mathewhe/aqua_rat huggingface dataset:
Question: A number x is multiplied by 5, and this product is then divided by 7. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ?
(A) 25/9
(B) 9/5
(C) 5/7
(D) 3/5
(E) 9/25
Rationale: sqrt(5x/7) to be perfect square x has to 5/7
Ans: C
Answer: (C) 5/7
Question: if 12 men working 2 hours a day take 10 days to complete a job, how long will 8 men working 6 hours a day take to do the same work?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 12 men working 2 hours in a day means,
= 12 * 2hrs
= 24hours of work complete in 1day.
Therefore for 10 days,
= 10 *24hours
= 240hours of work done by 12men.
8 men working for 6hours in a day means,
= 8 *6hours
= 48hours of work is completed in 1 day.
Therefore,
= 240/48
= 5days take to work by 8 men for 6hours in a day.
ANSWER:C
Answer: (C) 5
Question: A, B and C started a business with a total investment of Rs. 90000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find B's share.
(A) Rs. 2592
(B) Rs. 2520
(C) Rs. 2880
(D) Rs. 3360
(E) None of these
Rationale: Explanation:
Let C's investment = Rs. x
B's investment = Rs. (x - 3000)
A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)
Now, (A + B + C)'s investment = Rs. 90000
=> x + (x - 3000) + (x + 3000) = 90000
=> 3x = 90000
=> x = 30000
Hence, A's investment = Rs. 33000
B's investment = Rs. 27000
C's investment = Rs. 30000
Ratio of the capitals of A, B and C
= 33000 : 27000 : 30000
= 11 : 9 : 10
A's share = Rs. [(9/30) Ã— 8640] = Rs. 2592
Answer: Option A
Answer: (A) Rs. 2592
Question: Month	Average Price
per Dozen
April $1.2
May $1.20
June $3.00
The table above shows the average (arithmetic mean) price per dozen of the large grade A eggs sold in a certain store during three successive months. If 2/3 as many dozen were sold in April as in May, and twice as many were sold in June as in April, what was the average price per dozen of the eggs sold over the three-month period?
(A) 1.8
(B) 2.2
(C) 2
(D) 1.9
(E) 2.4
Rationale: Say x dozen eggs were sold in May.
Then 2x/3 dozen eggs were sold in April and 2*2x/3=4x/3 dozen eggs were sold in May.
Total x+2x/3+4x/3=3x dozen eggs were sold in three months.
Total sales: 2x/3*1.2+x*1.2+4x/3*3.00=$6.00x. The average price per dozen 6.00x/3x=$ 2.00
C
Answer: (C) 2
Question: 789.009 - ? + 56.84 = 215.943
(A) 899.015
(B) 752.804
(C) 714.642
(D) 629.906
(E) None of these
Rationale: Explanation:
629.906
Answer: Option D
Answer: (D) 629.906
Question: The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 19009
(B) 19074
(C) 19008
(D) 19000
(E) 19002
Rationale: Explanation:
Money paid in cash = Rs. 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: Option D
Answer: (D) 19000
Question: I. p-14, p, p, p, p+14
II. b, b+1, b+2, b+3, b+4
III. c, c, c, c, c
The data sets I, II, and III above are ordered from greatest standard deviation to least standard deviation in which of the following?
(A) I, II, III
(B) I, III, II
(C) II, III, I
(D) III, I, II
(E) III, II, I
Rationale: S.D is a non-negative entity. Also, for a given set with all the elements same, the S.D is Zero(It is zero even if there is only one element in the set too). From the given sets, we can see that the last set has a standard deviation of zero. Also, because the other sets can not have all the terms equal for any values of p or b, thus the S.D for the third set(III) has to be the minimum. Select the option which has III in the end.
A.
Answer: (A) I, II, III
Question: A password of a computer consists of nine digits 1 through 7. What is the probability that the first digit is a 2 and the second digit is divisible by 3 ?
(A) 1/9
(B) 1/21
(C) 1/24.5
(D) 1/49
(E) 1/98
Rationale: There is one possibility out of seven that the first digit is correct, and two possibilities that the second digit is correct (3 and 6). We don't care about the remaining digits, so the overall probability is 1/7 * 2/7 or 1/24.5 (answer C)
Answer: (C) 1/24.5
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 425.01
(A) 71.81
(B) 81.71
(C) 84.74
(D) 88.65
(E) None of these
Rationale: Explanation:
a - 796.21 + 498.05 = 215.50 - 425.01
a = 88.65
ANSWER: D
Answer: (D) 88.65
Question: A person travels from P to Q a speed of 30 km/hr and returns by increasing his speed by 30%. What is his average speed for both the trips?
(A) 33
(B) 77
(C) 48
(D) 99
(E) 34.5
Rationale: Speed on return trip = 130% of 30 = 39 km/hr.
Average speed of trip = 30 + 39 /2 = 69/2 = 34.5 km/hr
Answer : E
Answer: (E) 34.5
Question: There are 136 employees in Company X. If the number of employees who birth in June is the greatest, what is the least possible number of the employees in the company who birth in June?
(A) 15
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: IMO 15
Take each answer choice and substract it from 136 and the divided this with 11. A
Answer: (A) 15
Question: A train passes a station platform in 50 sec and a man standing on the platform in 15 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 227
(B) 500
(C) 550
(D) 525
(E) 171
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 15 = 225 m.
Let the length of the platform be x m . Then,
(x + 225)/50= 15 => x = 525m.
Answer:D
Answer: (D) 525
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
(A) 1 hr
(B) 2 hr
(C) 7 hr
(D) 8 hr
(E) 4 hr
Rationale: Let the duration of the flight be x hours. Then,
600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
Answer:A
Answer: (A) 1 hr
Question: On an order of 99 dozen boxes of a consumer product, a retailer receives an extra dozen free. This is equivalent to allowing him a discount of:
(A) 0.1%
(B) 0.5%
(C) 1%
(D) 5%
(E) 10%
Rationale: Clearly, the retailer gets 1 dozen out of 100 dozens free.
Equivalent discount = 1/100 * 100 = 1%.
Answer C) 1%
Answer: (C) 1%
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 45km/hr
(B) 50 km/hr
(C) 54 km/hr
(D) 55 km/hr
(E) 60 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
ANSWER B
Answer: (B) 50 km/hr
Question: A set of 11 positive integers has an average of 26. Which of the following is the greatest possible value for the median of this set?
(A) 25
(B) 30
(C) 36
(D) 45
(E) 46
Rationale: for the median to be max , we should take all the values below meadian to be the lowest and the remaining values to be the same..
here 1 is the lowest value(positive int) so the lowest 5 int will equal 5..
remaining 6= 26*11-5=281..
therefore each valueof these 6 int =281/6=46
ans E
Answer: (E) 46
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
(A) 32
(B) 35
(C) 39
(D) 41
(E) 43
Rationale: 39
Option 'C'
Answer: (C) 39
Question: Two men started running simultaneously around a circular track of length 19200 m from the same point at speeds of 120 km/hr and 200 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
(A) 214
(B) 215
(C) 216
(D) 217
(E) 218
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 19200 / (120 + 200)5/18 = 19200* 18 / 320 * 5 = 216 seconds.
Answer:C
Answer: (C) 216
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
(A) Rs. 34
(B) Rs. 39
(C) Rs. 42
(D) Rs. 49
(E) Rs. 51
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: (C) Rs. 42
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
(A) 228
(B) 744
(C) 255
(D) 199
(E) 231
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 288
62% -------- ? => 744
Answer:B
Answer: (B) 744
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 1
(B) 2
(C) 8
(D) 7
(E) 0
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 8
Question: The sum of the digits of a two digit number is 9 less than the number. Which of the following digits is at units place of the number?
(A) 1
(B) 2
(C) 3
(D) Data inadequate
(E) None
Rationale: Sol.
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (x + y) = 9 or x = 1.
From the data, we cannot find y, the units digit.
So, the data is inadequate.
Answer D
Answer: (D) Data inadequate
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?
(A) 0.5%
(B) 1%
(C) 1.25%
(D) 3%
(E) 4%
Rationale: Required percentage
=	[	(3.00 + 2.52 + 3.84 + 3.68 + 3.96)	x 100	]	%
(288 + 342 + 324 + 336 + 420)
=	[	17	x 100	]	%
1710
~= 1%.
B)
Answer: (B) 1%
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 2 people take the trip rather than 8, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/8
(E)  3x/80
Rationale: Just plugging in values
X= 16
Cost per person if we consider 2 = 8
Cost per person if we consider 8 = 2
Difference between costs is 6 dollars.
Plugging in the value of x into the answer choices, let's see which one yields a result of 6. And that is D.
Answer: (D)  3x/8
Question: If m/77 is an integer, then each of the following must be an integer EXCEPT
(A) 3
(B) 4
(C) 5
(D) 6
(E) 13/2
Rationale: Now plug m =77 into the answer choices:
A. (77- 28)/7 =7. This is an integer
B. (77+ 21)/7 =14. This is an integer
C. 14(77)/98 =11. This is an integer
D. (77^2 - 49)/49 =120. This is an integer
E. (77+ 14)/14 = 13/2. This is NOT an integer
Answer: E
Answer: (E) 13/2
Question: John & Mary go for an interview for 2 vacancies. The probability for the selection of John is 1/3 & whereas the probability forthe selection of Mary is 1/5. What is the probabilitynone of them are selected?
(A) 2/11
(B) 3/14
(C) 8/15
(D) 7/13
(E) 8/11
Rationale: Let A = the event that John is selected and B = the event that Dani is selected.
Given that P(A) = 1/3 and P(B) = 1/5
We know that A¯ is the event that A does not occur and B¯ is the event that B does not occur
Probability that none of them are selected
=P(A¯∩B¯)(∵ Reference : Algebra of Events)
=P(A¯).P(B¯) (∵ Here A and B are Independent Events and refer theorem on independent events)
=[ 1 - P(A) ][ 1 - P(B)]
=(1−13)(1−15)
=23×45=8/15
C
Answer: (C) 8/15
Question: In a can, there is a mixture of milk and water in the ratio 1 : 5. If it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 3 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 8
(E) 56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 1/6 (T - 2)
After adding milk, quantity of milk in the mixture = 3/8 T.
3T/8 - 2 = 1/6=(T - 2)
10T = 96 - 16 => T = 8
Answer:D
Answer: (D) 8
Question: Six family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
(A) 48
(B) 56
(C) 64
(D) 72
(E) 80
Rationale: Let's consider Michael and Bobby as one unit.
There are 5! possible arrangements of 5 units.
Around a table, there would be repetitions of each arrangement, so we divide by 5.
Then there are 4! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 4!*2 = 48.
The answer is A.
Answer: (A) 48
Question: A reduction of 25% in the price of salt enables a lady to obtain 10kgs more for Rs.800, find the original price per kg?
(A) 25.67
(B) 26.67
(C) 27.2
(D) 26.98
(E) 27.76
Rationale: Answer:	800*(25/100) = 200 --- 10
? --- 1 => Rs.20
800 --- 600
? --- 20 => Rs.26.67.Answer: B
Answer: (B) 26.67
Question: What is the thousandths digit in the decimal equivalent of 64/5000?
(A) 2
(B) 1
(C) 3
(D) 5
(E) 6
Rationale: 64/5000 = 64 /(5*10^3)
= (64/5) *10^-3
=12.8 * 10^-3
=.0128
Thousandths digit = 2
Answer A
Answer: (A) 2
Question: On a baseball team, 5 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
(A) 2/5
(B) 3/5
(C) 3/10
(D) 7/10
(E) 11/20
Rationale: The total number of ways to choose three players is 5C3=10.
Excluding Alice, the number of ways to choose three players is 4C3=4.
P(Alice is not chosen)=4/10=2/5.
P(Alice is chosen)=1 - 2/5 = 3/5.
The answer is B.
Answer: (B) 3/5
Question: in a house there are two rooms in a cube form with surface area 150 and 96 respectively. then what is the ratio between their volumes?
(A) 125:64
(B) 64:125
(C) 5:4
(D) 4:5
(E) 1:2
Rationale: 6a12:a22=150:96
a12:a22=25:16
a1:a2=5:4
then volume a13:a23=:125:64
the answer is A
Answer: (A) 125:64
Question: If A's height is 40% less than that of B, how much percent B's height is more than that of A?
(A) 66.66%
(B) 66.68%
(C) 66.766%
(D) 86.66%
(E) 66.65%
Rationale: Excess of B's height over A's = [(40/(100 - 40)] x 100%
= 66.66%
Answer: A) 66.66%
Answer: (A) 66.66%
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) 3:4:4
(B) 3:4:7
(C) 3:4:3
(D) 3:4:9
(E) 3:4:1
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336
= 3:4:7
Answer: B
Answer: (B) 3:4:7
Question: The product of two successive numbers is 2652. Which is the smaller of the two numbers?
(A) 51
(B) 68
(C) 57
(D) 55
(E) 37
Rationale: A
51
From the given alternatives,
51 × 52 = 2652
∴ Smaller number = 51
Answer: (A) 51
Question: An electronics store purchased a CD player at a wholesale price of 60$ and then sold it at a 40 percent discount off the original retail price. If the store made a 25 percent profit on the whole price of the CD player, what was the stores profit as a percent of the original retail price?
(A) 10%
(B) 12%
(C) 15%
(D) 18%
(E) 20%
Rationale: Store makes 25% on WP so Store sold CD for $75 ($60*.25+$60). The question tells us that the store sold the CD 40% off its ORP so 75=.6(ORP)=125. From here we just need to answer the specific question of what percent of the ORP was the stores profit..hence 15=x/100(125)=12%;ANSWER:B
Answer: (B) 12%
Question: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of the three numbers is 45, what is the value of a?
(A) 21
(B) 25
(C) 28
(D) 30
(E) 33
Rationale: Let a=2k, b=3k, and c=4k.
a+b+c = 2k+3k+4k = 9k
Since the average is 45:
9k/3 = 45
3k = 45
k=15
Then a=30.
The answer is D.
Answer: (D) 30
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.25000, find their shares?
(A) 15005
(B) 15009
(C) 15004
(D) 15000
(E) 150012
Rationale: The ratio of their profits A:B = 8:12 = 2:3
Share of A in the total profit = 2/5 * 25000
= Rs.10000 Share of A in the total profit = 3/5 * 25000
= Rs.15000
Answer:D
Answer: (D) 15000
Question: From the below series find the remainder? 1201 × 1203 ×1205 × 1207 is divided by 6.
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: If you don't know the above rule, this problem is really calculation intensive.
But by applying the above rule, when 1201, 1201, 1203, 1204 divided by 6, leaves remainders 1, 3, 5, 1. The product of these remainders = 15.
When 15 is divided by 6, Remainder is 3
A
Answer: (A) 3
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 19students?
(A) 14 years
(B) 17 years
(C) 19 years
(D) 21 years
(E) None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 19
= 14 years.
Answer A
Answer: (A) 14 years
Question: In 15 year’s time the combined age of my four brothers will be 107. What will it be in the six year’s time?
(A) 61
(B) 78
(C) 71
(D) 68
(E) 94
Rationale: C
71
Combined age in 15 years = 107.
4 × 15 = 60,
Therefore combined age now is 107– 60 = 47.
In 6 years time, therefore, combined age will be 47 + 24(4 x 6) = 71.
Answer: (C) 71
Question: If x#y is defined to equal x^2/y for all x and y, then (-1#2)#-3 =
(A) 1/12
(B) 1/3
(C) 1/2
(D) -1/12
(E) -4/3
Rationale: (-1)^2 / 2 = 1/2
(-1/2)^2 /- 3 =- 1/12
so D is my answer
Answer: (D) -1/12
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both
A and B, working together to do same job
(A) 49
(B) 249
(C) 349
(D) 449
(E) None of these
Rationale: Explanation:
In this type of questions, first we need to calculate 1 hours work, then their collective work as
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
=
449
Answer: D
Answer: (D) 449
Question: If A lends Rs.1200 to B at 10% per annum and B lends the same sum to C at 18% per annum then the gain of B in a period of 2 years is?
(A) 190
(B) 188
(C) 192
(D) 145
(E) 188
Rationale: (1200*8*2)/100
=> 192
Answer: C
Answer: (C) 192
Question: Working alone, machine X can manufacture 1,000 nails in 12 hours. Working together, machines X and Y can manufacture 1,000 nails in 6 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone?
(A) 3 9/17
(B) 5 1/3
(C) 7
(D) 7 1/5
(E) 12
Rationale: rate of machine x = 1000/12
(1000/12 + y)6=1000
y=500/6=250/3
250/3 * t = 1000
t=12
E. 12
Answer: (E) 12
Question: If Sharon's weekly salary increased by 15 percent, she would earn $575per week. If instead, her weekly salary were to decreased by 12 percent, how much would she earn per week?
(A) Rs.540
(B) Rs.580
(C) Rs.560
(D) Rs.620
(E) Rs.650
Rationale: Soln:-
(575/115)112=560
In this case long division does not take much time.
(23/5)=4.6
4.6*112=Rs.560
ANSWER:C
Answer: (C) Rs.560
Question: Seed mixture X is 40% ryegrass and 60% bluegrass by weight; seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of X and Y contains 30% ryegrass, what percent of the weight of the mixture is X?
(A) 10%
(B) 33.33%
(C) 40%
(D) 50%
(E) 66.67%
Rationale: x - wt of Mix X added
y - wt of Mix Y added
0.4x + 0.25y = 0.3(x+y)
0.1x = 0.05y
x/y = 5/10 = 1/2
y/x = 2
(y+x)/x = 3
=> x/(y+x) * 100 = 100/3 = 33.33%
ANSWER:B
Answer: (B) 33.33%
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
(A) 22
(B) 21
(C) 88
(D) 37
(E) 29
Rationale: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21
Answer: B) 21
Answer: (B) 21
Question: In an election between two candidates, 75% of the voters cast thier thier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 15000
(B) 17000
(C) 16800
(D) 16600
(E) 15800
Rationale: Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x).
75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.
Answer is C.
Answer: (C) 16800
Question: What will come in place of the x in the following Number series? 6, 12, 21, 33 , 48 ,66 , x
(A) 33
(B) 35
(C) 39
(D) 41
(E) 87
Rationale: The pattern is + 6, + 9, + 12, +15 + 18+ 21 â€¦â€¦â€¦..
So the missing term is = 66 + 21 = 87
ANSWER : E
Answer: (E) 87
Question: In a shipment of televisions, 1/50 of the televisions are defective. What is the ratio of defective to nondefective televisions?
(A) 1/50
(B) 2/50
(C) 1/49
(D) 2/49
(E) 3/50
Rationale: If 1/50 then
1 - 1/50 = 49 / 50 are not defective
So if x is the total number of TV sets, then (1/50)x are defective and (49/5)x are not defective. Hence the ratio of defective to non defective is given by
x(1 / 50) / x(49 / 50) = (1/50)(50/49) = 1/49
correct answer C
Answer: (C) 1/49
Question: What percent is 5 gm of 1 kg?
(A) 0.5 %
(B) 1%
(C) 1.5%
(D) 2%
(E) 3%
Rationale: 1 kg = 1000 gm
5/1000 × 100 = 500/1000
=1/2 = 0.5 %
A)
Answer: (A) 0.5 %
Question: There are cats got together and decided to kill the mice of 999964. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
(A) 941,1009
(B) 991,1001
(C) 991,1009
(D) 791,1009
(E) 994,1006
Rationale: 999964 can be written as 1000000 â€“ 36
= 10002 â€“ 62 ie of the form a2-b2=(a+b)(a-b)
=(1000+6)*(1000-6)
= (1006)*(994)
Given that number of cats is less than number if mice.
So number of cats is 994 and number of mice were 1006
Answer E
Answer: (E) 994,1006
Question: The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1.
a ∇ b = ( a x b)a+b if a x b is positive else a ∇ b = 1.
(2 # 1 ) / (1 ∇ 2) =
(A) 1/8
(B) 1
(C) 3/8
(D) 3
(E) 7
Rationale: Explanation :
Here, a and b both are positive numbers.
Hence, the required value is (2 + 1) / 23 i.e 3 / 8.
Answer : C
Answer: (C) 3/8
Question: From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
(A) 432
(B) 594
(C) 864
(D) 1330
(E) 7980
Rationale: C112∗C29=12∗36=432, where C112 is ways to select 1 astronaut with previous experience out of 12 and C29 is ways to select 2 astronauts without experience out of 9 remaining astronauts (21-12=9).
Answer: A.
Answer: (A) 432
Question: If x=3, which of the following is(are) true? I. x^2=2x II x/3 = 1 III |x|=-x
(A) I only
(B) III only
(C) II only
(D) I,II only
(E) I,III only
Rationale: 3/3 =1
Answer : C
Answer: (C) II only