mathewhe/aqua_rat huggingface dataset:
Question: A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
(A) 8.5 km/hr
(B) 8 km/hr
(C) 9 km/hr
(D) 10 km/hr
(E) 7 km/hr
Rationale: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
ANSWER:D
Answer: (D) 10 km/hr
Question: sixty men can build a wall in 40 days.but they begin the work together,5 men quit after 10 day.the time needed to build the wall is
(A) 42.72 days
(B) 52.72 days
(C) 46.72 days
(D) 48.72 days
(E) 62.72 days
Rationale: actually 60 men can build a wall in 40 days
suppose same 60 men work for 10 days
then 5 men quit 55 men work for remaining 30 days
then finally remaining work will be 30 * 5 =150 days work
the 55 men can do the 150 days work in 2.72 days
for completion they will take 42.72 days
ANSWER:A
Answer: (A) 42.72 days
Question: Which of the following numbers is not prime?
(A) 396+103
(B) 494+97
(C) 159+159
(D) 322-5
(E) 121-11
Rationale: 159 is divisible by 3 so i can not be a prime number. --> 3*(53+53). The correct choice is C.
Answer: (C) 159+159
Question: The sum of three from the four numbers A, B, C, D are 4024, 4087, 4524 and 4573. What is the largest of the numbers A, B, C, D?
(A) 1712
(B) 1716
(C) 1713
(D) 1714
(E) 1715
Rationale: a+b+c=4024
b+c+d= 4087
a+c+d=4524
a+b+d=4573
Combining all we get 3(a+b+c+d) = 17208
⇒ a + b + c +d = 3736
Now we find individual values. a = 1649, b = 1212, c = 1163, d = 1712. So maximum value is 1712.
Answer:A
Answer: (A) 1712
Question: A, B and C start a business each investing 20,000. After 5 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 69,900 was recorded. Find the share of B
(A) 20,000
(B) 21,000
(C) 28,200
(D) 20,500
(E) None of these
Rationale: Ratio of the capitals of A, B and C
= 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7
= 205000 : 212000 : 282000 = 205 : 212 : 282.
B’s share = (69900 × 212⁄699) = 21200;
Answer C
Answer: (C) 28,200
Question: If 15/x is an integer and 5/x is an integer, which of the following must be true? I. 4/x is an integer II. 18/x is an integer III. 5/x is an integer
(A) I only
(B) II only
(C) II,III only
(D) III only
(E) I,II only
Rationale: The question asks which of the following MUST be true, not COULD be true. The largest possible value of x is 5, GCD of 15 and 5, and if x=5 then ONLY III is true.
Answer: D
Answer: (D) III only
Question: A 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2. 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more. At the end of the two removal and replacement, what is the ratio E of milk and water in the resultant mixture?
(A) 17 : 3
(B) 9 : 1
(C) 3 : 17
(D) 5 : 3
(E) 11: 2
Rationale: he 20 litre mixture contains milk and water in the ratio of 3 : 2. Therefore, there will be 12 litres of milk in the mixture and 8 litres of water in the mixture.
Step 1.
When 10 litres of the mixture is removed, 6 litres of milk is removed and 4 litres of water is removed. Therefore, there will be 6 litres of milk and 4 litres of water left in the container. It is then replaced with pure milk of 10 litres. Now the container will have 16 litres of milk and 4 litres of water.
Step 2.
When 10 litres of the new mixture is removed, 8 litres of milk and 2 litres of water is removed. The container will have 8 litres of milk and 2 litres of water in it. Now 10 litres of pure milk is added. Therefore, the container will have 18 litres of milk and 2 litres of water in it at the end of the second step. Therefore, the ratio of milk and water is 18 : 2 or 9 : 1.
Shortcut.
We are essentially replacing water in the mixture with pure milk.
Let W_o be the amount of water in the mixture originally = 8 litres.
Let W_r be the amount of water in the mixture after the replacements have taken place.
Then,{W_r}/{W_o}= (1-R/M)^n
where R is the amount of the mixture replaced by milk in each of the steps, M is the total volume of the mixture and n is the number of times the cycle is repeated.
Hence, {W_r}/{W_o} =(1/2)^2  =1/4
Therefore E,W_r ={W_o}/4= 8/4 = 2 litres.B
Answer: (B) 9 : 1
Question: If n is a positive integer, which of the following is a possible value of |61 - 5n|?
(A) 7
(B) 14
(C) 12
(D) 15
(E) 20
Rationale: When 61>5n, then |61- 5n| = 61- 5n = (60-5n) + 1 = {multiple of 5} + 1
When 61<=5n, then |61 - 5n| = -(61- 5n) = (5n-60) - 1 = {multiple of 5} - 1
So, the correct answer must be 1 greater or 1 less than a multiple of 5. Only B fits.
Answer: B
Answer: (B) 14
Question: Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647
(A) 16
(B) 18
(C) 20
(D) 19
(E) 17
Rationale: E
Explanation :
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
Answer: (E) 17
Question: Sinha and Mitra started a business by investing Rs.52000 and Rs.55000 respectively, after three months Mitra invested Rs.5000 more in the business. What is the share of Mitra in the half year profit of Rs.26280 ?
(A) Rs.13800
(B) Rs.12000
(C) Rs.14200
(D) Rs.13980
(E) Rs.13860
Rationale: Sinha = 52000 x 6 = 312000.
Mitra = 55000 x 3 = 165000 + 60000 x 3 = 180000 = 345000.
Ratio of investments = Sinha : MItra = 312000 : 345000 = 104 : 115 => [219 units].
Mitra share in the profit = 25280 × 115 / 219 = Rs.13800
Option A
Answer: (A) Rs.13800
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 3 miles, and then ran 3 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
(A) 1 ≤ n ≤23
(B) 3 ≤ n ≤21
(C) 5 ≤ n ≤19
(D) 6 ≤ n ≤18
(E) 9 ≤ n ≤15
Rationale: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-3+3=18 for the maximum, and 12-6+3-3=6 for the minimum, so D is the answer
Answer: (D) 6 ≤ n ≤18
Question: If Logx (1 / 8) = - 3 / 2, then x is equal to
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Rewrite the logarithmic equations using exponential equation
x- 3 / 2 = 1 / 8
The above equation may be rewritten as
x - 3 / 2 = 1 / 23 = 2-3
(√x)-3 = 2-3
The above equation gives
√x = 2 or x = 4
answer = B
Answer: (B) 4
Question: If a^x = b^5y, then
(A) log a/b= x/y
(B) log a/ log b = x/y
(C) log a/ log b = 5y/x
(D) log b/a = x/y
(E) log b/a = y/x
Rationale: a^x = b^5y => log a^x = log b^5y => x log a = 5y log b
=> log a/ log b = 5y/x
ANSWER:C
Answer: (C) log a/ log b = 5y/x
Question: a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers W was deleted?
(A)  a
(B)  b
(C)  c
(D)  d
(E)  e
Rationale: a+b+c+d+e => 1+2+3+4+5=15
20%*15= 3 =>C
Answer: (C)  c
Question: A started a business with Rs.21,000 and is joined afterwards by B with Rs.36,000. After how many months did B join if the profits at the end of the year are divided equally?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
Suppose B joined after x months
then,
21000*12=36000*(12-x)
=> 36x = 180
=> x = 5
Option B
Answer: (B) 5
Question: When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?
I. n is even
II. n is a multiple of 5
III. n is a factor of 20
(A) III only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: m*n=20
put values of m
m=1 n=20
m=2 n=10
m=4 n=5
I. not true
II. true
III. true
D. correct
Answer: (D) II and III only
Question: John makes $40 a week from his job. He earns a raise andnow makes $55 a week. What is the % increase?
(A) 15%
(B) 16.66%
(C) 17.8%
(D) 19%
(E) 37.5%
Rationale: Increase = (15/40)*100 = 37.5%.
E
Answer: (E) 37.5%
Question: The sum of number of boys and girls in a school is 100. If the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is?
(A) 50
(B) 40
(C) 60
(D) 100
(E) 70
Rationale: We have x+x% of 100 = 100
x + x/100 * 100 = 100
2 * x = 100
x = 50
Answer is A
Answer: (A) 50
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 1/6
(B) 5/8
(C) 3/8
(D) 5/6
(E) 7/8
Rationale: Explanation:
P(at least one graduate) = 1 - P(no graduates) =
1 - ⁶C₃/¹⁰C₃ = 1 - (6 * 5 * 4)/(10 * 9 * 8) = 5/6
ANSWER IS D
Answer: (D) 5/6
Question: Running at the same constant rate, 4 identical machines can produce a total of 16 bottles per minute. At this rate, how many bottles could 8 such machines produce in 3 minutes?
(A) 11
(B)  92
(C)  96
(D)  174
(E)  115
Rationale: Let's take the approach that uses the answer choices to eliminate wasted time.
16/4=4. 8 machines = 32 per minute. 3 minutes worth = 96 bottles.
Looking at the answers it is clear...we can only choose (C)
THE CORRECT ANSWER IS C.
Answer: (C)  96
Question: Which of the following must be true.?
1) The sum of N consecutive integers is always divisible by N
2) If N is even then the sum of N consecutive integers is divisible by N.
3) If N is odd then the sum of N consecutive integers is divisible by N.
4) The Product of K consecutive integers is divisible by K.
5) The product of K consecutive integers is divisible by K!
(A) 1,4,5
(B) 3,4,5
(C) 4 and 5
(D) 1,2,3,4
(E) only 4
Rationale: Sum=n/2[2a+(n-1)*1] sum is always divisible by n irrespective of n being even or odd.
Product=a(a+1)(a+2)...(a+k-1) = (a+k-1)!/(a-1)! Product of k consecutive integers contains k terms with at least one multiple of k
Answer: 1,2,3,4 = D
ANSWER:D
Answer: (D) 1,2,3,4
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
(A) 1
(B) 3
(C) 5
(D) 8
(E) 9
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
A
Answer: (A) 1
Question: Given a certain number (A), find A given that 4.5 is 15% of 20% of A?
(A) 120
(B) 130
(C) 150
(D) 100
(E) 110
Rationale: Using elimination method to pick the correct option it will be discovered that option C i.e 150 is the correct option because 20% of 150 is 30 and 15% of 30 is 4.5.
ANSWER:C
Answer: (C) 150
Question: A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
(A) 18 km/hr
(B) 17 km/hr
(C) 48 km/hr
(D) 28 km/hr
(E) 19 km/hr
Rationale: Speed on return trip
= 150% of 40
= 60 km/hr.
Average speed
= (2 * 40 * 60)/(40 + 60)
= 48 km/hr.
Answer: C
Answer: (C) 48 km/hr
Question: A meeting has to be conducted with 4 managers. Find the number of ways in which the managers be selected from among 7 managers, if 2 managers will not attend the meeting together?
(A) 40
(B) 45
(C) 35
(D) 30
(E) 25
Rationale: we can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together
so 5C4 + (5C3 * 2C1)
this is 5 + 20=25
Answer : E
Answer: (E) 25
Question: The sum of the numbers is 177. If the ratio between the first and the second be 5:3 and that between the second and third be 4:9, then find the second number?
(A) 12
(B) 20
(C) 45
(D) 60
(E) 52
Rationale: Given ratios
5 : 3
4 : 9
20:12:27
The second number = 177/(20+12+27) * 15 = 45
Answer is C
Answer: (C) 45
Question: What will be the vulgar fraction of 0.8
(A) 3/5
(B) 4/5
(C) 3/2
(D) 3/7
(E) 3/8
Rationale: Explanation:
0.8 = 80/100 = 4/5
Option B
Answer: (B) 4/5
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
(A) 2400
(B) 1871
(C) 1167
(D) 1890
(E) 1628
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400
Answer:A
Answer: (A) 2400
Question: This year, MBB Consulting fired 9% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
(A) 98.5%
(B) 100.1%
(C) 102.8%
(D) 104.5%
(E) 105.0%
Rationale: 100 employees getting 1000$ avg, so total salary for 100 ppl = 100000
9% reduction in employees lead to 91 employees and a salary increase of 10% of previous avg salary
Thus the new avg salary is = 10%(1000)+1000 = 1100
so total salary of 91 employees is 91*1100 = 100100
Now the new salary is more than previous salary by x%. x = (100100/100000)*100 = 100.1%
So the Answer is B
Answer: (B) 100.1%
Question: If the cost price of 50 articles is equal to the selling price of 25 articles, then the gain or loss percent is?
(A) 16
(B) 127
(C) 12
(D) 18
(E) 100
Rationale: Percentage of profit = 25/25 * 100 = 100%
Answer: E
Answer: (E) 100
Question: 96% of the population of a village is 23040. The total population of the village is ?
(A) 32256
(B) 24000
(C) 24936
(D) 25640
(E) None
Rationale: Answer
∵ 96% of P = 23040
∴ P = (23040 x 100) / 96 = 24000
Correct Option: B
Answer: (B) 24000
Question: If the positive integer x is a multiple of 1 and the positive integer y is a multiple of 7, then xy must be a multiple of which of the following?
I. 7
II. 2
III. 3
(A) II only
(B) I and II only
(C) I only
(D) II and III only
(E) I, II, and III
Rationale: x=1a
y=7b
xy=7ab
where a,b are integers
Hence , xy will always be divisible by 7 .
C is the answer.
Answer: (C) I only
Question: If the simple interest on a certain sum of money for 5 years is one–fifth of the sum, then the rate of interest per annum is
(A) 4%
(B) 7%
(C) 6%
(D) 4%
(E) 3%
Rationale: Explanation:
Let the Principal(P) be x
Then, Simple Interest(SI) = x/5
Time(T) = 5 years
Rate of interest per annum(R) = (100×SI)/PT
= (100 × (x/5)/(x × 5) = 20/5 = 4%
Answer: Option D
Answer: (D) 4%
Question: Ayesha's father was 30 years of age when she was born while her mother was 22 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 16
(B) 14
(C) 15
(D) 12
(E) 2
Rationale: Mother's age when Ayesha's brother was born = 22 years.
Father's age when Ayesha's brother was born = (30 + 4) years = 34 years.
Required difference = (34 - 22) years = 12 years.
Answer:D
Answer: (D) 12
Question: How much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction?
(A) 55
(B) 99
(C) 88
(D) 76
(E) 12
Rationale: The distance to be covered = Sum of their lengths = 250 + 300 = 550 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 550/10 = 55 sec.
Answer:A
Answer: (A) 55
Question: Beth received 2/5 of the votes cast in a certain election. What fraction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/6
(B) 2/7
(C) 3/10
(D) 7/20
(E) 1/2
Rationale: Let the total votes be 10. Beth received 4 votes, other votes 10-4=6. In order to have received 1/2 of the votes she needed 5 votes so 1 more, which is 1/6 of the other votes.
Answer: A.
Answer: (A) 1/6
Question: 60, 67, 63, 15, 61, 10, 15
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
(A) 25
(B) 36
(C) 53
(D) 60
(E) 62
Rationale: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 10, 15 ,15, 60, 61, 63, 67
Median is very easy to tell - its 60. Now we want a number lower than 55 and greater than mean. How many numbers are lower than 60
DE are already out.
Now, we have 25, 36 and 53 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 53. (Notice, if 25 is more than mean then 53 is also. If 36 is more than mean, 53 is also. )
Hence C it is!
Answer: (C) 53
Question: A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.
(A) 8 kmph
(B) 3 kmph
(C) 6 kmph
(D) 4 kmph
(E) None of these
Rationale: Let x and y be the upstream and downstream speed respectively.
Hence, 50/x + 72/y = 9 and 70/x + 90/y = 12
Solving for x and y we get x = 10 km/hr and y = 18 km/hr
We know that Speed of the stream = 1/2 * (downstream speed - upstream speed) = 1/2 (18 - 10) = 4 km/hr.
ANSWER:D
Answer: (D) 4 kmph
Question: What is the smallest positive integer x such that 120-x is the cube of a positive integer?
(A) 10
(B) 6
(C) 5
(D) 0
(E) 1
Rationale: Given 130-x is a perfect cube
so we will take 125 = 5*5*5
130-x = 125
x = 130-125 = 5
correct option is C
Answer: (C) 5
Question: If the perimeter of a rectangular garden is 600 m, its length when its breadth is 100 m is?
(A) 292
(B) 237
(C) 200
(D) 299
(E) 232
Rationale: 2(l + 100) = 600 => l = 200 m Answer: C
Answer: (C) 200
Question: 20% of the students in a class failed in an examination. Out of the students who failed, 75% were males. Male students who failed constitute 90% of the economically poor students in the class. What is the ratio of the number of economically poor students to the number of students in the class?
(A) 1:4
(B) 1:5
(C) 5:6
(D) 1:6
(E) None of these
Rationale: Explanation :
Let, the total number of students in the class be 't' and the total number of students in the class who are economically poor be 'p'.
So,Total number of students who failed = t/5.
Total number of male students who failed are:-
=>(3/4)×(t/5)=9p/10.
=>p/t=1/6.
Hence,Number of economically poor students/Number of Students=1/6=1:6.
Answer : D
Answer: (D) 1:6
Question: A 16% stock yielding 8% is quoted at?
(A) 165
(B) 170
(C) 175
(D) 180
(E) 200
Rationale: Assume that face value = Rs.100 as it is not given
To earn Rs.8, money invested = Rs.100
To earn Rs.16, money invested = 100×16/8 = Rs.175
ie, market value of the stock = Rs.200
Answer is E.
Answer: (E) 200
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 19,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
(A) 5,476,811 kilometers squared
(B) 9,500,148 kilometers squared
(C) 9,843,123 kilometers squared
(D) 1,878,965 kilometers squared
(E) 4,787,900 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
19,098,242 - 9,598,094 = 9,500,148 kilometers squared
correct answer B
Answer: (B) 9,500,148 kilometers squared
Question: a and b are two bus stations 400 km apart. if two separate buses depart from both stations and travel towards each other, at what time do they meet each other given that the first bus left at 8 am and travels at a speed of 70 km/hr while the second bus left at 9 am and travels at a speed of 40 km/hr.
(A) 12 p.m
(B) 2 p.m
(C) 1 p.m
(D) 10 p.m
(E) 2.20 p.m
Rationale: Suppose they meet x hours after 8 a.m.
Distance moved by first BUS in x hours + distance moved by 2nd BUS in x-1 hrs = 400
70x+40(x-1) = 400
70x+40x-40= 400
110x= 440
x = 4
So they meet 4 hr after 8 a.m. is at 12 p.m.
Answer is A
Answer: (A) 12 p.m
Question: Solution A is 20% barium and Solution B is 80% barium. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% barium solution?
(A) 6:4
(B) 6:14
(C) 4:4
(D) 4:6
(E) 3:7
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 20) = 1/1
So the volume of the two solutions will be equal. Answer has to be 4:4=C
Answer: (C) 4:4
Question: If a coin is tossed twice, what is the probability that the coin lands on heads on both tosses?
(A) 1/6
(B) 1/3
(C) 1/4
(D) 1/2
(E) 1
Rationale: P(2 heads) = 1/2*1/2=1/4
The answer is C.
Answer: (C) 1/4
Question: A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag?
(A) 30
(B) 35
(C) 40
(D) 42
(E) 80
Rationale: A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 30. Hence
3x = 30
Solve for x
x = 10
The total number of coins is given by
5x + 3x = 8x = 8 × 10 = 80
E
Answer: (E) 80
Question: Seven years ago the average age of a family of 2 members was 23 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
(A) 35years
(B) 32years
(C) 30years
(D) 25years
(E) 20years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 23
= (23+ 7) * 2 = 37 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 37 = 32 years
Answer: Option B
Answer: (B) 32years
Question: The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.14000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
(A) 20
(B) 21
(C) 22
(D) 23
(E) 28
Rationale: Solution
Let the toatl number of workers be x.
Then 8000x=(14000 x 7) + 6000 (x -7)
x= 28.
Answer E
Answer: (E) 28
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 11 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
(A)  18/79
(B)  1/6
(C)  1/25
(D)  1/50
(E)  17/900
Rationale: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/11 = 17
P = 17/900 = 1/50
Ans:E
Answer: (E)  17/900
Question: Average of 10 matches is 32, How many runs one should should score to increase his average by 4 runs.
(A) 70
(B) 76
(C) 78
(D) 80
(E) 88
Rationale: Explanation:
Average after 11 innings should be 36
So, Required score = (11 * 36) - (10 * 32)
= 396 - 320 = 76
Answer: Option B
Answer: (B) 76
Question: In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
(A) 1
(B) 40
(C) 20
(D) 26
(E) 30
Rationale: Explanation :
Assume that in x days, one cow will eat one bag of husk.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
⇒ 40 × 1 × 40 = 1 × 40 × x
⇒ x = 40 Answer : Option B
Answer: (B) 40