mathewhe/aqua_rat huggingface dataset:
Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 300 kmph
(B) 360 kmph
(C) 600 kmph
(D) 720 kmph
(E) 650 kmph
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 2/3hours as 5/3 hours]
Required speed = (1200 x3/5)	km/hr	= 720 km/hr.
Answer :D
Answer: (D) 720 kmph
Question: The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?
(A) (mb + nc) / (m+ m)
(B) (mb + nc) / (n+ n)
(C) (mb + nc) / (m+ n)
(D) (mb + nm) / (m+ n)
(E) (mb + nc) / (m+ n)
Rationale: (mb + nc) / (m+ n)
Answer: C
Answer: (C) (mb + nc) / (m+ n)
Question: At a dinner party, 8 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 1) 5234
(B) 2)5210
(C) 3) 5760
(D) 4)5732
(E) 5) 5120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 8 guests, so number of distinct arrangements = 7! = 5760
Answer : C
Answer: (C) 3) 5760
Question: How many positive integers C less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Rationale: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Answer: (D) 54
Question: a man follows the following steps..
1)4km towrds north
2)3km towards east
3)8km towards south
4)6km towars west
5)7km towards north
6)5km towards east
7)6km towards south
8)4km towards 4
9)finally 3km towards north
how far he is from starting point and in which direction??
(A) 3km west
(B) 2km west
(C) 4km west
(D) 2km east
(E) 2km north
Rationale: final position = (4+7+3)km north (3+5)km east (8+6)km south (6+4)km west
=14km north 8km east 14km south 10km west
=(14-14)km north (10-8)km west
=2km west
ANSWER:B
Answer: (B) 2km west
Question: If |z|/w = 3,which of the following must be true?
(A) z = -3w
(B) z = 3w
(C) z^2 = 9w^2
(D) z^2 = 9w^3
(E) z^3 = 27w^3
Rationale: |z|/w = 3.
|z| = 3w.
Then z = 3w or -3w and so z^2 = 9w^2.
The answer is C.
Answer: (C) z^2 = 9w^2
Question: If 3a = 4b and ab ≠0, what is the ratio of a/4 to b/3?
(A) 64/27
(B) 9/16
(C) 1
(D) 6/8
(E) 8/6
Rationale: A nice fast approach is the first find a pair of numbers that satisfy the given equation: 3a = 4b
Here's one pair: a =4 and b =3
What is the ratio of a/9 to b/8?
In other words, what is the value of (a/4)/(b/3)?
Plug in values to get: (a/4)/(b/3) = (4/4)/(3/3)
= 1/1
= 1
C
Answer: (C) 1
Question: Look at this series: 404, 369, 334, 299, 264, 229, 194 ... What number should come next?
(A) 194
(B) 108
(C) 106
(D) 107
(E) 104
Rationale: 194
This is a simple subtraction series. Each number is 35 less than the previous number.
A
Answer: (A) 194
Question: a percent of b percent of c is decreased by y percent. What is the result?
(A) (100abc - ab^2c) / 1,000,000
(B) (ac - b) / 100
(C) (ac - b) / 10,000
(D) (abc - 2b) / 100
(E) (abc - 2b) / 10,000
Rationale: We're told that a percent of b percent of c is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
a = 10
b = 50
c = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when a=10, b=50 and c=100.
Answer A. (100abc - ab^2c) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5
This is a MATCH
A
Answer: (A) (100abc - ab^2c) / 1,000,000
Question: If books bought at prices ranging from Rs. 110 to Rs. 240 are sold at prices ranging from Rs. 150 to Rs 280, what is the greatest possible profit that might be made in selling 10 books ?
(A) Rs. 1700
(B) Rs. 3000
(C) Rs. 3500
(D) Rs. 3200
(E) Rs. 3600
Rationale: The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 10 books = 110*10 = Rs. 1,100
Maximum selling price of 10 books = 280 *10 = Rs. 2,800
So, maximum profit = 2800 - 1100 = Rs. 1,700
ANSWER : OPTION A
Answer: (A) Rs. 1700
Question: Jane and Ashley take 5 5/7 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ?
(A) 12.5 Days
(B) 13.5 Days
(C) 16 Days
(D) 18 Days
(E) 20 Days
Rationale: Let us assume that the work is laying 40 bricks.
Jane = 7 bricks per day
Ashley = 1 brick per day
Together =8 bricks per day
Let's say first 8 days Ashley works alone,
No of bricks = 8
Last 4 days Jane works alone,
No. of bricks = 28
Remaining bricks = 40 - 36 = 4
So together, they would take 4/8 = 0.5
Total no. of days = 8 + 4 + 0.5 = 12.5
Answer is A
Answer: (A) 12.5 Days
Question: A watch was sold at a loss of 10%. If it was sold for Rs.180 more, there would have been a gain of 5%. What is the cost price?
(A) Rs.1200
(B) Rs. 1100
(C) Rs. 1300
(D) Rs. 1400
(E) Rs. 1000
Rationale: 90%
105%
--------
15% ---- 180
100% ---- ? => Rs.1200
Answer: A
Answer: (A) Rs.1200
Question: If a sample of data has mean of 22 and SD of 3, which of the following values is more than 2.5 SDs from the mean?
(A) a. 15
(B) b. 13.5
(C) c. 17
(D) d. 23.5
(E) e. 26.5
Rationale: Value ismore than 2.5SDfrom the mean means that the distance between the mean and the value must be more than 2.5SD=7.5. So the value either <22-7.5=14.5 or >22+7.5=29.5.
Answer: B.
Answer: (B) b. 13.5
Question: Two children want to walk together to visit their aunt, who lives exactly 7 blocks north and 6 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 13 blocks. How many different 13-block routes may they take to travel the shortest possible distance to their aunt’s house?
(A) 13
(B) (13!)/(7!6!)
(C) (20!)/(13!7!)
(D) 7!6!
(E) 13!7!6!
Rationale: If they need to walk 7 blocks north and 6 blocks east, we can express this route as NNNNNNNEEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 13 things is 13!
We then divide by the repetitions of N's and E's, which are 7! and 6! respectively.
The number of walking routes is 13!/(7!6!).
The answer is B.
Answer: (B) (13!)/(7!6!)
Question: Albert buys 4 horses and 9 cows for Rs. 13,400. If he sells the horses at 10% profit and the cows at 20% profit, then he earns a total profit of Rs. 1880. The cost of a horse is:
(A) Rs. 1000
(B) Rs. 2000
(C) Rs. 2500
(D) Rs. 3000
(E) Rs. 3500
Rationale: Let C.P. of each horse be Rs. x and C.P. of each cow be Rs. y.
Then, 4x + 9y = 13400 -- (i)
And, 10% of 4x + 20% of 9y = 1880
2/5 x + 9/5 y = 1880 => 2x + 9y = 9400 -- (ii)
Solving (i) and (ii), we get : x = 2000 and y = 600.
Cost price of each horse = Rs. 2000.
ANSWER:B
Answer: (B) Rs. 2000
Question: If a quarter Kg of potato costs 60 paise, How many paise will 200 gm cost?
(A) 48
(B) 99
(C) 37
(D) 26
(E) 18
Rationale: Answer: A) 48 Paise
Answer: (A) 48
Question: On a map, 2.5 inches represent 40 miles. How many miles approximately is the distance if you measured 155 centimeters assuming that 1-inch is 2.54 centimeters?
(A) 990.4
(B) 970
(C) 972
(D) 976.4
(E) 975
Rationale: 1 inch = 2.54 cm
2.5 inch = 2.54 * 2.5 cm
6.35 cm = 40 miles
155 cms = 40/6.35*155= 976.4 miles
Answer : D
Answer: (D) 976.4
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $189 million, which represented 10 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 17,010
(B) 2,100
(C) 1,890
(D) 1,701
(E) 210
Rationale: 10% ---- 189 millions
for 100% => ( 189 * 100% )/10% = 1890.
Option C.
Answer: (C) 1,890
Question: How many seconds will a 700 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 287
(B) 288
(C) 600
(D) 277
(E) 121
Rationale: Let length of tunnel is x meter
Distance = 700+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
700+x = (65/3) * 60
700+x = 20 * 65 = 1300
x = 1300 - 700 = 600 meters
Answer: C
Answer: (C) 600
Question: In My, Xiang sold 15 used cars. For these 15 used cars the range of selling prices was 15,000 and the lowest selling price was 4,500. In June, Xiang sold 10 cars. For these 10 cars the range of selling was 12,000 and the lowest selling price was 6,100. What was the range of selling prices for the 25 used car sold by xiang in May and June?
(A) 15,600
(B) 15,750
(C) 16,820
(D) 18,100
(E) 19,200
Rationale: for 10 cars - 12000+ 6100 = 18,100
for 15 cars - 15000+ 4500 = 19,500
max = 19,500 min 4500
answer is approx 15000.
Option A is closest.
Answer: (A) 15,600
Question: P and Q can complete a work in 40 days and 24 days respectively. P alone started the work and Q joined him after 16 days till the completion of the work. How long did the work last?
(A) 5 days
(B) 10 days
(C) 14 days
(D) 22 days
(E) 25 days
Rationale: Explanation :
Work done by P in 1 day = 1/40
Work done by Q in 1 day = 1/24
Work done by P in 16 days = 16 Ã— (1/40) = 2/5
Remaining work = 1 â€“ 2/5 = 3/5
Work done by P and Q in 1 day = 1/40 + 1/24 = 1/15
Number of days P and Q take to complete the remaining work = (3/5) / (1/15) = 9
Total days = 16 + 9 = 25
Answer : Option E
Answer: (E) 25 days
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 400m
(B) 700m
(C) 120m
(D) 240m
(E) 350m
Rationale: Explanation:
Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer: E
Answer: (E) 350m
Question: The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (f) around the mirror, which of the following could be the value, in inches, of f ?
I. 2
II. 3 1/2
III. 5
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: Area of picture = 16x Area of frame = 33x
Area of picture / (Area of picture + area of frame) = 16x / 49x = 4x/7x.
This results in f value to be a multiple of 1.5 = multiple of 3/2 and since f is not constrained to be only integer all the three choices are possible
For i) the multiple of f is 4/3
For ii) the multiple of f is 7/3
For iii) the multiple of f is 10/3
The key is f can be any real positive number... very tricky problem.. took me > 15 minutes.
Answer is E
Answer: (E) I, II, and III
Question: If the Average (mean ) of 13 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 12x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: Let the 5 numbers be 1,2,3,4,5, ...,13 (since no restrictions are given). There mean is 7 (x).
Now the sum of greatest three would be 11+12+13= 36
so the answer has to be 12x....that is option B
Answer: (B) 12x
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
(A) 150
(B) 882
(C) 772
(D) 252
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter.Answer: A
Answer: (A) 150
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one closet, one bed and one of the following: a chair or a shelf?
(A) A)168.
(B) B)80.
(C) C)56.
(D) D)108.
(E) E)16.
Rationale: ways to select one closet = 3
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+2 = 10
ways to select all of them together = 3*4*9 = 108
Answer : D
Answer: (D) D)108.
Question: The average of 45 results is 25 and the average of other 25 results is 45 . what is the average of all the results?
(A) 24
(B) 32
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 70 result = sum of 45 result + sum of 25 result.
= 45 x 25 + 25 x 45
= 2250/70
Correct Option: B
Answer: (B) 32
Question: The age of a man is twice the sum of the ages of his two sons. Five years hence, his age will be 16 years more than the sum of the ages of his sons. What is the father's present age?
(A) 42 years
(B) 40 years
(C) 45 years
(D) 48 years
(E) 55 years
Rationale: let man's age be m and sons ages will be x&y
given that m=2(x+y)=x+y=m/2
m+5=x+5+y+5+16
m=x+y+21
m=m/2+21
m=42
ANSWER:A
Answer: (A) 42 years
Question: On a certain number line, conditions are a<b<c<d<e and abcd>0. Which of the following must be true?
I ab>0 II cd>0 III de>0 ,IV e+ve
=ve
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I II and IV
Rationale: Givena<b<c<d<e and abcde>0.
Suppose, for the product to be greater than 0, we can two variables as -ve or four variables can be -ve.
We are given : I ab>0 II cd>0 III de>0
case 1: a and b can be negative/positive and if they are... we get greater than 0.
case 2: we have cd , then c and d both can be negative/positive and if they are... we get greater than 0.
case 2: we have de , then c and d both can be negative/positive and if they are... we get greater than 0.
if cd both negative , then de both have to negative in order to get greater than 0. In order to abcde>0 , cde can't be negative else we get -ve value, then we need to have either a or b as negative then ab can't be greater than 0.
so cde have to be positive.
ab > 0 , cd > 0 obviouly e will be positive , since we have information de> 0 . ( Here we have relationship between cd and de , where d is common).
So cases 1 and 2 are fine.
OptionE
Answer: (E) I II and IV
Question: In given question, various terms of an alphabet series is given with one term missing as shown by (?). Choose the missing term out of the given alternatives.
D, G, J, M, ?, S, V
(A) P
(B) I
(C) U
(D) H
(E) H
Rationale: Explanation:
Given:
D, G, J, M, ?, S, V
Refer : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
We have,
letter coding
ANSWER: B
Answer: (B) I
Question: The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 500. What is the manager's monthly salary ?
(A) Rs.16003
(B) Rs.16029
(C) Rs.1288
(D) Rs.16108
(E) Rs.12000
Rationale: Explanation:
Manager's monthly salary Rs. (2000 * 21 - 1500 * 20) = Rs.12000.
Answer: E
Answer: (E) Rs.12000
Question: Two identical machines have the ability to produce both nuts and bolts. However, it takes 1 second to produce a bolt but 2 seconds to produce a nut. What is the fastest the two machines, working together, can produce 2,000 nuts and 2,000 bolts?
(A) 1,250 seconds
(B) 1,500 seconds
(C) 1,750 seconds
(D) 2,000 seconds
(E) 3,000 seconds
Rationale: I used the Rate formula (R=\frac{1}{T})
Rate of 1st machine = Rate of making 1 bolt + Rate of making 1 nut = 1 + \frac{1}{2}
Rate of 1st machine = Rate of 2nd machine
After this I got lost.
Please can you help how to approach using algebra?
I wouldn't complicate:
1 machine needs 2,000*1 seconds to produce 2,000 bolts, so 2 need half of that, so 2,000/2 seconds.
1 machine needs 2,000*2 seconds to produce 2,000 nuts, so 2 need half of that, so 2,000*2/2 seconds.
E
Answer: (E) 3,000 seconds
Question: a, b, c and d are four consecutive numbers. If the sum of a and dis 107, what is the product of b and c?
(A) 2862
(B) 2578
(C) 2534
(D) 3354
(E) 4234
Rationale: A
2862
Here d = a + 3
a + a + 3 = 107
2a = 104
a = 52
So, numbers are 52, 53, 54 and 55
∴ b × c= 53 × 54 = 2862
Answer: (A) 2862
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
(A) 3
(B) 8
(C) 7
(D) 6
(E) 2
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer:A
Answer: (A) 3
Question: 150 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 90 liters
(B) 20 liters
(C) 50 liters
(D) 20 liters
(E) 70 liters
Rationale: Milk = 3/5 * 150 = 90 liters
Water = 50 liters
90 : (50+P) = 3:4
150 + 3P = 360 => P = 70
50 liters of water are to be added for the ratio become 3:4.
ANSWER:C
Answer: (C) 50 liters
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 asquotient and the 15 as remainder?
(A) 1245
(B) 1567
(C) 1678
(D) 1335
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: y = 248 - 200x
Which of the following values of x gives the greatest value of y in the equation above?
(A)  -3
(B)  100
(C)  0.5
(D)  0
(E)  30
Rationale: Clearly, the negative value of x will result in maximum value of y.
Answer is A
Answer: (A)  -3
Question: To mail a package, the rate is a cents for the first pound and b cents for each additional pound, where a>b. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of a-b cents
(B) Combined, with a saving of a-b cents
(C) Combined, with a saving of a cents
(D) Separately, with a saving of a-b cents
(E) Separately, with a saving of b cents
Rationale: This means it costs a cent for the first pound in weight for example, 20 cents for the first pound.
It costs b cents for the every pound in weight above this, for example 10 cents for pound 2 and 10 cents for pound 3.
a is more than b. for example 20 cents vs. 10 cents
3 pounds: a+2b
5 pounds:a+4b
Total: 2a+6b
8 pounds: a+7b
So we are saving:
(2a+6b) - a+7b
= a-b cents
Combined is cheaper as we maximize y and minimize x.
Answer is:A
Answer: (A) Combined, with a saving of a-b cents
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 3/5.
The probability of drawing a green ball is 1/10.
If a jar cannot contain more than 50 balls, how many yellow balls are in the Jar?
(A) 33
(B) 7
(C) 14
(D) 21
(E) 9
Rationale: answer of 1st
just add the given probabilities p(blue)+p(red)+p(green) i.e
1/8+3/5+1/10=5+24+4/40 =33/40
now we know p(blue)+p(red)+p(green)+p(yellow)=1
33/40+p(yellow)=1
p(yellow)=7/40
i.e why yellow balls are 7.
B
Answer: (B) 7
Question: If 2x+3y=34 and ((x + y)/y)=13/8,then find the value of 5y+7x.
(A) 25
(B) 55
(C) 35
(D) 75
(E) 85
Rationale: The given equations are:
2x+3y=34 …(i) and, ((x + y) /y)=13/8 => 8x+8y=13y => 8x-5y=0 …(ii)
Multiplying (i) by 5,(ii) by 3 and adding, we get : 34x=170 or x=5.
Putting x=5 in (i), we get: y=8.
=> 5y+7x=((5*8)+(7*5))=40+35=75
Answer is D.
Answer: (D) 75
Question: How many pairs (q, q+1) have one or more prime factors common, where q is an integer and 2 ≤ q ≤9 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: q and q+1 are consecutive integers.
Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.
Answer: A.
Answer: (A) 0
Question: Hari spends 50% of his income. His income is increased by 10% and he increased his expenditure by 5%. Find the percentage increase in his savings?
(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let original income = $100
expenditure = $50
savings = $50
new income = $110
new expenditure = $105/100 * 50 = $105/2
New savings = 110 - 105/2 = $115/2
Increase in savings = 115/2 - 50 = $15/2
Increase % = 15/2 * 1/50 * 100 = 15%
Answer is B
Answer: (B) 15%
Question: A tempo is insured to an extent of 5/7 of its original value. If the premium on it at the rate of 3% amounts to $300, The original value of the tempo is?
(A) 12500
(B) 13280
(C) 17520
(D) 14000
(E) 12560
Rationale: Let the original value of the tempo is $x
3% of 5/7 of x = 300
(3/100)*(5/7)x = 300
x = $ 14000
Answer is D
Answer: (D) 14000
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 4 kg more than Peter. Together the three of them picked 28 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
(A) 6, 10 and 12
(B) 12, 10 and 6
(C) 10, 6 and 12
(D) 12, 6 and 10
(E) 6, 12 and 10
Rationale: M = 2P
L = P+4
M + P + L = 28
2P + P + (P+4) = 28
P = 6, M = 12, L = 10
Therefore, Mary, Peter, and Lucy picked 12, 6, and 10 kg, respectively.
The answer is D.
Answer: (D) 12, 6 and 10
Question: Consider a right triangle WBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle WBC
(A) [A] x+y+z/3
(B) [B] x-y+z/3
(C) [C] x-y+z/2
(D) [D] (x^2 + y^2 + z^2)/3
(E) [E] cannot be determined
Rationale: Radius of a circle inscribed in the right triangle WBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Answer: (C) [C] x-y+z/2
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
(A) 4 litres, 8 litres
(B) 6 litres, 6 litres
(C) 5 litres, 7 litres
(D) 7 litres, 5 litres
(E) 8 litres, 6 litres
Rationale: Explanation:
Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can =	3/4litre, C.P. of 1 litre mix. in 1st can Re.3/4
Milk in 1 litre mix. in 2nd can = 1/2litre, C.P. of 1 litre mix. in 2nd can Re.1/2
Milk in 1 litre of final mix. =	5/8litre, Mean price = Re.5/8
By the rule of alligation, we have:
C.P. of 1 litre mixture in 1st can C.P. of 1 litre mixture in 2nd can
Ratio of two mixtures =	1/8:1/8=1:1
So, quantity of mixture taken from each can =(1/2 x 12)=6 litres.
ANSWER IS B
Answer: (B) 6 litres, 6 litres
Question: If 16% of 40% of a number is 4, then the number is
(A) 200
(B) 225
(C) 62.5
(D) 320
(E) None of these
Rationale: Explanation:
Let 16/100×40/100×a=4
a = 4×100×100/16×40=62.5
Correct Option: C
Answer: (C) 62.5
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 4 employees to 2 different offices?
(A) 12
(B) 11
(C) 10
(D) 16
(E) 12
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2=2^4=16.
Answer: D.
Answer: (D) 16
Question: If a fair coin is tossed five times, what is the probability of getting exactly four heads in a row?
(A) 1/64
(B) 1/32
(C) 1/16
(D) 1/8
(E) 1/4
Rationale: P(HHHHT) = 1/32
P(THHHH) = 1/32
The sum of these probabilities is 2/32 = 1/16
The answer is C.
Answer: (C) 1/16
Question: A restaurant meal cost $30.00 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
(A)  $40 and $42
(B)  $39 and $41
(C)  $38 and $40
(D)  $37 and $39
(E)  $33 and $35
Rationale: The total amount for the meal was between 30.0*1.1=33.00 and 30.0*1.15=34.5. Only option which covers all possible values of the meal is E.
Answer: E.
Answer: (E)  $33 and $35
Question: A certain number X when divided by 243 leaves a remainder of 95. Which of the following can be subtracted from X to make X divisible by 79?
(A) 17
(B) 22
(C) 37
(D) 47
(E) 57
Rationale: Least possible value of the number is 243 + 95 = 338
Further it is given the number must be divisible by 79 .
338/79 = Gives remainder as 22
So, 22 must be subtracted from the number , answer is (B)
Answer: (B) 22