mathewhe/aqua_rat huggingface dataset:
Question: If Ajay completes a certain work in 8 days and Vijay can complete the same work in 24 days, find the time in which the work will be completed if both Ajay and Vijay work together.
(A) 6 days
(B) 9 days
(C) 2 days
(D) 7 days
(E) 1 days
Rationale: Explanation:
On working together Ajay and Vijay can complete the work in (8*24)/(8 + 24)
= 192/32
= 6 days
ANSWER: A
Answer: (A) 6 days
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 1 o'clock in the afternoon?
(A) 180°
(B) 154°
(C) 160°
(D) 170°
(E) 150°
Rationale: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.
In 5 hours, the angle traced by the hour hand is 5×30° = 150°
The answer is E.
Answer: (E) 150°
Question: A password of a computer used five digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
(A) 1/32
(B) 1/16
(C) 1/8
(D) 2/5
(E) 1/2
Rationale: We have five digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 * 5/10 =1/32 (A)
Answer: (A) 1/32
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is
(A) 38
(B) 40
(C) 28
(D) 12
(E) 19
Rationale: Explanation:
Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2.
x/2 = (83 - 63) => x/2 = 20 => x = 40.
Answer: B
Answer: (B) 40
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
(A) 33 1/4 %
(B) 33 9/3 %
(C) 33 1/3 %
(D) 33 1/5 %
(E) 33 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
Answer: (C) 33 1/3 %
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 3617
(C) 3187
(D) 7288
(E) 2661
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer: A
Answer: (A) 3630
Question: On my sister's birthday, she was 154 cm in height, having grown 10% since the year before. How tall was she the previous year?
(A) 150 cm
(B) 140 cm
(C) 142 cm
(D) 148 cm
(E) 146 cm
Rationale: Let the previous year's height be x.
1.1x = 154
x = 140
The answer is B.
Answer: (B) 140 cm
Question: Triangle STV has sides ST = TV = 10, and SV = 12. What is the area?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: Let the base B of the triangle be SV = 12. Then we need to find the height H.
H^2 = 100^2 - 6^2 = 64 and then H = 8.
The area is (1/2)*B*H = 6*8 = 48
The answer is D.
Answer: (D) 48
Question: A 240 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 260
(B) 250
(C) 240
(D) 230
(E) 220
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 240)/9 = 500/9 => x = 260.
Answer: Option A
Answer: (A) 260
Question: I. a3 - 212 = 131,
II. b2 - 72 = -23 to solve both the equations to find the values of a and b?
(A) a > b
(B) a ≥ b
(C) a < b
(D) a ≤ b
(E) a = b or the relationship between a and b cannot be established.
Rationale: a3 = 343 => a = 7
b2 = 49 => b = ± 7
a ≥ b
ANSWER:B
Answer: (B) a ≥ b
Question: Jennifer had $60 to spend on herself. She spent 1/5 of the money on a sandwich, 1/6 for a ticket
to a museum, and 1/2 of it on a book. How much money does Jennifer have left over?
(A) $8
(B) $14
(C) $5
(D) $15
(E) $0
Rationale: 1/5 x $60 = $12 for sandwich
1/6 x $60 = $10 for museum
1/2 x $60 = $30 for book
$12 + $10 + $30 = $52 spent
$60 - $52 = $8 left over
correct answer A
Answer: (A) $8
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
(A) 16.9
(B) 16.59
(C) 16.53
(D) 16.5
(E) 16.55
Rationale: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option D
Answer: (D) 16.5
Question: How many five-digit numbers can be formed from the digits 0, 1, 2, 3, 4, and 5, if no digits can repeat and the number must be divisible by 4?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 144
Rationale: Thus the last two digit must be 04, 12, 20, 24, 32, 40, or 52.
If the last two digits are 04, 20, or 40, the first three digits can take 4*3*2= 24 values.
Total for this case: 24*3 = 72.
If the last two digits are 12, 24, 32, or 52, the first three digits can take 3*3*2= 18 values (that's because the first digit in this case cannot be 0, thus we are left only with 3 options for it not 4, as in previous case).
Total for this case: 18*4 = 72.
Grand total 72 +72 =144.
Answer: E.
Answer: (E) 144
Question: By the how much is two-fifth of 100 greater than three -fifths of 25?
(A) 25
(B) 3
(C) 5
(D) 30
(E) None of these
Rationale: Reqd no. = 2â„5 Ã— 200 - 3â„5 Ã— 25
= 40 - 15 = 25
Answer A
Answer: (A) 25
Question: If |x|/|4| > 1, which of the following must be true?
(A) x>4
(B) x<4
(C) x=4
(D) x!=4
(E) x<-4
Rationale: Notice that if x = 4, then |x| / |4| = |4| / |4| = 1, so |x| / |4| is NOT more than 1, it's equal to 1. Thus if x = 4, the given inequality does NOT hold true.
As for the other options.
D. x ≠ 4 --> we know that x < -4 or x >4. Thus x cannot be 4. Thus this option is true.
ANSWER: D x!=4
Answer: (D) x!=4
Question: A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of colors in a pair does not matter)
(A) 4
(B) 5
(C) 6
(D) 12
(E) 24
Rationale: Let # of colors needed be nn, then it must be true that n+C2n≥12n+Cn2 - # of ways to choose the pair of different colors from nn colors when order doesn't matter) --> n+n(n−1)/2≥12 --> 2n+n(n−1)≥24 --> n is an integer (it represents # of colors) n≥5--> nmin=5
Answer: B.
Answer: (B) 5
Question: Which greatest possible length can be used to measure exactly 12 meter 15 cm, 10 meter 15 cm and 10 meter 65 cm
(A) 45cm
(B) 25cm
(C) 4cm
(D) 5cm
(E) 50cm
Rationale: Explanation:
Convert first all terms into cm.
i.e. 1215 cm, 1015cm, 1065cm.
Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 5.
Option D
Answer: (D) 5cm
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 3 hours?
(A) 60X/Y.
(B) 180X/Y.
(C) 60Y/X.
(D) 120Y/X.
(E) (X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 3 hrs(180mins)he can pack 180X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 180X/Y
(ANSWER B).
Answer: (B) 180X/Y.
Question: Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?
(A) Rs. 759
(B) Rs. 792
(C) Rs. 818
(D) Rs. 828
(E) Rs. 838
Rationale: Let the parts be x, y and [2379 - (x + y)]
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 2379
10k/11 + 20k/23 + 5k/6 = 2379
k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5
x = [10/11 * (3 * 11 * 23 * 6)/5] = 828
Hence, the first part is Rs. 828.
ANSWER:D
Answer: (D) Rs. 828
Question: The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?
(A) 17
(B) 12
(C) 20
(D) 27
(E) 18
Rationale: Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer:C
Answer: (C) 20
Question: David's Bank's saving amount is decreased 10% due to loan payment and current balance is Rs.90000. Find the actual balance before deduction?
(A) 8000
(B) 8500
(C) 9000
(D) 9500
(E) 100000
Rationale: 10% decreased
90% Balance = 90000
100% = 90000/90*100 = 100000
Answer : E
Answer: (E) 100000
Question: Find the odd man out. 2, 3, 7, 11, 19, 32
(A) 32
(B) 9
(C) 1
(D) 3
(E) 19
Rationale: 32 is an not prime number. All other given numbers are prime
Answer : Option A
Answer: (A) 32
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
(A) 276
(B) 271
(C) 200
(D) 278
(E) 268
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50
= 200 km away from Mumbai.
Answer: C
Answer: (C) 200
Question: Find value of X: (422+404)^2−(4×422×404)=X.
(A) 234
(B) 267
(C) 324
(D) 356
(E) 577
Rationale: Given Equation is in the form (a+b)2−4ab where a=422 and b=404
Hence answer
=(a+b)2−4ab=(a−b)2=(422−404)2=182=324
C
Answer: (C) 324
Question: What is 30 % of 80?
(A) 24
(B) 66
(C) 367
(D) 28
(E) 267
Rationale: 30 % of 80
= 30/100 × 80
= (30 × 80)/100
= 2400/100
= 24
Answer:A
Answer: (A) 24
Question: A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?
(A) 3 : 1
(B) 4:1
(C) 5:1
(D) None of these
(E) Cannot be determined
Rationale: Explanation :
Let tunnel = 8 km and speed of the cat is 1 km/hr.
Time taken to reach entrance of tunnel by cat = 3 hr
Time taken to reach exit of tunnel by cat = 5 hr
Train will cover the sum ( length of tunnel) = 2 hr.
Therefore, ratios of speeds of train and cat = 4 : 1
=> Speed of the train is greater by 3 : 1 than that of the cat.
Answer : A
Answer: (A) 3 : 1
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 50%?
(A) 3
(B) 5
(C) 7
(D) 8
(E) 6
Rationale: We need on-time departure rate to be higher than 5/10, so it should be at least 6/11, which means that 6 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 6-3=3 subsequent flights need to depart on-time.
Answer: A
Answer: (A) 3
Question: The length of a rectangualr hll is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is
(A) 15 m
(B) 22.5 m
(C) 25 m
(D) 30 m
(E) None
Rationale: Solution
Let the length = xmetres.
Then length = (x +5)metres.
Then,x(x +5)= 750
= x² + 5x - 750= 0
(x+30)(x-25)= 0
x=25.
Answer C
Answer: (C) 25 m
Question: Find the L.C.M of 12, 8, 24 and 16.
(A) 48
(B) 96
(C) 80
(D) 44
(E) 140
Rationale: Explanation:
2x3x2x2x2 = 48
Answer: Option A
Answer: (A) 48
Question: The Banker’s gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
(A) 30
(B) 40
(C) 50
(D) 60
(E) None
Rationale: Sol.
T.D. = B.G. * 100 / R * T = Rs.[6 * 100 / 12 * 1] = Rs.50
Answer C
Answer: (C) 50
Question: A train covers a distance in 1 h 40 min, if it runs at a speed of 96 km/h on an average. Find the speed at which the train must run reduce the time of journey to 1 h 20 min.
(A) 120 km/h
(B) 90 km/h
(C) 144 km/h
(D) 150 km/h
(E) 160 km/h
Rationale: Distance= Speed x Time = 96 x (100/60) = 160 km
New time = 80/60 h = 4/3 h
New speed = 160 x 3/4 = 40 x 3 =120 km/h
Answer :A
Answer: (A) 120 km/h
Question: A tortoise is making its way to eat a piece of lettuce at a constant speed. On its way to the lettuce, it takes 10 seconds to walk past a grain of sand. It then passes a piece of wood 20 cm long in 30 seconds to get to the lettuce. What is the length of the tortoise?
(A) 4 cm
(B) 5 cm
(C) 7.5 cm
(D) 9 cm
(E) 10 cm
Rationale: Sol.Let the length of the tortoise be x centimetres and its speed be y cm/sec. Then, x / y = 10 ⇒ y = x / 10∴ (x + 20) / 30 = x / 10 ⇔ x = 10 cm. Answer E
Answer: (E) 10 cm
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II. Regine,Brian
III.Regine
(A) I only
(B) II only
(C) III only
(D) I or II only
(E) I, or III only
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: E.
Answer: (E) I, or III only
Question: Graph G has a line of symmetry of x = –1. Graph G passes through the point (3, 3). What is the x-coordinate of another point that must have a y-coordinate of 3?
(A)  –8
(B)  –7
(C)  –5
(D)  –4
(E)  2
Rationale: Line of symmetry is X=-1; one point is (3,3)
Right side distance =1+3(distance from origin) = 4; therefore Left side distance should be same from line of symmetry =4;
therefore left side co-ordinate=4+ 1(distance from origin) = 5; as the X coordinate is in 2nd quadrant hence -5
Therefore answer is C
Answer: (C)  –5
Question: A certain tax rate is $.32 per $100.00. What is the rate, expressed as a percent?
(A) 32%
(B) 3.2%
(C) 0.82%
(D) 0.032%
(E) 0.32%
Rationale: Here in question it is asking $.32 is what percent of $ 100.Suppose $ .32 is x% of 100 means
100* (x/100) = .32
Hence x = .32 %
So answer is E
Answer: (E) 0.32%
Question: If a is an integer greater than 2 but less than 11 and b is an integer greater than 11 but less than 21, what is the range of a/b?
(A) 52/45
(B) 23/47
(C) 60/41
(D) 51/42
(E) 41/60
Rationale: The way to approach this problem is 2<a<11 and 11<b<21
Minimum possible value of a is 3 and maximum is 10
Minimum possible value of b is 12 and maximum is 20
Range = max a/min b - min a/max b
(Highest - lowest)
10/12 - 3/20 = 41/60
Hence E
Answer: (E) 41/60
Question: A man swims downstream 48 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 2
(B) 8
(C) 9
(D) 11
(E) 14
Rationale: 48 --- 3 DS = 16
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (16 + 6)/2 = 11
Answer: D
Answer: (D) 11
Question: A shopkeeper sold some articles @ 35 per article and earned a profit of 40%. At what price each article should have been sold so that 60% profit was earned?
(A) 25
(B) 29
(C) 30
(D) 40
(E) 45
Rationale: SP = 140% of CP; :. CP = 35 × 100/140 = 25
Then, 60% of CP = 2.5 × 6 = 15
To set a profit of 60% the SP = 25 + 15 = 40.
Option 'D'
Answer: (D) 40
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 7 inches. Two pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
(A)  5
(B)  15
(C)  24
(D)  32
(E)  120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 15.
Answer: option B
Answer: (B)  15
Question: The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 42, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 86
Rationale: there are 5 days so the sum of temperature can be 50*5=250
lowest is 42. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*42=168.
on the fifth day it is 250-168=281
range is therefore 128-42=86
answer E
Answer: (E) 86
Question: What is the place value of 7 in the numeral 55468?
(A) 5
(B) 50
(C) 5000
(D) 55
(E) 500
Rationale: place value of 5 = 5* 1000 = 5000
Answer is C
Answer: (C) 5000
Question: The temperatures in degrees Celsius recorded at a certain specific point in the evening in various parts of a country were 10°, 5°, -2°, -1°, -5°, 15°. What is the median of these temperatures?
(A) -2°C
(B) -1°C
(C) 2°C
(D) 3°C
(E) 5°C
Rationale: Explanation:
To get the median first we need to sort the temperatures in ascending order:
-5°, -2°, -1°, 5°, 10°, 15°
When the number of values in a list is even, the median is the average of the middle two values in the list in this case -1 and 5, i.e. 2.
Answer: Option C
Answer: (C) 2°C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
(A) 1/8
(B) 1/2
(C) 1/5
(D) 1/5
(E) 1/3
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: (C) 1/5
Question: what is the sum of the first 18 odd natural numbers
(A) 300
(B) 400
(C) 500
(D) 324
(E) 700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 18 odd natural numbers=(18)^2=324
ans 324
ANSWER:D
Answer: (D) 324
Question: A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled completely or emptied completely as the case may be? .
(A) Emptied; 16 mins
(B) Filled; 8 mins
(C) Emptied; 12 mins
(D) Filled; 12 mins
(E) None of These
Rationale: if A and B open together
since B can empty faster than A so tank will empty not fill.
the whole tank will empty in 16*8/(16-8)
=16 min
since tank is half so it will take only 8 min to empty.
ANSWER:E
Answer: (E) None of These
Question: A person want to give his money of $4500 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
(A) $2000
(B) $1500
(C) $2500
(D) $1800
(E) $1600
Rationale: B's share = 4500*3/9 = $1500
Answer is B
Answer: (B) $1500
Question: Scott's average (arithmetic mean) golf score on his first four rounds was 38.What score does he need on his fifth round to drop his average score by 2 points?
(A) 68
(B) 28
(C) 78
(D) 88
(E) 312
Rationale: Average score for first 4 rounds = 38
Average score after 5 rounds = 36
Score Scott needs on his 5th round to drop average score by 2 points =38 - (2*5) = 28
Answer B
Answer: (B) 28
Question: What is the units digit of 18! + 7 ?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Any number above 4!, such as 5!, 6!, etc... are always multiples of 10, so their units digit is 0.
The units digit of 18! + 7 is 7.
The answer is D.
Answer: (D) 7
Question: Without stoppages a train travels a certain distance with an average speed of 80 km/h and with stoppages with an average speed speed of 60 km/h. How many minutes per hour does the train stops ?
(A) 25 min
(B) 10 min
(C) 18 min
(D) 15 min
(E) 20 min
Rationale: let us assume the distance is x km.
if the train travels 80km/h without stopages then it takes (x/80) hour to rech.
and with stopage it takes (x/60) hour.
let the train stops t min per hour.
then according to the question
(x/80)=(x/60)+(t/60)*(x/60)
then t=15 min.
ANSWER:D
Answer: (D) 15 min
Question: 4,25,121,289,?
(A) 345
(B) 445
(C) 515
(D) 529
(E) 645
Rationale: Prime numbers- 2,3,5,7,11,13,17,19,23.....
Series - 2^2,5^2,11^2,17^2,23^2
Series- 4, 25, 121, 289, 529.
So next term in series is- 529.
ANSWER:D
Answer: (D) 529
Question: Half of 7 percent written as decimal is
(A) 5
(B) 0.5
(C) 0.025
(D) 0.035
(E) None of these
Rationale: Explanation:
It will be 1/2(7%) = 1/2(7/100) = 7/200 = 0.035
Option D
Answer: (D) 0.035
Question: There are 6 red balls and 4 blue balls in a jar. If 3 balls are selected from the jar, what is the probability that all 3 balls selected are blue balls?
(A) 1/18
(B) 1/24
(C) 1/30
(D) 1/36
(E) 1/48
Rationale: The number of ways of choosing 3 balls from the jar is 10C3 = 120.
The number of ways of choosing 3 blue balls is 4C3 = 4.
P(3 blue balls) = 4/120=1/30.
The answer is C.
Answer: (C) 1/30
Question: The sum of money will be double itself in 20years and simple interest find rate of interest?
(A) 10%
(B) 5%
(C) 15%
(D) 20%
(E) 25%
Rationale: T = 20 years
P= principle amount = x
A = total amount = 2x
SI = simple interest = A-P = 2x-x = x
R = 100SI/PT = 100x/20x =5%
Answer is B
Answer: (B) 5%
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.98
(B) 2.88
(C) 2.82
(D) 2.86
(E) 2.81
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Answer: (B) 2.88
Question: P, Q and R have Rs.4000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) Rs.3000
(B) Rs.1600
(C) Rs.2400
(D) Rs.4000
(E) None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(4000 - r) => 3r = 8000 - 2r
=> 5r = 8000 => r = 1600.
ANSWER:B
Answer: (B) Rs.1600
Question: On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.9, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.009
(B) 0.128
(C) 0.488
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probablity of rain = 0.9
Therefore, probability of no rain = 0.1
0.1*0.1*0.9 = 0.009
Hence A
Answer: (A) 0.009
Question: What is the value of 3x^2 − 1.6x + 0.3 for x = 0.8?
(A) −0.3
(B) 0
(C) 0.3
(D) 0.94
(E) 2.46
Rationale: 3x^2-1.6x+0.3 for x=0.6
=3(0.8*0.8)-2*0.8*(0.8)+0.3
=0.8*0.8+0.3
=0.94
Correct Option : D
Answer: (D) 0.94
Question: A certain list consists of 21 different numbers. If n is in the list and n is 2 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 1/20
(B) 1/6
(C) 1/11
(D) 4/21
(E) 5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 2*x
Hence, a1+a2+..+a20+n = 22x
So, the fraction asked = 2x/22x = 1/11
Answer C
Answer: (C) 1/11