mathewhe/aqua_rat huggingface dataset:
Question: In May, the groundskeeper at Spring Lake Golf Club built a circular green with an area of 70π square feet. In August, the groundskeeper doubled the distance from the center of the green to the edge of the green. What is the total area of the renovated green?
(A) 1000π
(B) 400π
(C) 280π
(D) 200π
(E) 20π
Rationale: Area = πR^2, so doubling the radius results in an area that is 4 times the original area.
4(70π) = 280π
The answer is C.
Answer: (C) 280π
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
(A) 3999
(B) 3000
(C) 3882
(D) 2661
(E) 1234
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410
= 3000
Answer: B
Answer: (B) 3000
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 12% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 10%
(C) 15%
(D) 21%
(E) 31%
Rationale: 60-(x+12+z) + 50-(x+12+y) + 35-(z+12+y) + x + y + z +12 = 100
where x = people who bought MilkChicken
y = people who bought chickenApples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.
Hence solving the above equation we get,
121 -(x+y+z) = 100
Thus, x+y+z= 21
Answer: D
Answer: (D) 21%
Question: Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
(A) 930
(B) 870
(C) 450
(D) 330
(E) 220
Rationale: A
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer: (A) 930
Question: How many seconds will a 450 m 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) 20
(B) 27
(C) 42
(D) 32
(E) 60
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 450 * 3/50 = 27 sec.
Answer: Option B
Answer: (B) 27
Question: A boy has three trousers and 8 shirts. In how many different ways can he select a trouser and a shirt?
(A) 24 ways
(B) 27 ways
(C) 28 ways
(D) 18 ways
(E) 19 ways
Rationale: The boy can select one trouser in three ways.
The boy can select one shirt in 8 ways.
The number of ways in which he can select one trouser and one shirt is 3 * 8 = 24 ways.
Answer:A
Answer: (A) 24 ways
Question: How many number from 11 to 50 are there which are exactly divisible by 7 but not by 3?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 14,28,35,49
ANSWER:B
Answer: (B) 4
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 38 square meters. What is the area that is covered with three layers of wallpaper?
(A) 5 Square Meters
(B) 36 Square Meters
(C) 42 Square Meters
(D) 83.3 Square Meters
(E) 41 Square Meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 38 = 82 sq m of the wallpaper overlaps in three layers. 82 sq m makes two extra layers hence the area over which it makes two extra layers is 41 sq m.
Answer (E).
Answer: (E) 41 Square Meters
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 7 hrs 30 min
(B) 8 hrs
(C) 8 hrs 15 min
(D) 8 hrs 25 min
(E) 9 hrs
Rationale: Explanation:
Number of pages typed by Ronald in 1 hour = 32/6 = 16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3
Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min
ANSWER IS C
Answer: (C) 8 hrs 15 min
Question: 10^(655) Ã· 10^(652) = ?
(A) 1
(B) 100
(C) 10000
(D) 100000
(E) 1000
Rationale: 10^(655) Ã· 10^(652) = 10^ (655-652) = 10^3
= 1000
Answer : E
Answer: (E) 1000
Question: If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle?
I.	28
II.	36
III.	42
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
Rationale: x+y=30 & y+z=20 so x+2y+z=50
x+y+z=50-y
If perimeter is 28 then y=50-28=22, and y+z=20 z cannot be negative. I is out.
If perimeter is 36 then y=50-36 = 14. z=6, x=16. no problem here.
If perimeter is 42 then y=50-42 =8. x=22, z=12. x cannot be greater than sum of y & z. III is out.
B is answer.
Answer: (B) II only
Question: n is an integer chosen at random from the set
{5, 7, 9, 11 }
p is chosen at random from the set
{2, 6, 10, 14, 18}
What is the probability that n + p = 27 ?
(A) 0.1
(B) 0.2
(C) 0.25
(D) 0.3
(E) 0.05
Rationale: Set N: there is 4 ways to chose a number
Set P: there is 5 ways to chose a number
so total outcome is 4*5 = 20 which is represent 20 pairs of number
now we have 1 pairs can give us 27 which are (9,18)
1/20 = 0.05
Answer E
Answer: (E) 0.05
Question: A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes jerry can make using this recipe?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.
Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.
Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.
answer is A
Answer: (A) 5
Question: If x/4 years ago Roger was 21 years old and x/4 years from now he will be 4x years old, how old will he be 5x years from now?
(A) 32
(B) 35
(C) 30
(D) 40
(E) 70
Rationale: Assume the current age = a
a - x/4 = 28 (i)
a + x/4 = 4x
Or a = 15x/4 (ii)
Putting the value of a from (ii) in (i)
15x/4 - x/4 = 28
Or 14x/4 = 28 Therefore x = 8 and a = 30
5x years from now, age will be 30 + 5*8 = 70
Option E
Answer: (E) 70
Question: The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.8 kg. The weight of the new student is
(A) 22 kg
(B) 21.6 kg
(C) 22.4 kg
(D) 21 kg
(E) 23 kg
Rationale: The total weight of 29 students = 29* 28
The total weight of 30 students = 30* 27.8
Weight of the new student = ( 30*27.8 – 29*28)
= 834 - 812 = 22
ANSWER:A
Answer: (A) 22 kg
Question: What is the lowest positive integer that is divisible by 4 through 6, inclusive?
(A) 120
(B) 48
(C) 82
(D) 76
(E) 160
Rationale: The integer should be divisible by: 4, 5, and 6. The least common multiple of these integers is LCM=4*5*6=7920
Answer: A
Answer: (A) 120
Question: The difference between C.I. and S.I. on an amount of Rs. 15,000 for 2 years is Rs. 150. What is the rate of interest per annum?
(A) 8
(B) 2
(C) 10
(D) 4
(E) 6
Rationale: Explanation:
[15000 * (1 + R/100)2 - 15000] - (15000 * R * 2)/100 = 150
15000[(1 + R/100)2 - 1 - 2R/100] = 150
15000[(100 + R)2 - 10000 - 200R]/10000 = 150
R2 = (159 * 2)/3 = 100 => R = 10
Rate = 10%
Answer: Option C
Answer: (C) 10
Question: If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 2300
(B) 600
(C) 250
(D) 300
(E) none of these
Rationale: 1st line - 0 points
2nd line - new 1 point
3td line - new 2 points + old 1 point
4th line - new 3 points + old 2+1 points
5th line - new 4 points + old 3+2+1 points
n-th line - (n-1) points + (n-2) .... 3+2+1
therefore, S=1+2+3...(n-1)
S=(n-1)n/2=24*25/2=300
ANS;D
Answer: (D) 300
Question: john bakes 6 cakes for 6 friends. 3 of the friend arrive early and eat 3 cakes each. How many cakes are left over if the other friends all have the same number of cakes?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: john made 6*6 cakes = 36 cakes. 3 friends eat 3 cakes, leaving 27 remaining for 3 friends.
2+7=9, divisible by 3.
27 is divisible by 3. The 3 friends ate a cumulative number of cakes that must be divisible by 3, because the number is the same.
27-27=0
A is the correct answer
Answer: (A) 0
Question: Calculate 469200 x 9999 = ?
(A) 4586970843
(B) 4686970743
(C) 4691100843
(D) 4586870843
(E) 4691530800
Rationale: Answer
469200 x 9999 = 469200 x (10000-1)
= 4692000000 - 469200
= 4691100843.
Option: E
Answer: (E) 4691530800
Question: Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
(A) 20%
(B) 30%
(C) 40%
(D) 50%
(E) 60%
Rationale: 4C1/(6C3/2)
6C3 = 6!/3!3! = 20 sub committees
Michael will be included in 1/2 or 10 of these
If Michael and Anthony are in a 3 person committee together there is only one spot left and 4 people left to fill it.
4C1 = 4!/3! = 4
4/10 = 40%
Ans:B
Answer: (B) 30%
Question: The length of the bridge, which a train 170 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 876 m
(B) 157 m
(C) 205 m
(D) 156 m
(E) 167 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (170 + x)/30 = 25/2
=> 2(170 + x) = 750 => x
= 205 m.
Answer: C
Answer: (C) 205 m
Question: A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
(A) 69.5 km/hr
(B) 70 km/hr
(C) 79 km/hr
(D) 79.2 km/hr
(E) 89.2 km/hr
Rationale: Let the length of the train is x
x/8=x+264/20
on solving this we get x=176 m
Speed of the train=176/8=22m/sec
22*18/5=396/5=79.2 Kmph
ANSWER:D
Answer: (D) 79.2 km/hr
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:7
(C) 2:1
(D) 1:7
(E) 2:3
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer:A
Answer: (A) 2:5
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 7), (x, 7)?
(A) 64
(B) 121
(C) 169
(D) 225
(E) 441
Rationale: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 13.
The area is 13*13 = 169.
The answer is C.
Answer: (C) 169
Question: If a is 50% greater than b, then a is what % less than b?
(A) 33.33%
(B) 50%
(C) 66.78%
(D) 70.6%
(E) 10%
Rationale: if b=150 a=100
150-100=50
75 is 50% of b.
50 is little less than 75 so answer is 33.33%
Answer is A
Answer: (A) 33.33%
Question: A batsman in his 12th innings makes a score of 55 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 42
(B) 43
(C) 44
(D) 45
(E) 46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 1) + 55
∴ x = 44
Answer C
Answer: (C) 44
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 266
(C) 287
(D) 1661
(E) 211
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
Answer: (A) 480
Question: The smallest number which when diminished by 4, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1012
(C) 1022
(D) 1032
(E) 1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+4
= 1008 + 4
= 1012
Answer: B
Answer: (B) 1012
Question: A stockiest wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit?
i.	Sell sugar at 10% profit.
ii.	Use 900 g of weight instead of 1 kg.
iii.	Mix 10% impurities in sugar and selling sugar at cost price.
iv.	Increase the price by 5% and reduced weights by 5%.
(A) i or ii
(B) ii
(C) ii, ii and iv
(D) Profits are same
(E) None of these
Rationale: Solution: Let the CP of 1 kg of sugar be Rs. 100.
Then, CP of 900g sugar = (100*900)/1000 = Rs. 90
Hence, profit % = [(100-90)/90]*100 = 11.11%.
If he add 10% impurity then his CP for 1 kg = (100*1000)/1100 = Rs. 90.9;
And % profit = [(100-90.9)/90.9]*100 = 10.01%
If he reduces weight by 5 % Then, cost price of 950 g = (100*950)/1000 = Rs 95 and SP = 105;
% profit = [(105-95)/95]*100 = 10.25 %.
Answer: Option B
Answer: (B) ii
Question: IF IN A AP SERIES 18TH TERM IS 29 & 29TH TERM IS 18. THEN FIND THE 49TH TERM??
(A) 0
(B) -1
(C) -2
(D) 1
(E) 2
Rationale: 18th term = a + 17d..........(i)
29th term = a + 28d..........(ii)
Solving equation i and ii, we got
d = -1
put d = -1 in any of the above equations and we will get, a = 46
Now, we know 49th term can be written as, a + 48d
now putting the value of a and d in the above equation,
a + 48d = 46 + 48(-1)
= 46 - 48
= -2
ANSWER:C
Answer: (C) -2
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 11th and the 20th terms?
(A) 324
(B) 335
(C) 346
(D) 357
(E) 368
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 11th term is 11 × 11 – 3 = 118
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 335.
The correct answer is choice (B).
Answer: (B) 335
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
(A) 11
(B) 10
(C) 18
(D) 16
(E) 12
Rationale: 7*5: 5*x = 7:10
x = 10
Answer:B
Answer: (B) 10
Question: If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
spiders 1:7
Webs 7:1
1 x 7 x x = 7 x 1 x 7
=> x= 7
Answer is 7
Answer: (A) 7
Question: ratio of girl and boys in class is 5:6.if 20 girl leave the class and ratio become 2:3.calculate the no. of boys?
(A) 100
(B) 120
(C) 80
(D) 90
(E) none of the above
Rationale: girl 5x and boys 6x
5x-20/6x=2/3,15x-60=12x,3x=60,x=20
boys=6x=120
answer B
Answer: (B) 120
Question: 1704 x 1704 = ?
(A) A)3623216
(B) B)2903616
(C) C)3624316
(D) D)3625116
(E) E)3625216
Rationale: 1704 x 1704 = (1704)2
= (1700 + 4)2
= (1700)2 + (4)2 + (2 x 1700 x 4)
= 2890000 + 16 + 13600.
= 2903616.
B)
Answer: (B) B)2903616
Question: Consider the set N = {2, 3, 4, ..., 2n + 1}, where n is a positive integer larger than 10005. If O is the average of the odd integers in N and E is the average of the even integers in N then what is the value of O –E?
(A) 2
(B) 1
(C) 8
(D) 9
(E) 0
Rationale: No need to solve this question. Simply take n = 5. So N = {2, 3, 4, 5, ......11}
Now average of add integers = (3 + 5 + ........11)/5 = 7.
Average of Even integers = (2 + 4 + .....10) / 5 = 6
O - E = 1
Answer:C
Answer: (C) 8
Question: A boat can move upstream at 28 kmph and downstream at 50 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 54
(E) 11
Rationale: US = 28
DS = 50
M = (50 - 28)/2 = 11.Answer:E
Answer: (E) 11
Question: A dealer buys dry fruits at the rate of ` 100, ` 80 and ` 60 per kg. He bought them in the ratio 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain or no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity?
(A) 30%
(B) 40%
(C) 20%
(D) 50%
(E) None of these
Rationale: Total quantity rate =
(12 * 100 + 15 * 80 + 20 * 60) = 3600
For first 2 qtys, (12 * 100) + (15 * 80) = 2400
But he gets 20% profit = 2400 * 1.2 = 2880
So the third quantity = 3600 – 2880 = 720
Actual third quantity rate = 20  60 = 1200
Loss suffered = (1200 - 720) / 1200
= 480/1200 = 40 %
Answer: B
Answer: (B) 40%
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 2,450. What was Simran share in the profit?
(A) s 9500
(B) s 1000
(C) s 1,050
(D) s 1,100
(E) s 14,000
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs.2450 x	3/7	= Rs. 1,050.
ANSWER :C
Answer: (C) s 1,050
Question: If a, f, and c are consecutive even integers and a < f < c, all of the following must be divisible by 4 EXCEPT
(A) a + c
(B) f + c
(C) ac
(D) (bc)/2
(E) (abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - f + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: (B) f + c
Question: If 6^t is a factor of (10!)^2, What is the greatest possible value of t ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: t 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: (D) 8
Question: The successive discounts 20% and 15% are equal to a single discount of?
(A) 15
(B) 58
(C) 32
(D) 27
(E) 21
Rationale: Let the CP of an article be Rs. 100
Given that successive discounts are 20% and 15%.
SP = 85% of 80% of 100 = (85/100)(80/100)(100)
=> SP = Rs. 68
Clearly, single discount is 32%.
Answer: C
Answer: (C) 32
Question: What is the smallest positive integer x, such that 6000x is a perfect cube?
(A) 4
(B) 6
(C) 36
(D) 12
(E) 18
Rationale: Take out the factors of 6000 that will come 2*3*10^3. for perfect cube you need every no. raise to the power 3. for 6000x to be a perfect cube, need two 2 and 2 3 that means 36 or 6^2
C is the answer.
Answer: (C) 36
Question: The ratio of two quantities is 2 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?
(A) 2/5
(B) 5/8
(C) 7/13
(D) 22/25
(E) It cannot be determined from the information given.
Rationale: Correct Answer: E
Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.
For example, if x = 2 and y = 5, then (x+6)/(y+6) = (2+6)/(5+6) = 8/11. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+6)/(y+6) = (4+6)/(10+6) = 10/16. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).
Answer: (E) It cannot be determined from the information given.
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ?
(A) 0.5908
(B) 0.5904
(C) 0.5906
(D) 0.5904
(E) 0.5901
Rationale: P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
Answer: B
Answer: (B) 0.5904
Question: If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 2000 papers and 20% discount after first 10000 papers, how much will it cost to buy 25000 sheets of xerox paper?
(A) $1250
(B) $1060
(C) $1350
(D) $900
(E) $1000
Rationale: For first 2000 pages - cost 5 cents/paper
For 2001 - 10000 - cost 4.5 cents/paper
For 10000+ - 4 cents/paper
So Cost = (5 cents * 2000 ) + (4.5 cents * 8000 ) + (4 cents * 15000) = $1060
alternatively, (0.05 x 2000)+(0.045x8000)+(0.04x 15000) = 1,060
ANSWER:B
Answer: (B) $1060
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 500 nuts and 500 bolts?
(A) 250 seconds
(B) 500 seconds
(C) 750 seconds
(D) 2,000 seconds
(E) 3,000 seconds
Rationale: To minimize the amount of time, we should make both machines work all the time while producing 500 nuts and 500 bolts.
Two machines to produce 500 bolts will need (500*1)/2 = 250 seconds.
Two machines to produce 500 nuts will need (500*2)/2 = 500 seconds.
Total = 250+500=750.
Answer: C
Answer: (C) 750 seconds
Question: Two trains, traveling towards each other, left from two stations that are 900 miles apart, at 4 pm. If the rate of the first train is 72 mph and the rate of the second train is 78 mph, at whatt time will they pass each other?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: After t hours, the two trains will have traveled distances D1 and D2 (in miles) given by
D1 = 72 t and D2 = 78 t
After t hours total distance D traveled by the two trains is given by
D = D1 + D2 = 72 t + 78 t = 150 t
When distance D is equal to 900 miles, the two trains pass each other.
150 t = 900
t = 6 hours.
Answer:C
Answer: (C) 6
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
(A) 3377
(B) 268
(C) 1200
(D) 2877
(E) 1681
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP
= 1200
Answer: C
Answer: (C) 1200
Question: Find the compound interest on $ 66,000 at 20% per annum for 9 months, compounded quarterly
(A) 2532.12
(B) 2552.2
(C) 9524.32
(D) 10403.25
(E) 20512.54
Rationale: Principal = $ 66000; Time = 9 months =3 quarters;
Rate = 20% per annum = 5% per quarter.
Amount = $ [66000 x (1+(5/100))^3] = $ 76403.25
CI. = $ (76403.25 - 66000) = $ 10403.25
Answer D.
Answer: (D) 10403.25