mathewhe/aqua_rat huggingface dataset:
Question: Sid obtained 76, 65, 82, 67 and 80 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) A)87
(B) B)99
(C) C)68
(D) D)82
(E) E)74
Rationale: Average = (76 + 65 + 82 + 67 + 80)/5
= 370/5
= 74.
Answer:E
Answer: (E) E)74
Question: How many integer values are there for x such that 1 < 3x + 5 < 17?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Six
Rationale: The inequality given is 1 < 3x+5 < 17
it can further reduced to -4 < 3x < 12
finally -4/3 < x < 4
So can only take 5 integer values i.e. -1,0,1,2,3
Correct answer - D
Answer: (D) Five
Question: Nine persons went to a hotel for taking their meals. Eight of them spent Rs 12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them?
(A) 117
(B) 180
(C) 150
(D) 200
(E) 250
Rationale: Exp. Let the total expenditure be x, Then the average = x/9,
8*12+ [x/9+8] =x or [ x-x/9] =104.
8x/9 = 104, x =104*9/8 =117.
Answer: A
Answer: (A) 117
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 110
(B) 120
(C) 130
(D) 140
(E) 150
Rationale: Solution:
Let xx be the number he chose, then
2⋅x−138=102
2x=240
x=120
Answer B
Answer: (B) 120
Question: How many pounds of salt at 50 cents/lb must be mixed with 40 lbs of salt that costs 38 cents/lb so that a merchant will get 20% profit by selling the mixture at 48 cents/lb?
(A) 2
(B) 5
(C) 8
(D) 15
(E) 25
Rationale: Selling price is 48 cents/lb
For a 20% profit, cost price should be 40 cents/lb (CP*6/5 = 48)
Basically, you need to mix 38 cents/lb (Salt 1) with 50 cents/lb (Salt 2) to get a mixture costing 40 cents/lb (Salt Avg)
weight of Salt1/weight of Salt2 = (Salt2 - SaltAvg)/(SaltAvg - Salt1) = (50 - 40)/(40 - 38) = 5/1
We know that weight of salt 1 is 40 lbs. Weight of salt 2 must be 8 lbs.
Answer (C)
Answer: (C) 8
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 752
(B) 278
(C) 289
(D) 750
(E) 278
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2
= 750
Answer:D
Answer: (D) 750
Question: The smallest value of n, for which 2n+1 is not a prime number, is
(A) 3
(B) 4
(C) 5
(D) None
(E) 6
Rationale: Solution
(2×1 + 1)	= 3.
(2×2 + 1)	= 5.
(2×3 + 1)	= 7.
(2×4 + 1)	= 9.
which is not prime ,	n=4.
Answer B
Answer: (B) 4
Question: How many pages the book have, if total 303 digits are used to form the page numbers?
(A) 135 pages
(B) 136 pages
(C) 137 pages
(D) 138 pages
(E) 139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 38 pages ... 114 digits
----------------------
Total ...137 pages ...303 digits
ANSWER:C
Answer: (C) 137 pages
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 126° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 70%
Rationale: ANSWER: D 126° divided by 360° equals 0.35, therefore the sector is equal to 35% of the total
Answer: (D) 35%
Question: in a school the ratio of boys and girls are in the ration 5:6 .25% of boys will get scholar ship and 20% of girls will get scholar ship what % of students wont get scholarship?
(A) 60%
(B) 78%
(C) 88%
(D) 98%
(E) 99%
Rationale: Boys : Girls => 5x : 6x
Total no. of students including boys nd girls = 5x+6x = 11x
25% of boys => 5x*25/100 = 5x/4
20% of girls => 6x*20/100 =6x/5
No. of students who are getting scholarship => 5x/4 + 6x/5 = 49x/20
No. of students who are not getting scholarship = 11x - 49x/20 = 171x/20
% of students not getting scolorship => 171x/20/11x * 100
=> 100*171x/220x
= 77.7%
ANSWER:B
Answer: (B) 78%
Question: How many positive integer solutions does the equation 2x+1y = 100 have?
(A) 44
(B) 33
(C) 50
(D) 35
(E) 14
Rationale: formula: (constant)/(lcm of two nos)
=100/(2*1)=50
ANSWER:C
Answer: (C) 50
Question: A travel agent offers a vacation plan which costs x dollars for the first day, and x/2 for each additional day.
How much does a vacation of y days cost, where y > 1.
(A) yx/2
(B) (yx+x)/2
(C) (yx+x)/3
(D) (yx+x)/5
(E) (yx+x)/6
Rationale: Cost = x + (y-1)*x/2 = (2x + (y - 1)*x)/2 = (yx+x)/2
Answer is B
Answer: (B) (yx+x)/2
Question: If n is an integer, then which of the following statements is/are FALSE?
I)n^3 – n is always even.
II)8n^3 +12n^2 +6n +1 is always even.
III)√ (4n^2 – 4n +1) is always odd.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: 1) n^3 – n
n^2(n-1)
two cases
if n=odd then n-1 is even thus n^2(n-1) is even
if n=even then n^2 is even thus n^2(n-1) is even------>true for all cases
2) 8n^3 +12n^2 +6n +1
8n^3 +12n^2 +6n=Even
but Even +1 =odd------------>Always False
3) for this i tried picking number upto 15 and find all cases True------>True
However will be looking for any algebraic solution
Ans B
Answer: (B) II only
Question: k, l, m together started a business. k invested Rs.6000 for 5 months l invested Rs.3600 for 6 months and m Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of l ?
(A) 2162
(B) 2112
(C) 2160
(D) 2212
(E) 2100
Rationale: => 60x5 : 36x6 : 75x3
=> 100 : 72 : 75
=> 72/247 x 7410 = Rs.2160
Answer: C
Answer: (C) 2160
Question: A car drives 60 miles on local roads at 20 mph, and 120 miles on the highway at 60 mph, what is the average speed of the entire trip?
(A) 36 mph
(B) 40 mph
(C) 44 mph
(D) 52 mph
(E) 58 mph
Rationale: So The Answer is Plainly A....
we have a general relation for speed , time and distance : v (velocity) * t ( time)= d (distance)
for first part we have d=60 miles , and v= 20 mph so we can obtain time : 20*t = 60 Or t= 60/20 = 3 hours the needed time to cover 60 miles
in the same way we should divide 120 to 60 to find the needed time to cover 120 miles ,so t= 2 hours
so the total time for covering total distance would be 3+2 = 5 hours and total distance is 60+120= 180 miles
Final stage : average speed is total distance divide to total time : 180/5 = 36 miles per hour....
Answer: (A) 36 mph
Question: A barrel holds 4 quarts of tar and 4 quarts of turpentine. How many quarts of turpentine must be added to the container to create a mixture that is 3 parts tar to 5 parts turpentine by volume?
(A) 4/3
(B) 5/3
(C) 7/3
(D) 8/3
(E) 10/3
Rationale: An alternate to the alligation method is the more direct/algebraic method:
Let x be the amount of turpentine to be added.
New total amount of turpentine = 4+x
Total amount of tar= 4
New total = 4+4+x=8+x
Final ratio required (for turpentine) = 5/(5+3)=5/8
Thus, (4+x)/(8+x) = 5/8 --> solving for x you get x = 8/3.
D is thus the correct answer.
Answer: (D) 8/3
Question: Mice can multiply very fast. Adult mice can give birth once every month, and baby mice grow into adult mice in just two months after they are born. If you would buy a baby mouse just after it was born, how many mice would you have in 10 months?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: One. You cannot have more mice if you start with one!
Answer A
Answer: (A) 1
Question: Find the number of ways in which 5 identical balls can be distributed among 10 identical boxes, if not more than one ball can go into a box?
(A) 21
(B) 252
(C) 78
(D) 145
(E) 312
Rationale: Required number of ways = 10C5 = 10!/5!5! = 252
Answer is B
Answer: (B) 252
Question: Sum of 3 consecutive even no.'s is 38 more than the 1st no. of the series. Find the middle no.?
(A) 8
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+38
3x + 6 = x + 38
2x = 32
\inline \therefore x = 16
\inline \therefore Middle number = x + 2 = 16+2 = 18
E
Answer: (E) 18
Question: Joshua and Jose work at an auto repair center with 6 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) 1/15
(B) 1/12
(C) 1/28
(D) 1/6
(E) 1/3
Rationale: Two Methods
1) Probability of chosing Josh first = 1/8
Probability of chosing Jose second = 1/7
total = 1/56
Probability of chosing Jose first = 1/8
Probability of chosing Josh second = 1/7
Total = 1/56
Final = 1/56+ 1/56 = 1/28
C
Answer: (C) 1/28
Question: A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 75,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
(A) a) 250
(B) b) 750
(C) c) 1,000
(D) d) 1,250
(E) e) 1,500
Rationale: Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 75,000 = 18,750
So required ratio = 18,750/75 = 250
Answer A
Answer: (A) a) 250
Question: Find the compound interest accrued on an amount of Rs.14,800 at 13.5% p.a at the end of two years. (Round off your answer to nearest integer)
(A) 2277
(B) 2888
(C) 2988
(D) 4266
(E) 1781
Rationale: CI = 14800{ [ 1 + 13.5/100]2 - 1 }
= 14800 { [1 + 27/200]2 - 1
= 14800 { 2 + 27/200}{27/200}
= (74)[2 + 27/200](27) =
1998[2 + 27/200] = 3996 + 269.73 = Rs. 4266
Answer: D
Answer: (D) 4266
Question: For any four digit number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d). What is the value of (n – m) if m and n are four digit numbers for which *m* = (3^r)(5^s)(7^t)(11^u) and *n* = (25)(*m*)?
(A) 2000
(B) 200
(C) 25
(D) 20
(E) 2
Rationale: bcd is a four digit number where a, b, c and d are the 4 digits.
*abcd*= (3^a)(5^b)(7^c)(11^d). The '**' act as an operator.
Given: *m* = (3^r)(5^s)(7^t)(11^u)
So m = rstu where r, s, t, and u are the 4 digits of m.
Say, r = 1 and s = 0, t = 0 and u = 0
m = 1000
Then *m* = 3
Now,
*n* = (25)(*m*) = 25(3) = (3^1)(5^2)(7^0)(11^0)
n = 1200
n - m = 1200 - 1000 = 200
ANSWER:B
Answer: (B) 200
Question: Ajay can ride 50km in 1 hour. In how many hours he can ride 1500km?
(A) 30hrs
(B) 15hrs
(C) 20hrs
(D) 25hrs
(E) 18hrs
Rationale: 1 hour he ride 50km
he ride 1500km in = 1500/50 * 1 = 30hours
Answer is A
Answer: (A) 30hrs
Question: A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%.
(A) Rs 25300
(B) Rs 22300
(C) Rs 24300
(D) Rs 21300
(E) None of these
Rationale: Explanation:
This type of question can be easily and quickly solved as following:
Let at Rs x it can earn 15% pr0fit
85:18700 = 115:x [as, loss = 100 -15, Profit = 100 +15]
x = (18700*115)/85
= Rs.25300
Answer: A
Answer: (A) Rs 25300
Question: For all integers a and b, a%b = (a + b)(a - b). If 9%x = 17, then which of the following could be a value of x?
(A) -8
(B) -7
(C) 2
(D) 3
(E) 6
Rationale: 9%x = (9+x)(9-x)
81-x^2 = 17
x^2 = 64
x=-8,8
Ans: A
Answer: (A) -8
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 920
(B) 289
(C) 999
(D) 270
(E) 267
Rationale: a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer:C
Answer: (C) 999
Question: An aeroplane covers a certain distance at a speed of 300 kmph in 6 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:
(A) 1008 kmph
(B) 760 kmph
(C) 1080 kmph
(D) 1070 kmph
(E) none
Rationale: Explanation: Distance = (300 x 6) = 1800 km.
Speed = Distance/Time
Speed = 1800/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]
Required speed = 1800 x 3/5 km/hr = 1080 km/hr.
Answer: Option C
Answer: (C) 1080 kmph
Question: If each edge of cube increased by 30%, the percentage increase in
(A) 69
(B) 72
(C) 64
(D) 61
(E) 75
Rationale: 100 × (130)/100 × (130)/100 = 169 => 69%
Answer is A.
Answer: (A) 69
Question: In how many different number of ways a combination of 3 men and 2 women can be selected from 6 men and 5 women?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20
B)
Answer: (B) 20
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 2882
(B) 2277
(C) 2697
(D) 6725
(E) 2681
Rationale: CP = SP * (100/(100 + profit%))
= 8339(100/124)
= Rs. 6725.
Answer:D
Answer: (D) 6725
Question: The average salary per month of 55 employees in a company is Rs 8500. If the managers salary is added, the average salary increases to Rs 8800, what is the salary of the manager ?
(A) 10000
(B) 12000
(C) 23000
(D) 25300
(E) 45000
Rationale: Explanation :
Salary of the manager = (56*8800 - 55*8500)
= 25300
Answer : D
Answer: (D) 25300
Question: The contents of a certain box consist of 24 plums and 30 kiwis. How many kiwis must be added to the box so that exactly 30% of the pieces of fruit in the box will be plums?
(A)  24
(B)  26
(C)  30
(D)  46
(E)  50
Rationale: plums = (plums + kiwi + x)*0.3
24 = (30 + 24 + x)*0.3
x = 26.
Answer: B.
Answer: (B)  26
Question: A sum of money at simple interest amounts to Rs. 815 in 4 years and to Rs. 854 in 5 years. The sum is:
(A) 659
(B) 698
(C) 780
(D) 910
(E) None
Rationale: Sol.
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 4 years = Rs. (39 * 4) = Rs. 156.
âˆ´ Principal = Rs. (815 - 156) = Rs. 659
Answer A
Answer: (A) 659
Question: 9 engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?
(A) 20 metric tonnes
(B) 22 metric tonnes
(C) 24 metric tonnes
(D) 26 metric tonnes
(E) 28 metric tonnes
Rationale: Explanation:
Let required amount of coal be x metric tones
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 13 unit which is it’s the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 14 unit which is it’s the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
Hence we can write as
(engines) 9:8
(consumption rate )13:14
(hours) 8:13::24}::x
⇒9×1/3×8×x=8×1/4×13×24
⇒3×8×x=8×6×13
⇒3×x=6×13
⇒x=2×13=26
Answer: Option D
Answer: (D) 26 metric tonnes
Question: Operation#is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half. If operation#is repeated 10 times, what is the probability that it will yield at least two integers?
(A) 0%
(B) 10%
(C) 20%
(D) 30%
(E) 40%
Rationale: Any multiple of 8 is even.
Any two-digit prime number is odd.
(even+odd)/2 is not an integer. Thus # does not yield an integer at all.
Therefore P=0.
Answer: A.
Answer: (A) 0%
Question: 16 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
(A) 23 days
(B) 26 days
(C) 22 days
(D) 29 days
(E) 20 days
Rationale: E
20 days
16 * 25 = 20 * x => x = 20 days
Answer: (E) 20 days
Question: Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?
(A) 2.5 hours
(B) 2 hours
(C) 3.5 hours
(D) 3 hours
(E) None of these
Rationale: Explanation:
Part filled by A in 1 hour = 1/5
Part filled by B in 1 hour = 1/10
Part filled by C in 1 hour = 1/30
Part filled by (A+B+C) in 1 hour =1/5 +1/10 +1/30
=1/3
So all pipes will fill the tank in 3 hours.
Answer is D
Answer: (D) 3 hours
Question: A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly M new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
(A)  5^1/12
(B)  3^11 * 5^11
(C)  3^12 * 5^12
(D)  3^11 * 5^12
(E)  60^12
Rationale: At the end of the first week, there are 5 new members;
At the end of the second week, there are 5M new members (since each 5 new members from the previous week brings M new members);
At the end of the third week, there are 5M^2 new members (since each 5M new members from the previous week brings M new members);
...
At the end of the twelfth week, there are 5M^11 new members (since each 5M^10 new members from the previous week brings M new members).
We are given that 5M^11=y. Out of the answers only D yields integer value for M: 5M^11=3^11 * 5^12 --> M=3*5=15.
Answer: D.
Answer: (D)  3^11 * 5^12
Question: The average age of a family of 6 members is 24 years.If the age of the youngest member is 8 years,what was the average age of the family at the birth of the youngest member?
(A) 15
(B) 16
(C) 21
(D) 12
(E) 19
Rationale: Present age of total members = 6 X 24 = 144
8 yrs back their ages were = 6 x 8 = 48
Ages at the birth of youngest member = 144 - 48 = 96
Therefore, avg age at the birth of youngest member = 96/6 = 16.
ANSWER:B
Answer: (B) 16
Question: If log 0.318=0.3364 and log 0.317=0.33320 then log 0.319 =?
(A) 0.33365
(B) 0.3368
(C) 0.3396
(D) 0.3369
(E) 0.3469
Rationale: log 0.318 / log 0.317 = log (0.318 - 0.317) = log 0.001 = 0.3364 / 0.33320 = 1.0096
now,
log 0.318 * log 0.001 = log (0.318 + 0.001) = log 0.319 = 0.3364 * 1.0096 = 0.3396
so option c
ANSWER:C
Answer: (C) 0.3396
Question: in a certain flower shop, which stocks four types of flowers, there are 1/4 as many violets as carnations, and 1/4 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?
(A) 31
(B) 30
(C) 29
(D) 28
(E) 27.27
Rationale: Given :-
Violets - C/4
Carnations - C
Tulip - C/16
Rose - C/16
Total flowers in terms of C = C/4+C+C/16+C/16 = 22C/6
Percentage of Carnations = C/22C/6 *100 =27.27
Answer E
Answer: (E) 27.27
Question: The length of a rectangular floor is more than its breadth by 100%. If Rs. 600 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
(A) 15.0m.
(B) 14.4m.
(C) 12.0m.
(D) 16.2m.
(E) 16.5m.
Rationale: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 100% of b = l + 1b = 2b
Area of the floor = 600/3 = 200 sq m
l b = 200i.e., l * l/2 = 108
l2 = 216 => l = 14.4m.
ANSWER:B
Answer: (B) 14.4m.
Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
(A) 4.14 kmph
(B) 5.10 kmph
(C) 4.50 kmph
(D) 4.4 kmph
(E) 5.00 kmph
Rationale: A speed = (5*5/18) = 25/18
time taken by A to cover 100 m = (100*18/25) = 72
time taken by B to cover 92 m = (72+8) = 80 sec
B's speed = (92/80 * 18/5) = 4.14
ANSWER A
Answer: (A) 4.14 kmph
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 588 sq meters, then what is the width (in meters) of the rectangular plot?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Area = L*W = 3W^2 = 588
W^2 = 196
W = 14
The answer is A.
Answer: (A) 14
Question: When Alice entered the Forest of Forgetfulness, she forgot the day of
the week. She met the Lion and the Unicorn resting under a tree. The
Lion lies on Mondays, Tuesdays and Wednesdays and tells the truth
on the other days of the week. The Unicorn, on the other hand, lies
on Thursdays, Fridays, and Saturdays, but tells the truth on the other
days of the week. They made the following statements:
Lion: \Yesterday was one of my lying days."
Unicorn: \Yesterday was one of my lying days."
From these two statements, Alice was able to deduce the day of the
week. What day was it?
(A) Monday
(B) Wednesday
(C) Thursday
(D) Friday
(E) Sunday
Rationale: If the Lion is telling the truth, the day of the week must be Thursday. If he
is lying, then the day of the week must be Monday. So the day of the week must be
either Thursday or Monday. If the Unicorn is telling the truth, the day of the week must
be Sunday. If he is lying, then the day of the week must be Thursday. The day of the
week cannot be Sunday (since we have already said that it must be Thursday or Monday).
Therefore, it must be Thursday
correct answer C
Answer: (C) Thursday
Question: A furniture manufacturer has two machines, but only one can be used at a time. Machine Q is utilized during the first shift and Machine B during the second shift, while both work half of the third shift. If Machine Q can do the job in 12 days working two shifts and Machine B can do the job in 15 days working two shifts, how many days will it take to do the job with the current work schedule?
(A) 14
(B) 13
(C) 11
(D) 9
(E) 7
Rationale: machine Q finish the job in 2*12 shifts = 24 shifts
machine B finish the job in 2*15 shifts = 30 shifts
Lets assume total work require 120 shifts
Therefore,
rate of Q = 5 shifts/day
rate of B = 4 shifts/day
rate of (Q+B) = 9 shifts/day
According to current schedule work complete in a day = 5+4+(9/2) =13.5 shifts/day
Therefore, Time required to finish 120 shifts = (120/13.5) = 8.88.. days ~ 9 days=D
Answer: (D) 9
Question: A circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it. As a result the plate lost 1/6th its original weight. The radius of the circular plate is
(A) 16sqrt2
(B) 8sqrt2
(C) 32sqrt2
(D) sqrt72
(E) sqrt82
Rationale: Area of 12 holes=12*Pi*1^2=12*Pi
As 12*Pi=(1/6)th weight,so total Area of Plate=12*Pi/(1/6)=72*Pi
If r=radius of the plate,then its Area=Pi*r^2=72*Pi, So r=Sqrt72
ANSWER:D
Answer: (D) sqrt72
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 2328
(B) 2798
(C) 5460
(D) 2799
(E) 2771
Rationale: 5000 * 104/100 * 105/100 => 5460.Answer: C
Answer: (C) 5460
Question: By selling 100 pens, a trader gains the cost of 30 pens. Find his gain percentage?
(A) 30%
(B) 33%
(C) 31%
(D) 32%
(E) 34%
Rationale: Let the CP of each pen be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 30 pens
= Rs. 30
Profit% = 30/100* 100
= 30%
Answer: A
Answer: (A) 30%
Question: How many integers are between 7 and 57/4, inclusive?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 10
Rationale: 57/4 = 14.xx
We are not concerned about the exact value of 57/4 as we just need the integers.
Since the values are small, we can write down the integers.
The different integers between 7 and 57/4 would be 7, 8, 9, 10, 11, 12,13,14
Total number of integers = 8
Option D
Answer: (D) 8
Question: If the sum of 6 consecutive integers is y, which of the following must be true?
I. y is an even number
II. y is an odd number
III. y is a multiple of 6
(A)  I only
(B)  II only
(C)  III and I only
(D)  I onlyII
(E)  II and III
Rationale: I. If you start off with an even number, the sum (y) is even, and if you start off with an odd number the sum (y) is odd. Therefore this is not always true.
II. Same as above. This need not be always true.
III. Say, the first number is p. Then the sum of the five numbers = p + (p+1) + (p+2)...... + (p+4)
= 6p + 12 = 6 (p+2) => divisible by 6. There this must be true in all cases.
Therefore D is the answer.
Answer: (D)  I onlyII
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 126 km/hr, what is the length of the platform?
(A) 338
(B) 240
(C) 560
(D) 267
(E) 191
Rationale: Speed = (126 * 5/18) m/sec = 35 m/sec. Length of the train = (35 x 20)m = 700 m. Let the length of the platform be x meters. Then, (x + 700)/36 = 35 ==> x + 700 = 1260 ==>
x = 560 m.
Answer: C
Answer: (C) 560