mathewhe/aqua_rat huggingface dataset:
Question: Set A consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set A?
(A) 13
(B) 1
(C) 5
(D) 67
(E) 7
Rationale: Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
B
Answer: (B) 1
Question: Find the number of different prime factors of 6440
(A) 4
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Explanation:
L.C.M of 6440 = 2 x 2 x 2 x 5 x 7 x 23
2, 5,7,23
Number of different prime factors is 4.
Answer: Option A
Answer: (A) 4
Question: A train 110 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 9 sec
(D) 4 sec
(E) 3 sec
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [110 * 3/55] sec
= 6 sec
Answer:B
Answer: (B) 6 sec
Question: If Tim had lunch at $60.80 and he gave 20% tip, how much did he spend?
(A) $30.60
(B) $60.60
(C) $72.96
(D) $40.60
(E) $50.60
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 60.80 = (20/100)*60.80 = $12.16
Total spent
60.80 + 12.16 = $72.96
correct answer C
Answer: (C) $72.96
Question: In a group of cows and chickens, the number of legs was 20 more than twice the number of heads. The number of cows was:
(A) 5
(B) 7
(C) 10
(D) 12
(E) 14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 20 more than twice the number of heads.
Therefore, 2 × (x + y) + 20 = 4x + 2y.
or, 2x + 2y + 20 = 4x + 2y.
or, 2x + 20 = 4x [subtracting 2y from both sides].
or, 20 = 4x – 2x [subtracting 2x from both sides].
or, 20 = 2x.
or, x = 10 [dividing by 2 on both sides].
Therefore, the number of cows = 10.
Correct Answer:C)10
Answer: (C) 10
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 2nd year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
(A) 36
(B) 38
(C) 40
(D) 42
(E) 48
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 2nd year = 50,
3rd year = 50- 2 = 48
4th year = 48-3 = 45
5th year = 45-4 = 41.
6th year= 41-5 = 36
The correct answer is A.
Answer: (A) 36
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 5 minutes?
(A) 120 m
(B) 200 m
(C) 170 m
(D) 100 m
(E) 250 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 5 minutes = 1/60 * 5 = 1/12 km = 80 m.
Distance between the thief and policeman = 200 - 80 = 120 m
A
Answer: (A) 120 m
Question: What is the probability of rolling one six-sided dice, and getting a different number on each die?
(A) 1/12
(B) 1/3
(C) 1
(D) 5/9
(E) 7/18
Rationale: MAGOOSHOFFICIAL SOLUTION
For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.
6= 6 possibilities out of 216 total possibilities. (For total possibilities we get 6 = 6).
6/ 6 =1
Answer: C.
Answer: (C) 1
Question: Ratio between two numbers is 3: 4 and their sum is 420. Find the smaller number?
(A) 23
(B) 180
(C) 287
(D) 137
(E) 192
Rationale: Explanation:
3x + 4x = 420
x = 60 => 3x = 180
Answer: B
Answer: (B) 180
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.
(A) 83.5%
(B) 87.5%
(C) 88.5%
(D) 89.5%
(E) 484 rupees
Rationale: Explanation:
In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.
4/15A= 2/5B
A=(2/5∗14/4)B
A=3/2B
A/B=3/2
A:B=3:2
B's Share = 2/5∗1210=484
Option E
Answer: (E) 484 rupees
Question: A man can swim in still water at 7.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 2.5
(D) 1.5
(E) 1.1
Rationale: M = 7.5
S = x
DS = 7.5 + x
US = 7.5 + x
7.5 + x = (7.5 - x)2
7.5 + x = 15 -2x
3x = 7.5
x = 2.5
Answer: C
Answer: (C) 2.5
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) 2.89
(B) 2.88
(C) 2.82
(D) 2.87
(E) 2.84
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: A boat can move upstream at 30 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 2.5
Rationale: US = 30
DS = 35
M = (35 - 30)/2 = 2.5
Answer: E
Answer: (E) 2.5
Question: The ratio of two numbers is 3:4 and their sum is 14. The greater of the two numbers is?
(A) 12
(B) 14
(C) 16
(D) 8
(E) 19
Rationale: 3:4
Total parts = 7
= 7 parts --> 14 (7 Ã— 2 = 14)
= 1 part ---->2 (1 Ã— 2 = 2)
= The greater of the two number is = 4
= 4 parts ----> 2 (2 Ã— 4 = 8)
D)
Answer: (D) 8
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
(A) 52.7
(B) 52.9
(C) 52.4
(D) 52.5
(E) 52.1
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5
Answer: D
Answer: (D) 52.5
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 878
(B) 768
(C) 800
(D) 778
(E) 876
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer:C
Answer: (C) 800
Question: A man saves Rs 150 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
(A) Rs 452
(B) Rs 492.01
(C) Rs 496.52
(D) Rs 496.03
(E) None of these
Rationale: Explanation:
=[150(21/20Ã—21/20Ã—21/20)+150(21/20Ã—21/20)+150(21/20)]=496.52
Option C
Answer: (C) Rs 496.52
Question: A number when divided by 214 gives a remainder 35, what remainder will be obtained by dividing the same number 14?
(A) 7
(B) 10
(C) 11
(D) 2
(E) 3
Rationale: Explanation:
214 + 35 = 249/14 = 11 (Remainder)
Answer: C
Answer: (C) 11
Question: If x is chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7}, then what is the probability that xy will be even?
(A) 5/6
(B) 2/6
(C) 2by3
(D) 1/2
(E) 1/4
Rationale: S = {(1,5), (1,6), (1,7), (2,5), (2,6), (2,7), (3,5), (3,6), (3,7), (4,5), (4,6), (4,7)}
Total element n(S) = 12
xy will be even when even x or y or both will be even.
Events of xy being even is E.
E = {(1,6), (2,5), (2,6), (2,7), (3,6), (4,5), (4,6), (4,7)}
n(E) = 8
P(E) = n(E)/n(S)
= 8/12
= 2/3
ANSWER:C
Answer: (C) 2by3
Question: A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 5 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
(A) 0.5< t < 0.75
(B) 1.75< t < 2.0
(C) 1.0 < t < 1.5
(D) 2.5 < t < 3.0
(E) 3 < t < 3.5
Rationale: D=2, and R=1
circumference thus is 2pi miles
we know that she walked 5mph
knowing the formula rt=D, we can deduce that t= D/r
D is 2pi miles and r is 5mph
t = 2pi/5
pi can be rewritten as 22/7
2*22/7 = 44/7 and multiply this by 1/5 = 44/35. This is greater than 1, but less than 1.5, therefore, 1<t<1.5. Answer choice C.
Answer: (C) 1.0 < t < 1.5
Question: A horse and cow were sold for Rs.12000 each. The horse was sold at a loss of 20% and the cow at a gain of 20%. The entire transaction resulted in :
(A) No loss or gain
(B) Loss of Rs.1000
(C) Gain of Rs.1000
(D) Gain of Rs.2000
(E) None of these
Rationale: Explanation:
In the special case of profit and loss percentages are equal and Selling price is same, then the transaction always results in Loss. This loss percentage is given by a simple formula −(x/10)2
So in this case, Profit% = Loss% = 20. So x = 20
Loss percentage = −(20/10)2=−4
Total S.P = Rs.24000
Cost price = 24000×100/96 = 25000
Loss = Rs.1000
Correct Option : B
Answer: (B) Loss of Rs.1000
Question: A train passes a station platform in 42 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 177 m
(B) 176 m
(C) 240 m
(D) 187 m
(E) 330 m
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 15
x + 300 = 630
x = 330m.
Answer: E
Answer: (E) 330 m
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be?
(A) 77 years
(B) 67 years
(C) 20 years
(D) 55 years
(E) 61 years
Rationale: Explanation:
Clue : (60 - x) - 6 = 5(x - 6)
Answer: C
Answer: (C) 20 years
Question: In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 720
(B) 1720
(C) 2880
(D) 5040
(E) 10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 4 chairs to sit. The remaining 6 people can sit in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: C.
Answer: (C) 2880
Question: Which of the following fractions is the largest?
(A) 5/6
(B) 11/14
(C) 12/15
(D) 17/21
(E) 29/35
Rationale: another way is by taking LCM of denominators(2*3*5*7)
(a) 175 (as lcm is 2*3*5*7 where 2*3 part is already in denominator just multiply 5*7 to numerator) ,similarly
(b) 165
(c)168
(d)170
(e)174
clearly (a) is largest..
Ans A
Answer: (A) 5/6
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 17608
(B) 17606
(C) 17604
(D) 17600
(E) 117601
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600.Answer: D
Answer: (D) 17600
Question: An automobile company has a production target to get profits annually. The target production this year is 1/10 of last year's production. If the target production is reduced by 20% of last year's target what percentage of target production of last year's target does he need to complete in order to get profit?
(A) 15/20
(B) 17/10
(C) 6/20
(D) 4/5
(E) 14/20
Rationale: We have 1/10 and 20% that is 1/5
Let us assume the last year's target to be 20
This year's target is 20% less than last year's target=16
The target reached this year is 1/10*20=2
Remaining is 16-2=14
Required 14/20
Answer (E)
Answer: (E) 14/20
Question: A merchant has announced 25% rebate on prices of ready-made garments at the time of sale. If a purchaser needs to have a rebate of Rs. 400, then how many shirts, each costing Rs. 320, should he purchase?
(A) 10
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Solution: Discount on one shirt,
= 25% of 320 = 320*25/100 = Rs. 80.
Hence, number of shirt he must buy to get a rebate of Rs. 400 = 400/80 = 5.
Answer: Option D
Answer: (D) 5
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
(A) Rs. 10,500, Rs. 13,500, Rs. 16,500
(B) Rs. 10,500, Rs. 13,500, Rs. 16,509
(C) Rs. 10,500, Rs. 13,500, Rs. 16,555
(D) Rs. 10,500, Rs. 13,500, Rs. 16,506
(E) Rs. 10,500, Rs. 13,500, Rs. 16,504
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer: A
Answer: (A) Rs. 10,500, Rs. 13,500, Rs. 16,500
Question: If k is a positive even integer, what is the smallest possible value of k such that 3675*k is the square of an integer?
(A) 3
(B) 9
(C) 12
(D) 15
(E) 20
Rationale: 3675=31∗52∗72
Now , is the most important part of this question
K must be even ( negate options A, B and D ) W e are left with C and E
Try one to confirm the answer...
Let's try (E)
20=22∗51
3675∗20=22∗31∗53∗72 ( Can not square of an Integer )
So, Answer must be (C)....
Answer: (C) 12
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 80 miles per hour. At 2 o’clock the faster train is 20 miles behind the slower one. How far apart are the two trains at 5 o'clock?
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 130 miles
(E) 400 miles
Rationale: Answer = D. 130 miles
Relational speed = 130 - 80 = 50 miles per hour
In 3 hours, difference = 50 * 3 = 150 miles
Fast train trailing 20 miles, so effective difference = 150 - 20 = 130 miles
Answer: (D) 130 miles
Question: An oil cylinder was 3/4th full. When SIX bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?
(A) 120
(B) 115
(C) 140
(D) 130
(E) 135
Rationale: (4/5 -3/4) cylinder is filled by 6 bottles
0.8 -0.75 = 0.05 cylinder is filled by 6 bottles
1 cylinder is filled by 6/0.05 = 120 bottles
ANSWER:A
Answer: (A) 120
Question: How many cuboids of length 5 m, width 6 m and height 3 m can be farmed from a cuboid of 18 m length, 15 m width and 2 m height.
(A) 4
(B) 6
(C) 10
(D) 8
(E) 11
Rationale: (18 Ã— 15 Ã— 12)/(5 Ã— 3 Ã— 2) = 6
Answer is B.
Answer: (B) 6
Question: What is the units digit of (22^4)(16^3)(41^8)?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: The units digit of 22^4 is the units digit of 2^4 which is 6.
The units digit of 16^3 is the units digit of 6^3 which is 6.
The units digit of 41^8 is the units digit of 1^8 which is 1.
The units digit of 6*6*1 is 6.
The answer is E.
Answer: (E) 6
Question: A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, 14 men leave the bus and seven women enter. Now, number of men and women is equal. In the beginning, how many passengers entered the bus ?
(A) 63
(B) 30
(C) 36
(D) 45
(E) 46
Rationale: Explanation:
Originally, let number of women = x. Then, number of men = 2x.
So, in city Y, we have : (2x - 14) = (x + 7) or x = 21.
Therefore Total number of passengers in the beginning = (x + 2x) = 3x = 63.
Answer: A
Answer: (A) 63
Question: A box contains 10 black,5 red and 4 green marbles. 3 marbles are drawn from the box at random. What is the probability that all the three marbles are of the same color?
(A) 143/969
(B) 134/969
(C) 120/969
(D) 19/969
(E) 120/134
Rationale: Explanation:
Total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles
3 marbles are drawn from 19 marbles at random. Therefore,
n(S) = 19C3= 969 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 10C3+ 5C3 + 4C3 = 120 +10 + 4 = 134
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 134/969
ANSWER:B
Answer: (B) 134/969
Question: The cost price of 12 articles is equal to the selling price of 10 articles. What is the profit percent?
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
Rationale: 10*SP = 12*CP
SP = 1.2*CP
The profit percent is 20%.
The answer is B.
Answer: (B) 20%
Question: Calculate 469157 x 9999 = ?
(A) 4586970843
(B) 4686970743
(C) 4691100843
(D) 4586870843
(E) NONE
Rationale: Answer
469157 x 9999 = 469157 x (10000-1)
= 4691570000 - 469157
= 4691100843.
Option: C
Answer: (C) 4691100843
Question: Anmol can eat 27 pastries in a hour.
Aakriti can eat 2 pastries in 10 minutes.
Divya can eat 7 pastries in 20 minutes.
How long will it take them to eat a 180 pastries ?
(A) 2 hours.
(B) 1 hours.
(C) 5 hours.
(D) 4 hours.
(E) 3 hours.
Rationale: In one hour, Anmol eats 27 pastries, Aakriti eats 12, and Divya eats 21. A total of 60 pastries. Therefore 180 pastries would take 180 ÷ 60 = 3 hours.
ANSWER E
Answer: (E) 3 hours.
Question: For any non-zero a and b that satisfy |ab| = ab and |C| = -c
|b - 4| + |ab - b| = ?
(A) a) ab - 4
(B) b) b - 2b + 4
(C) c) ab + 4
(D) d) 2b - ab - 4a
(E) e) 4 - ab
Rationale: |a| = -a Suggests that 'a' is Negative
|ab| = ab Suggests that 'ab' is Positive
'ab' is Positive Suggests that 'a' and 'b' have same Sign i.e. either both positive or both negative
But since 'a' is Negative therefore 'b' is Negative too.
Since b is negative so |b - 4| = -b+4
Since ab is Positive and b is Negative so |ab - b| = ab - b
i.e. |b - 4| + |ab - b| = -b+4 + ab - b =ab - 2b + 4
Answer: Option B
Answer: (B) b) b - 2b + 4
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 50 packages of gaskets. If 20 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
(A) 1105
(B) 1245
(C) 1275
(D) 1215
(E) 1150
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 20 % of the gaskets to X = 10 gaskets = 25*10 = 250
2.he sold 30 % of the gaskets to Y = 15 gaskets = 25*10+20*5= 350
3.he sold remaining 50% to z =25 gaskets = 25*10 =250 + 20*15=550
thus ,total money earned
250+350+550 = 1150
Answer is E
Answer: (E) 1150
Question: Average of all prime numbers between 40 to 50
(A) 37
(B) 37.8
(C) 43.6
(D) 39.8
(E) 40
Rationale: Explanation:
Prime numbers between 40 and 50 are:
41, 43, 47
Average of prime numbers between 40 to 50 will be
(41+43+47 / 3)=131 / 3 =43.6
Option C
Answer: (C) 43.6
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 51 percent were employees. What percent were stockholders, who were not employees?
(A) 52
(B) 49
(C) 54
(D) 55
(E) 56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
51% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 51% = 49%.
Answer: (B) 49
Question: What is the greatest 6-digit number when divided by 6, 7 ,8 , 9, and 10 leaves a remainder of 4, 5, 6, 7, and 8 respectively?
(A) 456780
(B) 678910
(C) 997479
(D) 997918
(E) 997920
Rationale: When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so D is the only possible answer.
Answer: (D) 997918
Question: What is the square root of 3,249?
(A) A)18
(B) B)9
(C) C)45
(D) D)62
(E) E)57
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
57*57=3,249
3249 divided by x = 57
x=57
(E)57
Answer: (E) E)57
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
(A) 18
(B) 19
(C) 21
(D) 25
(E) 27
Rationale: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Answer: (C) 21
Question: For integers M and N, when M is divided by N, the remainder is odd. Which of the following must be true?
(A) The sum M + N is odd
(B) M and N share no common factors other than 1
(C) MN is odd
(D) M is odd
(E) either integer M or integer N is odd
Rationale: either integer M or integer N is odd
E
Answer: (E) either integer M or integer N is odd
Question: There are 6561 balls out of them 1 is heavy.Find the min. no. of times the balls have to be weighed for finding out the haevy ball.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: The simple logic is to divide total balls into three sets. Weigh any two sets against each other(these two must contain equal number of balls). From this we can identify which set contains the heavy ball. Divide this set into three and repeat until you find the heavier ball. Under this logic, the minimum number of weighings required turns out to be the smallest integer greater than or equal to log(n), where n is the total number of balls and the base of logarithm is 3. Or simply [log(n)/log(3)] with any base. Here, n = 6561. log 6561 / log 3 = 8
ANSWER:B
Answer: (B) 8
Question: A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. When A done the work?
(A) 10 days
(B) 12 days
(C) 13 days
(D) 9 days
(E) 14 days
Rationale: B+C ==>1/9+1/12 = 7/36
B ,C =in 3 days = 7/36*3 = 7/12
remaining work = 1-7/12 = 5/12
1/24 work is done by A in 1 day
5/12 work is done A 24*5/12 = 10 days
ANSWER A
Answer: (A) 10 days
Question: What is the area of a square with perimeter 12P ?
(A)  16p^2
(B)  4P
(C)  9P^2
(D)  P/16
(E)  P^2/16
Rationale: Each side is 3p
A = (3p)^2 = 9p^2
Answer C
Answer: (C)  9P^2
Question: Average of first five multiples of 3 is
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: Explanation:
Average=3(1+2+3+4+5) / 5=45 / 5=9
Option A
Answer: (A) 9