mathewhe/aqua_rat huggingface dataset:
Question: In a race with 10 competitors, the first-place finisher receives a gold medal, and the second-place finisher receives a silver medal. If there are no ties, in how many different ways may these two medals be awarded?
(A) 90
(B) 120
(C) 720
(D) 840
(E) 68
Rationale: Well in this case since there are 2 positions and they can be taken by 2 persons only ,so order matters over here .For gold there are 10 choices and for silver 9 remain (one who got gold cannot be given silver).
So total possibilities=10*9
Correct answer A=90
Answer: (A) 90
Question: Find the odd man out. 14,35,49,60,70
(A) 14
(B) 35
(C) 49
(D) 60
(E) 70
Rationale: All except 60 are multiples of 7
Answer is D
Answer: (D) 60
Question: If n is an integer and 5^n > 4,000,000,000, what is the least possible value of n?
(A) 7
(B) 8
(C) 14
(D) 10
(E) 11
Rationale: When you seperate the 4000000000 into factors of 5 and 2 you get - > 10^9 x 2^2 = 5^9 x 2^11
2 to the ^ 11 = 2048 so its 2048 x 5^9
that means 5^9 x 5^x must be greater
5^x > 2048
5^1=5
5^2=25
5^3= 125
5^5= 3125 - > so x must be at least 5
5^(9+5)= 5^14
C
Answer: (C) 14
Question: 50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?
(A) 327
(B) 799
(C) 2778
(D) 277
(E) 100
Rationale: After 5 days, the following situation prevails.
50 men can complete the work in 60 days.
30 men can complete the work in ? days.
M1 D1 = M2 D2
=> 50 * 60 = 30 * D2
=> D2 = (50 * 60)/30 = 100 days.
Answer:E
Answer: (E) 100
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
(A) 3 : 4 : 6
(B) 3 : 4 : 7
(C) 3 : 4 : 9
(D) 3 : 4 : 1
(E) 3 : 4 : 3
Rationale: Explanation:
A : B : C = (40000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 144 : 192 : 336
= 3 : 4 : 7.
Answer: B) 3 : 4 : 7
Answer: (B) 3 : 4 : 7
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 40 percent of the sales representatives prefer to stay at Hotel XYZ and 60 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
(A) 36
(B) 39
(C) 42
(D) 45
(E) 48
Rationale: 18 people stay in XYZ and 42 people stay in ABC.
24 people prefer XYZ and 36 people prefer ABC.
Let's put all 24 people who prefer XYZ in hotel ABC.
Then 18 people who prefer ABC will stay in XYZ.
The highest possible number who are not given their preference is 24+18=42.
The answer is C.
Answer: (C) 42
Question: 80 is increased by 50%. Find the final number.
(A) 100
(B) 110
(C) 120
(D) 30
(E) 160
Rationale: Final number = Initial number + 50%(original number) = 80 + 50%(80) = 80 + 40 = 120.
Answer C
Answer: (C) 120
Question: A and B enter into a partnership with respective capitals of Rs. 20,000 and Rs. 40,000. At the end of the year, the total profit is Rs. 36,000. If A receives Rs. 15,000 as both his salary and profit, then what is his salary?
(A) Rs. 2000
(B) Rs. 4000
(C) Rs. 3500
(D) Rs. 3000
(E) None of these
Rationale: Explanation:
A's capital : B 's capital
20000 : 40000 = 1 : 2
Since, the time period is fixed, the profit is distributed in the ratio of capital 1 : 2
Profit of A = (1/3) * 36,000 = Rs. 12,000
Salary of A = Rs. (15000 – 12000) = Rs. 3000
ANSWER: D
Answer: (D) Rs. 3000
Question: The C.P of 21 articles is equal to S.P of 18 articles. Find the gain or loss percent.
(A) 10%
(B) 18 1/3%
(C) 16 2/3 %
(D) 20%
(E) 30%
Rationale: Let C.P of each article be Re. 1.
Then C.P of 18 articles = Rs. 18,
S.P of 18 articles = Rs. 21.
Gain % = ( 3/18 * 100 ) % = 16 2/3
ANSWER:C
Answer: (C) 16 2/3 %
Question: The "length" of a positive integer greater than 1 is the number of prime numbers, including repeats, that are factors of that integer. For instance, the length of 20 is 3, because 2×2×5=202×2×5=20. What is the length of 5,950?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 5950
=5x1190
=5x5x238
=5x5x2x118
=5x5x2x2x59
5 prime factors including repeats
Answer E
Answer: (E) 5
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
(A) 10
(B) 20
(C) 40
(D) 45
(E) 50
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: (B) 20
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 100 m and they cross each other in 10 sec, then the speed of each train is?
(A) 22
(B) 18
(C) 36
(D) 88
(E) 21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (100 + 100)/10 => x = 5
Speed of each train = 5 m/sec.
= 5 * 18/5 =- 18 km/hr.Answer: B
Answer: (B) 18
Question: If 20 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
(A) 95
(B) 90
(C) 85
(D) 80
(E) 75
Rationale: Let x be the number of students in the school. 0.2x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.2x/0.25=0.8x students went to the camping which is 80%.
The answer is D
Answer: (D) 80
Question: If the sum of the interior angles of a regular polygon measures up to 540 degrees, how many sides does the polygon have?
(A) 7
(B) 5
(C) 3
(D) 8
(E) None of these
Rationale: 5 sides...Answer is B
Answer: (B) 5
Question: On a 20 mile course, Bil bicycled at an average rate of 30 miles per hour for the first 12 minutes and without a break, ran the rest of the distance at an average rate of 8 miles per hour. How many minutes did Pat take to cover the entire course?
(A) 75
(B) 105
(C) 117
(D) 150
(E) 162
Rationale: At an average rate of 30 miles per hour in 12 minute (1/5 hours) Bil covers (distance) = (time) * (rate) = 1/5*30 = 6 miles, thus she should cover the remaining distance of 20 - 6 = 14 miles at an average rate of 8 miles per hour.
To cover 14 miles at an average rate of 8 miles per hour Pat needs (time) = (distance)/(rate) = 14/8 = 1.75 hours = 105 minutes.
Therefore Bil needs total of 12 + 105 = 117 minutes to cover the entire course.
Answer: C.
Answer: (C) 117
Question: 96 64 128 192 128 256 288 192 ?
(A) 367
(B) 384
(C) 374
(D) 284
(E) 484
Rationale: After 3 terms the series repears. So 4th 5th 6th term are 2* 1st 2nd and 3rd term repectively. While the 7th 8th 9th are 3* 1st 2nd 3rd terms. So ans=128*3=384
ANSWER:B
Answer: (B) 384
Question: 13, 26, 18, 36, 28, 56, ?
(A) 43
(B) 25
(C) 58
(D) 47
(E) 48
Rationale: E
48
This is an alternating multiplication and subtracting series with a pattern x2, -8, x2, -8.
Answer: (E) 48
Question: Which of the following values is the greatest
(A) a) 11% of 89
(B) b) 22% of 78
(C) c) 45% of 67
(D) d) 44% of 56
(E) e) 55% of 45
Rationale: Are you sure that you checked the answer key correctly? I just signed up forVeritas(haven't started yet, not until March) but I have access to the materials and the answer key I'm looking at says C
Answer: (C) c) 45% of 67
Question: At present, the ratio between the ages of Arun and Deepak is 4:3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
(A) 17 years
(B) 15 years
(C) 18 years
(D) 12 years
(E) 19 years
Rationale: Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 6 = 26 => x
= 5
Deepak's age
= 3x
= 15 years.
Answer:B
Answer: (B) 15 years
Question: If integers ending in zero are excluded, what is the units digit of the product of the even integers from 202 to 298, inclusive?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: In such questions, it is of utmost importance that you select the list in a smart way.
Following will be the list of even integers:
202, 204, 206, 208 - Units digit of the product = units digit of 2*4*6*8 = 4
212, 214, 216, 218
222, 224, 226, 228
232, 234, 236, 238
.
.
.
.
282, 284, 286, 288
292, 294, 296, 298
We have 10 such sets, the units digit of which is 4
Hence the units digit of the whole product = units digit of 4^10
Since the cyclicity of 4 is 2, units digit of 4^10 = units digit of 4^2 = 6
Correct Option: C
Answer: (C) 6
Question: On a two-dimensional coordinate plane, the line A = x^2 - x^3 touches the x-axis in how many places?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: Apparently it's A = x^2 - x^3 instead of A = x^2 - A^3.
In this case: the x-intercept is the value(s) of x for A = 0.
0 = x^2 - x^3;
0 = x^2(1 - x);
x = 0 or x = 1.
Answer: C.
Answer: (C)  2
Question: A pipe can empty the tank in 8 hours and another fill 6 litres in 1 min. If both pipe opened, the tank is emptied in 12 hours. The capacity of tank is ?
(A) 8000
(B) 8240
(C) 8440
(D) 8640
(E) 8840
Rationale: Let Capacity of the Tank is 100%.
First Pipe can empty the tank in = 8 hours = 8 * 60 = 480 min
Work rate of the pipe = X/480 litre per min.
The work rate of both pipe = X/(12*60) litre per min =
(X/480) - (X/720 )= Work rate of Second pipe
720X - 480X = 6 litere * 720 *480
240X = 6*720*480
X = 8640 litres
ANSWER :OPTION D
Answer: (D) 8640
Question: If f(a)=2a+3, what is the value of (f(2a)+f(a)) ?
(A) 2a-4
(B) 6a+6
(C) 9a+5
(D) 6a+12
(E) 3a+5
Rationale: f(a)=2a+3
f(2a)= 4a+3
(f(2a)+f(a)) = 4a+3+2a+3 = 6a+6
Answer is B
Answer: (B) 6a+6
Question: A monkey ascends a greased pole 20 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
(A) 21st
(B) 22nd
(C) 23rd
(D) 24th
(E) 37th
Rationale: In 2 minutes, he ascends = 1 metre
âˆ´ 18 metres, he ascends in 36 minutes.
âˆ´ He reaches the top in 37th minute.
Answer E
Answer: (E) 37th
Question: Into a bag there are 20 honey and 5 cherry candies. If a boy pick only two candies simultaneous and randomly, what is the probability that he picks one candy of each flavor?
(A)  2/25
(B)  1/50
(C)  1/12
(D)  1/6
(E)  1/3
Rationale: We are told that we have 25 candies, 20 honey and 5 cherry candies. The candies are picked simultaneous and randomly, C1 and C2, in different flavors. There are two acceptable outcomes: 1) C1 is honey and C2 is cherry; 2) C1 is cherry and C2 is honey. Let's go: 1) C1 = (20/25)(5/24)= 1/6 chance of this happening. 2) C2 = (5/25)(20/24) = 1/6 chance of this happening. Then: (1/6)+(1/6)= 1/3, chance of getting the result that you wanted. Answer E.
Answer: (E)  1/3
Question: After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
(A) 19 days
(B) 10 days
(C) 20 days
(D) 12 days
(E) 15 days
Rationale: Explanation:
1/3 ---- 6
1 -------?
A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30
2/3 ----? => 20 days
Answer: C
Answer: (C) 20 days
Question: If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b + c ?
(A) 6
(B) 2
(C) 4
(D) -3
(E) -4
Rationale: consectutive even , X , X + 2 , X + 4 where X = Even
now subtract X - (X+2) + (X+4)
doing this leaves us with X + 2
what even number can we substitute in X to yield an answer choice
C works 4 (plug in 2 for X)
Answer: (C) 4
Question: What is the Compound Interest on Rs.4500 at 5% p.a. compounded half-yearly for 3 1/2 years.
(A) Rs. 859.09
(B) Rs. 349.09
(C) Rs. 449.09
(D) Rs. 749.09
(E) Rs. 849.09
Rationale: Compound interest : A = P(1 + r/n)nt
A = 5,349.09
C.I. >> 5,349.09 - 4500 >> Rs. 849.09
Answer:E
Answer: (E) Rs. 849.09
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
(A) 4
(B) 8
(C) 12
(D) 16
(E) 20
Rationale: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.or 5x + 20 = 305 or x = 57.So, required difference = (57 + 8) - 57 = 8 Answer : B
Answer: (B) 8
Question: The ratio of the volumes of two cubes is 3375 : 1331. What is the ratio of their total surface areas?
(A) 225 : 121
(B) 221 : 127
(C) 225 : 191
(D) 181 : 161
(E) 81 : 182
Rationale: Explanation:
Ratio of the sides = ³√3375 : ³√1331 = 15 : 11
Ratio of surface areas = 15^2 : 11^2 = 225 : 121
Answer: Option A
Answer: (A) 225 : 121
Question: If n is the greatest positive integer for which 4^n is a factor of 8!, then n =?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 8! = 40320
E. 4^10 = 1048576 (40320/1048576) - this is not a factor of 8!
D. 4^8 = 65536 (40320/65536) - this is not a factor of 8!
C. 4^6 = 4096 (40320/4096) - this is not a factor of 8!
B. 4^4 = 256 (40320/256) - this is not a factor of 8!
A. 4^2 = 16 (40320/16) - this is a factor of 8!
Answer: (A) 2
Question: Square ABCD shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for C to be in the position where B is now shown. The number of degrees through which ABCD is rotated is
(A)  135 degree
(B)  180 degree
(C)  225 degree
(D)  315 degree
(E)  270 degree
Rationale: From the options, I am assuming the positioning of B and C relative to each other to be as shown. To replace B by C, focus on OC. Say, you rotate OC clockwise (and with it the entire square) and bring it in place of OB. How many degrees did you go? You covered 3 right angles i.e. 270 degrees.
Answer : E
Answer: (E)  270 degree
Question: A team of 6 cooks is chosen from 8 men and 6 women. The team must have at least 2 men and at least 3 women. How many ways can this team be created?
(A) 1540
(B) 320
(C) 560
(D) 700
(E) 840
Rationale: Only possible combinations are a team of 2M, 4 W or 3M,3W.
Possible ways to make a team of 2M,4W = 8C2 * 6C4 =28*15 =420
Possible ways to make a team of 3M,3W = 8C3* 6C3 = 56*20 = 1120
Total possible ways = 420+1120 = 1540
Ans A it is.
Answer: (A) 1540
Question: The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1926 in revenue from the sales. How many orchestra tickets did they sell?
(A) 35
(B) 39
(C) 43
(D) 47
(E) 51
Rationale: Let x be the number of orchestra tickets.
Then 90-x is the number of upper tier tickets.
30x + 12(90-x) = 1926
18x = 1926-1080
x = 47
The answer is D.
Answer: (D) 47
Question: A juice manufacturer organized taste-testing sessions featuring four brands of orange juice, A, B, C and D. All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice. 61% preferred brand A and exactly half as many preferred brand B. Only 55 chose brand C. Which of the following could be the number of customers who preferred brand D?
(A)  1
(B)  8
(C)  19
(D)  20
(E)  27
Rationale: I get D, but I'm not sure that my method is sound.
You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.
x = total number of testers
A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x
I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.
x = 400
A = 244, B = 122, C = 65..also over 400
x = 600
A = 366, B = 183 C = 65....also over 600
x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.
x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.
C
Answer: (C)  19
Question: A sum of Rs. 2730 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 1629
(B) 1680
(C) 1677
(D) 1698
(E) 1679
Rationale: (x*8*3)/100 = ((2730 - x)*3*5)/100
24x/100 = 40950/100 - 15x/100
39x = 40950 => x = 1050
Second sum = 2730 â€“ 1050 = 1680
Answer:B
Answer: (B) 1680
Question: 1,3,5,7,9,..50 find the term of sequence for this?
(A) 1809
(B) 1879
(C) 1247
(D) 1900
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500 .
E
Answer: (E) 2500
Question: Tom can hit a target 3 times in 6 shots, Mike can hit the target 2 times in 6 shots & Johncan hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?
(A) 1/4
(B) 2/5
(C) 2/3
(D) 3/7
(E) 4/9
Rationale: John hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Mike hits tha target and Raja not hit the target.
or
Mike does not hit the target and Raja hits the target.
or.
Mike hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: (C) 2/3
Question: There are 5 sweets = Jamun, Kaju, Peda, Laddu, Jalebi which can be consumed in 5 consecutive days. Monday to Friday. A person eats one sweet a day, based on the following constraints.
(i)	Laddu not eaten on Monday.
(ii)	If Jamun is eaten on Monday, Laddu should be eaten of Friday.
(iii)	Peda is eaten the day following the day of eating Jalebi.
(iv)	If Laddu eaten on Tuesday, Kaju should be eaten on Monday.
Based on above, Peda can be eaten on any day except:
(A) Tuesday
(B) Monday
(C) Wednesday
(D) Friday
(E) sunday
Rationale: The answer lies in statement (iii)
It is given that peda is eaten the day following the day of eating jalebi.
So peda cannot be eaten on Monday
Answer--> (b) Monday
ANSWER:B
Answer: (B) Monday
Question: The average price of 10 oranges is Rs. 12 while the average price of 8 of these oranges is Rs. 11.75. Of the remaining two oranges, if the price of one orange is 25% more than the price of the other, what is the price of each of these two oranges?
(A) Rs 11.5, Rs 14.5
(B) Rs 8, Rs 12
(C) Rs 10, Rs 16
(D) Rs 12, Rs 14
(E) None of these
Rationale: Explanation :
Total price of the two oranges = Rs. [(12 x 10) (11.75 x 8)]
= Rs. (120 - 94) = Rs. 26.
Let the price of one orange be Rs. x.
Then, the price of other orange = Rs. (x + 25% of x) = Rs. x + 1/4x = Rs. 5x/4
So, x + 5x/4 = 26
9x = 104
x = 11.5
The prices of the two oranges are Rs. 11.5 and Rs. 14.5
Answer : A
Answer: (A) Rs 11.5, Rs 14.5
Question: For all integers a and b, a%b = (a + b)(a - b). If 5%x = 24, then which of the following could be a value of x?
(A) -4
(B) -3
(C) 2
(D) 3
(E) 1
Rationale: 5%x = (5+x)(5-x)
25-x^2 = 24
x^2 = 1
x=-1,1
Ans: E
Answer: (E) 1
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
III. Brian
(A) I only
(B) II only
(C) III
(D) only I or II only
(E) I, II, or III
Rationale: Let’s assume that Stephanie won the race in record time of 2.5 hrs. In that case
B = R + 0.5
Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.
The same is true with
B = S + 0.5
R came first, S and then B.
So we see that B is a loser in any case, however R or S have equal chances to win.
So (D) is the answer.
Answer: (D) only I or II only
Question: A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 7 with 4 students left over. What is the sum of the two smallest possible values of n?
(A) 66
(B) 70
(C) 74
(D) 78
(E) 82
Rationale: n = 4k+1 = 7j+4
Let's start at 1 = 4(0)+1 and keep adding 4 until we find a number in the form 7j+4.
1, 5, 9, 13, 17, 21, 25 = 7(3)+ 4
The next such number is 25 + 4*7 = 53.
25+53 = 78
The answer is D.
Answer: (D) 78
Question: The average of numbers 0.64204, 0.64203, 0.64202 and 0.64201 is ?
(A) 0.64202
(B) 0.64204
(C) 0.642022
(D) 0.642025
(E) None
Rationale: Answer
Average = (0.64204 + 0.64203 + 0.64202 + 0.64201)/ 4
=2.5681/ 4
=0.642025
Correct Option: D
Answer: (D) 0.642025
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 408 votes. Find the number of votes casted to the winning candidate?
(A) 288
(B) 1054
(C) 788
(D) 298
(E) 177
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 408
62% -------- ? => 1054
Answer: B
Answer: (B) 1054
Question: The first republic day of the India was celebrated on 26th January,1950. It was
(A) 221
(B) 28
(C) 276
(D) 20
(E) 22
Rationale: 1-1-1 AD fall on Monday. We calculate the number of odd days till 24th december, 1995.
Number of odd days till 1600 years = 0
1601 to 1700 = 5
1701 to 1800 = 5
1801 to 1900 = 5
49 years contains = 37 normal + 12 leap years =12 × 2 + 37 = 61 odd days = 61/7 = 5 odd days
25th January 1950 = 25/7 = 4 odd days
Total odd days =15 + 5 + 4 = 24/7 = 3 odd days
So 26th January,1950 is Thursday
Answer:B
Answer: (B) 28
Question: A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?
(A) 3 hrs 15 min
(B) 3 hrs 45 min
(C) 4 hrs
(D) 4 hrs 15 min
(E) 4 hrs 45 min
Rationale: time taken by one tank to fill half the tank=4*(1/6)
Part filled by the four taps in 1 hour=4*(1/6)
remaining part=1/2
therefore 2/3:1/2::1:x
x=3/4hr=(3/4)*60=45min
total time =3 hr 45 min
ANSWER:B
Answer: (B) 3 hrs 45 min
Question: How much time does a train 100 metres long running at 72 km/hr take to pass a pole?
(A) 7.9s
(B) 2.5s
(C) 5s
(D) 7.6s
(E) 7.4s
Rationale: Explanation:
72 km/hr = 72 * 5/18 = 20 m/s
Speed = distance/time; v = d/t
20 = 100/t
t = 5s
ANSWER: C
Answer: (C) 5s
Question: The sum of two numbers is 184. If one-third of the one exceeds one-seventh
of the other by 8, find the smaller number
(A) 53
(B) 18
(C) 68
(D) 112
(E) 72
Rationale: Let the numbers be x and (184 - x). Then,
(X/3) - ((184 – x)/7) = 8 => 7x – 3(184 – x) = 168 => 10x = 720 => x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.
Answer is E.
Answer: (E) 72
Question: If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
(A) 2
(B) 5
(C) 6
(D) 7
(E) None of these
Rationale: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
x = 7.
Answer:D
Answer: (D) 7
Question: There is a set consisting of 5 numbers--{1,2,3,4,5}. If all possible subsets including null set are created and one subset is picked up, what is the probability that the subset does not have 5 as its largest number?
(A) 1/5
(B) 1/4
(C) 1/3
(D) 1/2
(E) 4/5
Rationale: Total Number of possible subsets [ including Null Subset ] : 2525 -- (A number can occur or not occur in a subset -- 2 ways)
Possible subsets where 5 is not present [will include null subset] : 24∗124∗1.
P = 2424 / 2525 = 1 / 2.
ANSWER:D
Answer: (D) 1/2