mathewhe/aqua_rat huggingface dataset:
Question: How many 3 digit numbers that do not contain the digit 0 are there?
(A) 100
(B) 200
(C) 512
(D) 648
(E) 729
Rationale: Applying combinations....9 * 9 * 9 = 729...
8 for first digit...cant be 0
9 and 9 for 2nd and 3rd....cant be 0
ANSWER: E
Answer: (E) 729
Question: A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?
(A) 40%
(B) 45%
(C) 50%
(D) 60%
(E) 70%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% = 10 × 100 = 50%
20
Profit of 50% was made by the merchant.
C
Answer: (C) 50%
Question: Find the length of the wire required to go 12 times round a square field containing 104976 m2.
(A) 15840
(B) 3388
(C) 2667
(D) 8766
(E) 15552
Rationale: a2 = 104976 => a = 324
4a = 1296
1296 * 12 = 15552
Answer: E
Answer: (E) 15552
Question: Look at this series: 17, 24, 21, 28, ... What number should come next?
(A) 33
(B) 28
(C) 32
(D) 35
(E) 39
Rationale: Explanation:
This is a simple alternating addition and subtraction series. In the first pattern, 7 is added; in the second, 3 is subtracted.
Answer: Option C
Answer: (C) 32
Question: How many seconds will a train 100 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph?
(A) 22 sec
(B) 27 sec
(C) 30 sec
(D) 24 sec
(E) 11 sec
Rationale: Explanation:
D = 100 + 200 = 300
S = 36 * 5/18 = 10 mps
T = 300/10 = 10 sec
Answer: Option C
Answer: (C) 30 sec
Question: A train having a length of 270 meter is running at the speed of 120 kmph . It crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 320 m
(B) 190 m
(C) 210 m
(D) 230 m
(E) 240m
Rationale: Explanation:
Relative speed = 120+80 = 200 kmph = 200×10/36 m/s = 500/9 m/s
time = 9s
Total distance covered = 270 + x where x is the length of other train
(270+x)/9 = 500/9
=> 270+x = 500
=> x = 500-270 = 230 meter
Answer: Option D
Answer: (D) 230 m
Question: A train leaves Mumabai at 9 am at a speed of 30 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 60 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 27
(B) 279
(C) 60
(D) 278
(E) 379
Rationale: When the second train leaves Mumbai the first train covers 30 * 1 = 30 km
So, the distance between first train and second train is 30 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 30 / (60 -30) = 1 hours
So, the two trains meet at 11 a.m. The two trains meet 1 * 60 = 60 km away from Mumbai.
Answer:C
Answer: (C) 60
Question: Fifteen coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
(A) 2^9
(B) 2^14
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: Fix the third coin as H. The remaining 14 coins have 2^14 outcomes.
B
Answer: (B) 2^14
Question: If two sides of a triangle are 6 and 11, respectively, which of the following could NOT be the area of this triangle?
(A) 1
(B) 6
(C) 17
(D) 29
(E) 34
Rationale: For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 11.
We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)11 * 6 -or- (.5)6 * 11 will result in a maximum area of 33 for the triangle; therefore, the triangle could never have an area of 34.
E
Answer: (E) 34
Question: How many times in a day, the hands of a clock are straight?
(A) 22
(B) 24
(C) 44
(D) 48
(E) None
Rationale: EXPLANATION
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer C
Answer: (C) 44
Question: Mr. Mukhambo has two numbers and say that their difference, their sum and their product are to one another as 1:7:24. Mukhambo wants to find out whether you can get him the product of those two numbers:
(A) 24
(B) 6
(C) 48
(D) 12
(E) 18
Rationale: let the numbers are x and y so according to the given condition
x+y = 7k
x-y = k
and x*y = 24k
on solving 1st and 2nd equations we get x = 4k and y = 3k
so 4k*3k = 24k
or k = 2
so product of the numbers = 12(k^2) = 48
ANSWER:C
Answer: (C) 48
Question: Average age of students of an adult school is 42 years. 120 new students whose average age is 32 years joined the school. As a result the average age is decreased by 4 years. Find the number of students of the school after joining of the new students.
(A) 1200
(B) 120
(C) 360
(D) 200
(E) None of these
Rationale: Explanation :
Let the original no. of students be x.
According to situation, 42x + 120*32 = (x + 120)36 ⇒ x = 80
So, Required no. of students after joining the new students
= x + 120 = 200.
Answer : D
Answer: (D) 200
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 19. The larger of the two numbers is:
(A) 437
(B) 299
(C) 322
(D) 345
(E) 355
Rationale: Clearly, the numbers are (23 x 13) and (23 x 19).
Larger number = (23 x 19) = 437. Answer: Option A
Answer: (A) 437
Question: A class of 20 students took a science test. 10 students had an average (arithmetic mean) score of 80. The other students had an average score of 60. What is the average score of the whole class?
(A) 70
(B) 60
(C) 55
(D) 65
(E) 85
Rationale: hear, 10 students had average score of 80, so, 80X10=800
and 10 students had average score of 60, so, 60X10=600
total no of student are 20
(800+600)/20= 70
correct ans is A
Answer: (A) 70
Question: Sum of the squares of three numbers is 116 and the sum of their products taken two at a time is 70. Find the sum?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 116 + 2* 70
a + b + c = √256 = 16
C
Answer: (C) 16
Question: What is the sum of the multiples of 7 from 77 to 91, inclusive?
(A) 260
(B) 452
(C) 352
(D) 260
(E) 252
Rationale: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 7 and add 1.
(91/7) - (77/7) + 1 = 3
Multiply these together so what we show Average*Total Numbers=Sum
(91 + 77)/2 * 3 = Sum
84* 3 = 252
E
Answer: (E) 252
Question: The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is
(A) 22
(B) 88
(C) 27
(D) 99
(E) 11
Rationale: Explanation:
Other side=\inline {\color{Black}\sqrt{\frac{225}{4}-\frac{81}{4}}ft}
=\inline {\color{Black}\sqrt{\frac{144}{4}}ft}
=\inline {\color{Black}6ft}
Area of closest =(6 * 4.5) sq.ft =27 sq.ft
Answer: C) 27
Answer: (C) 27
Question: A snail has fallen in a 10 feet deep hole. It started climbing up - every day it
would climb 3 feet up but then it would fall 2 feet down while sleeping during
the night. After how many days will the snail climb out of the hole?
(A) 2
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Each 24 hour period the snail will climb up only 1 ft. It
does that for 7 days, but on the 8th day it goes out of the hole before
he falls asleep. Answer: 8 days.
corect answer D
Answer: (D) 8
Question: Four car rental agencies A, B, C and D rented a plot for parking their cars during the night. A parked 15 cars for 12 days, B parked 12 cars for 20 days, C parked 18 cars for 18 days and D parked 16 cars for 15 days. If A paid Rs. 1350 as rent for parking his cars, what is the total rent paid by all the four agencies?
(A) 2388
(B) 7380
(C) 1279
(D) 6150
(E) 2771
Rationale: The ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15
= 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60
Let us consider the four amounts to be 45k, 60k, 81k and 60k respectively.
The total rent paid by the four agencies = 45k + 60k + 81k + 60k= 246k
It is given that A paid Rs. 1350
45k = 1350 => k = 30
246k = 246(30) = Rs. 7380
Thus the total rent paid by all the four agencies is Rs. 7380.
Answer: B
Answer: (B) 7380
Question: Find the greatest possible length which can be used to measure exactly the lengths 4 m 95 cm, 9 m and 16 m 65 cm.
(A) 25
(B) 45
(C) 35
(D) 15
(E) 40
Rationale: Required length = H.C.F. of 495 cm, 900 cm and 1665 cm.
495 = 32 x 5 x 11, 900 = 22 x 32 x 52, 1665 = 32 x 5 x 37.
Therefore, H.C.F. = 32 x 5 = 45.
Hence, required length = 45 cm.
Answer is B.
Answer: (B) 45
Question: A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 42 liters of drink A to convert it to drink B?
(A) 7
(B) 9
(C) 12
(D) 14
(E) 18
Rationale: In 42 liters of drink A, there are 24 liters of milk and 18 liters of juice.
With 24 liters of milk, we need a total of 32 liters of juice to make drink B.
We need to add 14 liters of juice.
The answer is D.
Answer: (D) 14
Question: 6/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necessary to the nearest percent, the probability that a Juliet supporter chosen at random resides in Capulet is
(A) 28%
(B) 54%
(C) 45%
(D) 72%
(E) 78%
Rationale: Total population = 80 (assume).
6/8*80=60 people from Montague.
2/8*80=20 people from Capulet.
0.2*60=12 people from Montague support Juliet.
0.7*20=14 people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 14/(12+14)=~54
Answer: B.
Answer: (B) 54%
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be A's share in the total profit of Rs.27,000 earned at the end of 2 years from the starting of the business?
(A) Rs.7500
(B) Rs.9000
(C) Rs.9500
(D) Rs.10,800
(E) None
Rationale: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
A's share	=Rs.(27000×4/10)
= Rs.10800.
Answer D
Answer: (D) Rs.10,800
Question: The selling price of 40 apples is equal to cost price of 35 apples. Find the profit or loss obtained.
(A) Gain of 5.5 %
(B) Gain of 12.5 %
(C) Loss of 5.5 %
(D) Loss of 12.5 %
(E) Loss of 10 %
Rationale: Explanation:
Let C.P. of each apple be Re 1/-.
Therefore,
C.P. of 40 apples = Rs. 40
S.P. of 40 apples = Rs. 35
C.P. of 40 apples > S.P. of 40 apples
Loss = 40 – 35 = Rs. 5
Loss% =	Loss/c.p.	×100
Loss% =	5/40	×100
Loss% = 12.5%
ANSWER IS D
Answer: (D) Loss of 12.5 %
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25%, what is the total capacity of the pool in gallons?
(A) 1875
(B) 1250
(C) 1300
(D) 1600
(E) 1625
Rationale: 300 gallons of water increases capacity by 25% that means
25% is 300 gallons, so 100% would be = 300*100/25= 1200 gallons
Now 1200 +300 gallons is 80% capacity of tank.
so 100% capacity would be= 1500 *100/80= 1875
A is the answer
Answer: (A) 1875
Question: I chose a number and divide it by 9. Then I subtracted 100 from the result and got 10. What was the number I chose?
(A) 600
(B) 700
(C) 990
(D) 900
(E) None
Rationale: Solution:
Let x be the number I chose, then
x/9âˆ’100=10
x/9=110
x=990
Answer C
Answer: (C) 990
Question: The diagonals of a rhombus are 25 cm and 30 cm. Find its area?
(A) 250
(B) 300
(C) 375
(D) 550
(E) 750
Rationale: Area=0.5 x 25 x 30
=375 cmÂ²
Answer: C
Answer: (C) 375
Question: A lady goes to a bank near her newly possessed home. The bank's policies are weird, but she decides to open the account anyhow with a certain amount. The policy is that at the end of each year, the total amount gets doubled and Rs. 65 is deducted from that amount. After 6 years, when the lady checks her account, the total amount is 0.
Can you find out what was the original amount that she had deposited in the bank?
(A) 63.984375
(B) 63.984376
(C) 63.984377
(D) 63.984378
(E) none
Rationale: Explanation:
This question is hypothetical because you cannot transact in fractions in bank account. The following is the solution:
Year	Amount	Interest and Deduction
Start	63.984375
Y1 End	62.968750	63.984375 * 2 - 65
Y2 End	60.937500	62.96875* 2 - 65
Y3 End	56.875000	60.9375 * 2 - 65
Y4 End	48.750000	56.875 * 2 - 65
Y5 End	32.500000	48.75 * 2 - 65
Y6 End	0.000000	32.5 * 2 - 65 = 0
Answer A
Answer: (A) 63.984375
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 510
(B) 540
(C) 500
(D) 520
(E) 589
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer: Option C
Answer: (C) 500
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 40 km apart, if they walk in the same direction?
(A) 5hours
(B) 40hours
(C) 8hours
(D) 20hours
(E) 30hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 40 =20 hours
Answer is D
Answer: (D) 20hours
Question: Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years?
(A) 272.22
(B) 128.29
(C) 306.04
(D) 198.39
(E) 212.22
Rationale: Explanation:
A = 5000(51/50)3
= 5306.04
5000
-----------
306.04
Answer:C
Answer: (C) 306.04
Question: In a group of ducks and buffaloes, the total number of legs are 24 more than twice the number of heads. Find the total number of buffaloes.
(A) 8
(B) 10
(C) 12
(D) 24
(E) 28
Rationale: Explanation:
Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24
=> 2x = 24 => x = 12
Option C
Answer: (C) 12
Question: Find the area of a cuboid of length 8cm , breadth 10 cm . and height 12cm.
(A) 900 cm cube
(B) 910 cm cube
(C) 920 cm cube
(D) 930 cm cube
(E) 960 cm cube
Rationale: Area of a cuboid = lxbxh =8cm x 10cm x 12cm = 960 cm cube
answer :E
Answer: (E) 960 cm cube
Question: A speed of 14 metres per second is the same as
(A) 28 km.hr
(B) 46.6 km/hr
(C) 50.4 km/hr
(D) 70 km/hr
(E) None
Rationale: Solution
Speed	= 14 m / sec
=(14 x 18 / 5)km/hr
= 50.4 km/hr
Answer C
Answer: (C) 50.4 km/hr
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 6 minutes, then the area of the park (in sq. m) is
(A) 153200
(B) 153400
(C) 153600
(D) 154000
(E) 60000
Rationale: Perimeter = Distance covered in 6 min. = 12000 x 6 m = 1000 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1000 or x = 100.
Length = 300 m and Breadth = 200 m.
Area = (300 x 200) m2 = 60000 m2.
E
Answer: (E) 60000
Question: A certain restaurant offers 3 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
(A) 8
(B) 12
(C) 15
(D) 21
(E) 9
Rationale: As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:
A. 2 kinds of cheese and 2 kinds of fruits --> 3C2*2C2=3*1=3
B. 1 kind of cheese and 1 kind of fruit --> 3C1*2C1=3*2=6
A+B=3+6=9
Answer: E.
Answer: (E) 9
Question: An equity analyst needs to select 2 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 5, in how many ways can she choose and rank her top 2 picks?
(A) 20
(B) 30
(C) 10
(D) 40
(E) 80
Rationale: Number of ways of choosing 2 stocks = 5C2
Number of ways of ranking the chosen stocks = 2!
Hence total ways of chosing and ranking = 5C2 * 2! = 20
Correct Option: A
Answer: (A) 20
Question: The average age 12 members of a committee are the same as it was 4 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) 20 years
(B) 21 years
(C) 48 years
(D) 29 years
(E) 30 years
Rationale: 12 * 4 = 48 years
Answer:C
Answer: (C) 48 years
Question: A box contain the number of balls which is as much greater than 44 is less than 70. The number of balls is?
(A) 47
(B) 114
(C) 74
(D) 67
(E) 57
Rationale: Answer
Let the number be x.
Then, x - 44= 70- x
â‡’ 2x = 70+ 44= 114
â‡’ 2x = 114
âˆ´ x = 57
Correct Option: E
Answer: (E) 57
Question: Rs.8000 become Rs.11819 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
(A) 6 YEARS
(B) 7
(C) 5
(D) 3
(E) 8
Rationale: Explanation:
9261 = 11819(21/20)N
(21/20)8 = (21/20)N => N = 8
Answer: Option E
Answer: (E) 8
Question: A train 150 m long is running with a speed of 98 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 8 sec
(E) 9 sec
Rationale: Explanation:
Speed of the train relative to man = (98 - 8) kmph
= (90× 5/18) m/sec = 25 m/sec
Time taken by the train to cross the man I
= Time taken by It to cover 150 m at 25m / sec = 150 ×1/25 sec = 6sec
Answer: Option B
Answer: (B) 6 sec
Question: If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is:
(A) 20%
(B) 76%
(C) 26%
(D) 18%
(E) 26%
Rationale: Explanation:
Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: A
Answer: (A) 20%
Question: 300 first-time customers of a fashion store were surveyed for their shopping experience right after leaving the store. 60% of the customers in the survey had purchased clothes for less than $100. 40% of the customers in the survey reported they were overall satisfied with their purchase. 15% of the customers that had purchased clothes for less than $100 reported they were overall satisfied with their purchase. What percent of the customers surveyed purchased clothes for at least $100 and reported that they were NOT overall satisfied with their purchase?
(A) 31
(B) 25
(C) 35
(D) 45
(E) 75
Rationale: Out of 300 - 180 purchased for less than 100$120 for more
Out of 300 - 120 responded as satisfied and 180 responded disatisfied
Out of 180 ( Purchased less than 100$) - 15% = 27 responded as satisfied, So remaining Satisfied are 120 - 27 = 93
so 93 is what percentage of 300 - 31%
So the answer should be A
Answer: (A) 31
Question: If p≠q and p·q≠0, which of the following may be true?
(A) (p+q)(p-q)=0
(B) p=q
(C) p^2=q^2
(D) p.q=0
(E) p^2+q^2=0
Rationale: except A all answer are not as per qestion
A
Answer: (A) (p+q)(p-q)=0
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 28
(C) 299
(D) 277
(E) 21
Rationale: S = (100 + 300)/45 = 400/45 * 18/5 = 32
Answer: A
Answer: (A) 32
Question: What is the square root of 151,321?
(A) 476
(B) 389
(C) 497
(D) 411
(E) 524
Rationale: 1) Checking the last digits in the answer options A, C, E are out since last digit of the square is known to be 1.
2) B = 389^2 and D = 411^2
B = (400-11)^2 and D = (400 + 11)^2
Since we need the answer less than 160000 => D is out.
Thus we have B as the ans.
Answer: (B) 389
Question: The ratio of pens to pencils is 5 to 6. There are 9 more pencils than pens. How many pencils are there?
(A) 36
(B) 42
(C) 48
(D) 54
(E) 60
Rationale: Let the number of pens be 5x and the number of pencils be 6x.
6x - 5x = 9
x = 9
The number of pencils is 54.
The answer is D.
Answer: (D) 54
Question: In what ratio must rice of Rs.25 per kg be mixed with rice of Rs.12 per kg so that cost of mixture is Rs.20 per kg?
(A) 8:5
(B) 5:8
(C) 20:25
(D) 12:20
(E) 25:12
Rationale: (20-12)/(25-20=8/5=8:5
ANSWER:A
Answer: (A) 8:5
Question: A military camp has a food reserve for 250 person for 40 days. If after 10 days 50 more person are added to the camp, find the number of days the reserve will last for?
(A) 20
(B) 36
(C) 25
(D) 42
(E) None of these
Rationale: Explanation :
As the camp has a reserve for 250 person that can last for 40 days, after 10 days the reserve left for 250 person is for 30 days. Now 50 more person are added in the camp.
Hence, the food reserve for 300 person will last for:
250:300::x:30 ..(it is an indirect proportion as less men means more days)
x = (250*30)/300
x = 25 days
Answer : C
Answer: (C) 25
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is?
(A) 5/8
(B) 5/9
(C) 5/7
(D) 5/5
(E) 5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: (B) 5/9
Question: A starts business with a capital of Rs.1200 B and C join with some investments after 3 and 6 months respectively. If the end of a year, the profit is divided in the ratio 2:3:5 respectively. What is B's investment in the business?
(A) 2400
(B) 299
(C) 277
(D) 268
(E) 266
Rationale: 1200 * 12: x * 9 = 2:3
x = 2400
Answer: A
Answer: (A) 2400
Question: When certain number of marbles are divided into groups of 4, one marble remained. When the same number of marbles are divided into groups of 7 and 12 then 4, 9 marbles remained. If the total marbles are less than 10,000 then find the maximum possible number of marbles.
(A) 9992
(B) 9993
(C) 9994
(D) 9995
(E) 9996
Rationale: Ans: In this case the difference between the remainders and divisors is constant. i.e., 3. so N = K (LCM (4, 7, 12) - 3 = 84K - 3. Where K = natural number.
But we know that 84K - 3 < 10,000 ⇒⇒ 84 x 119 - 3 < 10,000 ⇒⇒ 9996 - 3 = 9993
Answer B
Answer: (B) 9993
Question: What is the least value of x. So that 23x59 is divisible by 3.
(A) 2
(B) 0
(C) 1
(D) 3
(E) 4
Rationale: Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 9 = 19 + x
Least value of x may be 2
Therefore 19 + 2 = 21 is divisible by 3.
Answer: Option A
Answer: (A) 2
Question: Sheik Abdullah decides to buy 3 new cars for his collection. If he has to choose between eight different cars, what is the number of purchasing possibilities he has?
(A) 6
(B) 28
(C) 56
(D) 112
(E) 8!
Rationale: Sheik Abdullah decides to buy 3 new cars for his collection. He has to choose between eight different cars
8C3= 8*7*6/(3*2*1) = 56 ANS:C
Answer: (C) 56
Question: The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is
(A) 33
(B) 37
(C) 18
(D) 99
(E) 22
Rationale: Explanation:
Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have :
Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice
{\color{Blue} \therefore } (20-x)/(x-15) = 2/3 60 - 3x = 2x - 30
5x = 90 x = 18.
Answer: C) Rs. 18
Answer: (C) 18
Question: A car ferry can hold up to 70 tons of cargo. What is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average (arithmetic mean) weight of 0.75 tons and half of the vehicles are trucks with an average (arithmetic mean) weight of 5 tons?
(A) 12
(B) 24
(C) 36
(D) 48
(E) 60
Rationale: The weight of one car and one truck is 5.75 tons.
70/5.75 = 12 plus a remainder
The ferry could carry 12 cars and 12 trucks for a total of 24 vehicles.
The answer is B.
Answer: (B) 24