two letters are chosen at random (without replacement) from the word HORSEBACK, what is the probability that none of the letters are vowels?
A.4/9
B.5/9
C.5/12
D.7/24
Answer: C.5/12
Explanation: The number of ways to choose two letters is 9C2 = 36
The number of ways to choose two consonants is 6C2 = 15.
P(no vowels) = 15/36 = 5/12
The answer is C.
Question: You collect baseball cards. Suppose you start out with 11. Maria takes half of one more than the number of baseball cards you have. Since you're nice, you give Peter 1 baseball card. Since his father makes baseball cards, Paul decides to triple your baseball cards. How many baseball cards do you have at the end?
A.12
B.18
C.19
D.20
Answer: A.12
Explanation: Solution
Start with 11 baseball cards.
Maria takes half of one more than the number of baseball cards you have. So Maria takes half of 11 + 1 which is 6,
so you're left with 11 - 6 = 5.
Peter takes 1 baseball card from you: 5 - 1 = 4 baseball cards.
Paul triples the number of baseball cards you have: 4 Ã— 3 = 12 baseball cards.
So you have 12 at the end.
Correct answer : A
Question: Find the smallest number which when divided by 11 and 12 leaves respective remainders of 2 and 3.
A.131
B.197
C.207
D.219
Answer: A.131
Explanation: Let 'N' is the smallest number which divided by 11 and 12 leaves respective remainders of 2 and 3.
Required number = (LCM of 11 and 12) - (common difference of divisors and remainders) = (132) - (1) = 131.
ANSWER:A
Question: A two-digit number is seven times the sum of its digits. If each digit is increased by 2, the number thus obtained is 4 more than six times the sum of its digits. Find the number.
A.42
B.24
C.48
D.Data inadequate
Answer: A.42
Explanation: Let the two-digit number be l0 x + y.
10x + y = 7(x + y) Þ x = 2y...(i)
10(x + 2) + y + 2 = 6(x + y + 4) +4
or 10x + y + 22 = 6x + 6y + 28 Þ 4x – 5y = 6 ... (ii)
Solving equations (i) and (ii), we get x = 4 and y = 2
Answer A