mathewhe/aqua_rat huggingface dataset:
Question: A , B and C are standing on a circular track of 4300m such that A and C are diametrically opposite and B is in between A and C .There clockwise order are ABC , B and C runs clockwise while A runs anti-clockwise .If the speed of A B and C are 5m/s , 8m/s and 10m/s respectively . They all start running at 10:00 AM. calculate the distance covered by B when A and C meet for the first time after 10:05AM .
(A) 3240 metres
(B) 3440 metres
(C) 3640 metres
(D) 4440 metres
(E) 2440 metres
Rationale: Relative speed of A & C will be.. 15 m/s.. hence for first they will meet at
2150/15= 143.33 sec (around 2min 23sec).. so time will be 10:02:23..this case will not be considered as it is before 10:05.. Again they will meet at
4300/15=286.66 sec(around 4min 46sec).. time will be 10:07:10.. this case will be considered
Hence in 7min10 sec i.e 430
In 430sec B will cover 430*8 metres=3440 metres
ANSWER:B
Answer: (B) 3440 metres
Question: Janey covered a distance of 340 miles between city A and city B taking a total of 5 hours. If part of the distance was covered at 60 miles per hour speed and the balance at 80 miles per hour speed, how many hours did she travel at 60 miles per hour?
(A) 1 hour 45 minutes
(B) 2 hours
(C) 2 hours 30 minutes
(D) 3 hours
(E) None of these
Rationale: Janey covered a distance of 340 miles between city A and city B taking a total of 5 hours.time taken at 60:time taken at 80::(greater speed-average speed):(average speed-lower speed)
average speed is 340/5=68
That gives the answer 3:2=D
Answer: (D) 3 hours
Question: A circular rim 50 inches in diameter rotates the same number of inches per second as a circular rim 15 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 48x
(D) 24x
(E) 200x
Rationale: Revolutions - circumference of the rim.
=> 50pi*X*60 = 15pi*Revolutions
=> 10/3 *X *60 = Revolutions => 200X - Option E
Answer: (E) 200x
Question: 8^100 is divisible by 17 then find the remainder?
(A) 8
(B) 10
(C) 16
(D) 17
(E) 18
Rationale: This is an extremely difficult problem to solve with out Fermat's little theorem. By applying Fermat's little theorem , We know that 816 when divided by 17, the remainder is 1.
So divide 100 by 16 and find the remainder. Remainder = 4
Therefore, 100 = (16 × 6) + 4
Now this problem can be written as 810017 = 816×6+417 = (816)6×8417
Now this problem simply boils down to (1)6×8417 = 8417
84 = 82×82, we need to find the remainder when 64 × 64 is divisible by 17. Or 13 × 13 = 169. When 169 is divided by 17, remainder is 16.
C
Answer: (C) 16
Question: I chose a number and divide it by 4. Then I subtracted 175 from the result and got 10. What was the number I chose?
(A) 200
(B) 740
(C) 780
(D) 500
(E) 100
Rationale: Let x be the number I chose, then
x/4−175=10
x/4=185
x=740
Answer is B.
Answer: (B) 740
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?
(A) 2/21
(B) 3/25
(C) 4/41
(D) 4/23
(E) 8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: (E) 8/21
Question: The total age of A and B is 17 years more than the total age of B and C. C is how many years younger than A ?
(A) 12
(B) 27
(C) 21
(D) 17
(E) 11
Rationale: (A+B) - (B+C) = 17
A - C = 17.
C is younger than A by 17 years.
Answer: D
Answer: (D) 17
Question: The operation # is defined for all nonzero x and y by x#y = x + x/y. If S>0, then 1#(1#S) =
(A) S
(B) S+1
(C) S/(S+1)
(D) (S+2)/(S+1)
(E) (2S+1)/(S+1)
Rationale: x#y = x + x/y. If S>0, then 1#(1#S) =
You can see that a stands for y and 1 stands for x. I like to work with numbers so I did x=1 S=2 and S=y so y=2
1#S= 1+(1/2)=1.5 so now a is 1.5 --> 1+(1/1.5)=1 2/3 = 5/3
So now you can check by filling in S, which is 2:
A. S --> 2
B. S+1 --> 2+1=3
C. S/(S+1)-->2/(2+1)=2/3
D. (S+2)/(S+1)-->(2+2)/(2+1)=4/3
E. (2S+1)/(S+1)-->(2*2+1)/(2+1)=5/3
So E is the answer.
Answer: (E) (2S+1)/(S+1)
Question: A shopkeeper sells two articles at Rs.1000 each, making a profit of 20% on the first article and a loss of 20% on the second article. Find the net profit or loss that he makes?
(A) 6%
(B) 8%
(C) 4%
(D) 3%
(E) 5%
Rationale: C
4%
SP of first article = 1000
Profit = 20%
CP = (SP)*[100/(100+P)] = 5000/6 = 2500/3
SP of second article = 1000
Loss = 20%
CP = (SP)*[100/(100-L)] = 5000/4 = 1250
Total SP = 2000
Total CP = 2500/3 + 1250 = 6250/3
CP is more than SP, he makes a loss.
Loss = CP-SP = (6250/3)- 2000 = 250/3
Loss Percent = [(250/3)/(6250/3)]*100 =
0.04 * 100 = 4%
Answer: (C) 4%
Question: The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 4 and then added to the smaller of the two original integers. Which of the following represents this operation?
(A) 6t-2
(B) 10t-2
(C) -2
(D) 3
(E) -2-4t^2
Rationale: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.
therefore 4* 2t + 2t-2 = 10t-2.
option B.
Answer: (B) 10t-2
Question: Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 20 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?
(A) 3%
(B) 5%
(C) 7%
(D) 10%
(E) 12%
Rationale: Bob's time = 620 secs.
His sis' time = 576 secs.
Percent increase needed = (620-576/620) * 100 = 44/640 * 100 = 7%. Ans (C).
Answer: (C) 7%
Question: If n = 2ef, where e and f are distinct prime numbers greater than 2, how many different positive even divisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: Answer - 'C' - Four.
For a number 2ef with primes ef,there will be four even divisors - 2,2*e,2*f,2*e*f
Answer: (C)  Four
Question: According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 4 cans of water to make orange juice. How many 12 ounce cans of concentrate are required to prepare 140 six-ounce servings of orange juice?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: 1 X 12 ounce can of concentrate + 4 X 12 ounce cans of water = 60 ounces of the mixture.
60 ounces of mixture gives (60 / 6 ) = 10 servings.
Thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture.
To make 140 servings of the mixture, we need 140 / 10 = 14 cans of the concentrate.
The answer is B.
Answer: (B) 14
Question: A hexagon of side a cm is folded along its edges to obtain another hexagon
What is the % decrease in the area aof orignal hexagon
(A) 30%
(B) 50%
(C) 75%
(D) 80%
(E) 90%
Rationale: As we know, area of hexagon is = (3√3)(a^2)/2
now lets take a=2
then area = 6√3
after fold it will side become half ; a=1
new area = 1.5√3
percentage= 6√3/ 1.5√3* 100=25 %
so decrease in area =100 - 25=75%
ANSWER:C
Answer: (C) 75%
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?
(A) 190
(B) 195
(C) 200
(D) 205
(E) 210
Rationale: We're asked for the average of all of the multiples of 10 from 10 to 400, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
40(10) = 400
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 400 = 410
20 + 390 = 410
30 + 380 = 410
Etc.
Since there are 40 total terms, this pattern will create 20 'pairs' of 410.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(20)(410)/(40) =
410/2 =
205
Final Answer:D
Answer: (D) 205
Question: A firm is comprised of partners and associates in a ratio of 2:63. If 45 more associates were hired, the ratio of partners to associates would be 1:34. How many partners are currently in the firm?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The ratio 1:34 = 2:68 so the ratio changed from 2:63 to 2:68.
68-63 = 5 which is 1/9 of the increase in 45 associates.
The ratio changed from 18:567 to 18:612.
Thus the number of partners is 18.
The answer is D.
Answer: (D) 18
Question: If 35% of a number is 24 less than 50% of that number, then the number is ?
(A) 180
(B) 450
(C) 160
(D) 170
(E) 185
Rationale: Explanation:
Let the number be n. Then,
50% of n - 35% of n = 24
50/100 n - 35/100 n = 24
n = (24 x 100)/15 = 160.
Answer C
Answer: (C) 160
Question: A single discount equivalent to the discount series of 16%, 10% and 5% is?
(A) 28.18
(B) 38.9
(C) 41.6
(D) 31.4
(E) 31.1
Rationale: 100*(84/100)*(90/100)*(95/100) = 71.82
100 - 71.82 = 28.18
Answer: A
Answer: (A) 28.18
Question: In how many ways Chief Minister and Minister be elected from a team of 12 members?
(A) 128
(B) 134
(C) 132
(D) 145
(E) 150
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: A grocer has a sale of Rs. 435, Rs. 927, Rs. 855, Rs. 230 and Rs. 562 for 5 consecutive days. How much sale must he have in the sixth day so that he gets an average sale of Rs. 625?
(A) Rs 741
(B) Rs 5991
(C) Rs 6001
(D) Rs 6991
(E) None of these
Rationale: Explanation :
Total sale for 5 days = Rs. (435 + 927 + 855 + 230 + 562)
= Rs. 3009.
Required sale = Rs. [ (625 x 6) - 3009 ]
= Rs. (3750 - 3009)
= Rs. 741.
Answer : A
Answer: (A) Rs 741
Question: When n liters of fuel was added to a tank that was already 1/3 full, the tank was filled to 4/9 of its capacity. In terms of n, what is the capacity of the tank, in liters?
(A) 10/9 n
(B) 4/3 n
(C) 3/2 n
(D) 9/4 n
(E) 7/3n
Rationale: E is the answer.
To solve this problem, draw diagram or use algebra. I'm more comfortable with algebra.
Given
- tank was already 1/3 full.
- When n ltr added, it became 4/9
So 1/3 + n = 4/9
n = 4/9 - 3/9
n = 1/9
capacity of the tank is full fraction . i.e. 1 i.e. 9/9
so the question is 9/9 is how much times n
= 9/9 = 1 = xn
so x = 9/1
and total = 9/1n=9n
Answer: (E) 7/3n
Question: Four people each roll a die once. Find the probability that at least two people will roll the same number?
(A) 13/18
(B) 14/18
(C) 15/18
(D) 16/18
(E) 17/18
Rationale: atleast 2 means
1-p(no one has same number)
p(no person has same number)=6*5*4*3/6^4=10/36
reqd probability=1-10/36
=26/36=13/18
ANSWER:A
Answer: (A) 13/18
Question: Gary’s Gas Station serves an average of 16 cars per hour on Saturdays, 10 cars per hour on Sundays, and 9 cars per hour on all other days of the week. If the station is open from 6 a.m. to 10 p.m. every day, how many cars does Gary’s station serve over the course of a typical week?
(A) 1,136
(B) 1,200
(C) 1,240
(D) 1,280
(E) 1,320
Rationale: 6 a.m. to 10 p.m. = 16 hours
Number of cars serviced on weekdays = (16 * 9 * 5)
Number of cars serviced on Saturday = (16 * 16)
Number of cars serviced on Sunday = (16 * 10)
Number of cars served in a week = 16(45 + 16 + 10) = 16 * 71 = 1136
Answer: A
Answer: (A) 1,136
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 5 minutes A is turned off. After how much more time will the cistern be filled?
(A) 8 1/7
(B) 8 1/1
(C) 3 3/4
(D) 8 1/2
(E) 8 3/7
Rationale: 5/12 + (5 + x)/15 = 1
x = 3 3/4
Answer: C
Answer: (C) 3 3/4
Question: Along a yard 434 metres long, 32 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between two consecutive trees
(A) 14
(B) 16
(C) 10
(D) 11
(E) 12
Rationale: Explanation:
32 trees have 31 gaps between them,
Required distance (434/31) = 14
Option A
Answer: (A) 14
Question: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
(A) 22
(B) 20
(C) 92
(D) 82
(E) 28
Rationale: 1: 2/5 = 5: 2
2/7 * 70 = 20.Answer:B
Answer: (B) 20
Question: Find the least number must be subtracted from 378461 so that remaining no.is divisible by 13?
(A) 4
(B) 5
(C) 7
(D) 6
(E) 8
Rationale: On dividing 378461 by 13 we get the remainder 5, so 5 should be subtracted
B
Answer: (B) 5
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability T that private Benjamin will be chosen for latrine duty?
(A) 1/10
(B) 1/5
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability T= 1- 3/5 = 2/5. Thus C is the correct answer.
Answer: (C) 2/5
Question: Speed of a boat in standing water is 10kmph and speed of the stream is 2kmph. A man can rows to a place at a distance of 100km and comes back to the starting point. The total time taken by him is?
(A) 24hours
(B) 21hr 30min
(C) 20hr 50min
(D) 18hr 15min
(E) 22hrs
Rationale: Speed upstream = 8kmph
Speed downstream = 12kmph
Total time taken = 100/8 + 100/12 = 20 hours 50min
Answer is C
Answer: (C) 20hr 50min
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 270 kilos of plankton, how many kilos did he consume on the sixth hour?
(A) 33
(B) 47
(C) 50
(D) 53
(E) 62
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 270/9 = 30, so the median is also 30, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 33.
option A
Answer: (A) 33
Question: If 8 men or 12 women can do a piece of work in 15 days, in how many days can the same work be done by 6 men and 11 women?
(A) 9 days
(B) 11 days
(C) 13 days
(D) 15 days
(E) 17 days
Rationale: 8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/15
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*15= 1/180
so, 20 women work= 20/180=1/9
ans: 9 days
ANSWER:A
Answer: (A) 9 days
Question: The difference between the place values of 9 and 4 in the number 927435 is
(A) 899600
(B) 856200
(C) 875200
(D) 896200
(E) None
Rationale: Sol.= (Place value of 9) – (place Value of 4)= (900000 - 400)= 899600 Answer A
Answer: (A) 899600
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?
(A) Rs. 4, Rs. 23
(B) Rs. 13, Rs. 17
(C) Rs. 15, Rs. 14
(D) Rs. 17, Rs. 13
(E) Rs. 17, Rs. 15
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=77 or 6x+9y= 231
3x+2y =73 or 6x+4y= 146
subtracting
5y = 85
y= Rs 17.
Hence B. Rs. 13, Rs. 17
ANSWER:B
Answer: (B) Rs. 13, Rs. 17
Question: Last year a worker saved 5% of her annual salary. This year, she made 20% more money than last year and she saved 6% of her salary. The amount she saved this year was what percent of the amount she saved last year?
(A) 136%
(B) 140%
(C) 144%
(D) 148%
(E) 152%
Rationale: Let x be the worker's salary last year.
Last year, she saved 0.05x.
This year, she saved 0.06(1.2x)=0.072x
0.072x/0.05x=144%
The answer is C.
Answer: (C) 144%
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 2777
(B) 5760
(C) 2766
(D) 8987
(E) 2681
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer: B
Answer: (B) 5760
Question: An empty wooden vessel weighs 20% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
(A) 3/5
(B) 5/9
(C) 1/24
(D) 9/19
(E) 2/5
Rationale: An empty wooden vessel weighs 20% of its total weight when filled with paint:
Vessel = 0.2(Vessel + Paint);
20V = V + P (so the weight of completely filled vessel is 10V)
P = 19V (so the weight of the paint when the vessels is completely filled is 19V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*20V;
P' = 9V (so the weight of the paint when the vessels is partially filled is 9V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 9V/19V = 9/19.
Answer: D.
Answer: (D) 9/19
Question: How many ways can a selection be done of 5 letters out of 5 A's, 4B's, 3C's, 2D's and 1 E.
(A) 60
(B) 75
(C) 71
(D) 121
(E) 221
Rationale: We have the following letters: {AAAAA}, {BBBB}, {CCC}, {DD}, {E}
There are 7 different cases of 5 letter selections possible:
(5) - all letters are alike - 1 way, all A's;
(4, 1) - 4 letters are alike and 1 different - C12∗C14=8C21∗C41=8, where C12C21 is # of ways to choose which letter provides us with 4 letters from 2 (A or B) and C14C41 is # of ways to choose 5th letter from 4 letters left;
(3, 2) - 3 letters are alike and other 2 are also alike - C13∗C13=9C31∗C31=9, where C13C31 is # of ways to choose which letter provides us with 3 letters from 3 (A, B or C) and C13C31 is # of ways to choose which letter provides us with 2 letters from 3 (for example if we choose A for 3 letters then we can choose from B, C or D for 2 letters);
(3, 1, 1) - 3 letters are alike and other 2 are different - C13∗C24=18C31∗C42=18, where C13C31 is # of ways to choose which letter provides us with 3 letters from 3 (A, B or C) and C24C42 is # of ways to choose which 2 letters provides us with one letter each;
(2, 2, 1) - 2 letters are alike, another 2 letters are also alike and 1 is different - C24∗C13=18C42∗C31=18, where C24C42 is # of ways to choose which 2 letters provides us with 2 letters from 4 (A, B, C or D) and C13C31 is # of ways to choose which provides us with 5th letter from 3 letters left;
(2, 1, 1, 1) - 2 letters are alike and other 3 are different - - C14∗C34=16C41∗C43=16, where C14C41 is # of ways to choose which letter provides us with 2 letters from 4 (A, B, C or D) and C34C43 is # of ways to choose which 3 letters out of 4 provides us with one letter each;
(1, 1, 1, 1, 1) - all letters are distinct - 1 way (A, B, C, D, E).
Total: 1+8+9+18+18+16+1=71.
Answer: C.
Answer: (C) 71
Question: There are 100 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position at the beggining, How many lights are switched On by the end of this operation?
(A) 13
(B) 41
(C) 47
(D) 48
(E) 53
Rationale: Number of switches = 100
Number of switches turned on by A: 3, 6, ... 99 = 33
Number of switches turned on by B: 5, 10, .... 100 = 20
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off.
Number of switches that are turned on = (33 - 6) + (20 - 6) = 41
Answer: B
Answer: (B) 41
Question: ((-1.9)(0.6) – (2.6)(1.2))/7.0 = ?
(A) -0.61
(B) 1.0
(C) 1.07
(D) 1.71
(E) 2.71
Rationale: Dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option.
-0.61
Answer A
Answer: (A) -0.61
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –5), K = (–2, 1), L = (6, 7), and M = (6, –5). What is its perimeter?
(A)  34
(B)  35
(C)  38
(D)  40
(E) (F) 42
Rationale: JK = 6
LM = 11
KL =using distance formula 10
JM = using distance formula 8
Sum of all is 35
B
Answer: (B)  35
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 28, by how much does the temperature in degrees Celsius (C) increase?
(A) 9
(B) 15.55
(C) 47
(D) 48 3/5
(E) 59
Rationale: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+28=60 --> C=5/9*28=15.55.
Increase = 15.55 degrees.
Answer: B.
Answer: (B) 15.55
Question: Look at this series: 90, 87, 92, 89, 94, 91, ... What number should come next?
(A) 94
(B) 96
(C) 90
(D) 98
(E) 92
Rationale: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option B
Answer: (B) 96
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) Rs. 16.58
(B) Rs. 16.51
(C) Rs. 16.59
(D) Rs. 16.50
(E) Rs. 16.52
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer:D
Answer: (D) Rs. 16.50
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.00 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
(A) 1.40$
(B) 1.58$
(C) 1.60$
(D) 1.64$
(E) 1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2+4*1.5+2*1=$14, hence amount of the snacks sales per ticket is $14/10=~$1.4.
Answer: A.
Answer: (A) 1.40$
Question: A shop sells bicycles and tricycles. In total there are 9 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
(A) b=8,t=1
(B) b=5,t=3
(C) b=6,t=2
(D) b=2,t=5
(E) b=3,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=9...........(1)
2b+3t=19............(2)
Rearrange equation (1) and substitute into equation (2)
2b+27-3b=19
-b=-8
b=8
Calculate the number of tricycles t
t=9−b
=9−8
=1
There are 1 tricycles and 8 bicycles.
Answer is A.
Answer: (A) b=8,t=1
Question: In a game, one player throws two fair, six-sided die at the same time. If the player receives at least a four or a one on either die, that player wins. What is the probability that a player wins after playing the game once?
(A) 1/3
(B) 4/9
(C) 5/9
(D) 2/3
(E) 3/4
Rationale: We're looking for the number of outcomes that include AT LEAST a 1 or a 4.
#getting a one in 1st die = {(1,1), (1,2), ...(1,6) }= 6
#getting a one in 2nd die {(2,1), ...(5,1),(6,1) } = 4 [exclude 1,1 and 4,1] since it will be counted twice
#getting a three in 1st die {(3,1), (3,2), ...(3,6) }= 6
#getting a three in 1st die {(2,4), (3,4), ...(6,4) } = 4 [exclude 1,4 and 4,4] since it will be counted twice
Total possibities = 20
Probability of rolling at least a 1 or a 4 on two dice: 20/36 = 5/9
C
Answer: (C) 5/9
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 5
(B) 4
(C) 8
(D) 9
(E) 2
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: (B) 4
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together.
(A) 720
(B) 740
(C) 760
(D) 790
(E) 800
Rationale: 720
Option 'A'
Answer: (A) 720