mathewhe/aqua_rat huggingface dataset:
Question: A group of hikers is planning a trip that will take them up a mountain using one route and back down using another route. They plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up, but the time each route will take is the same. If they will go up the mountain at a rate of 8 miles per day and it will take them two days, how many miles long is the route down the mountain?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 25
Rationale: On the way down, the rate is 1.5*8 = 12 miles per day.
The distance of the route down the mountain is 2*12 = 24 miles.
The answer is D.
Answer: (D) 24
Question: If x:y=9:4 then (7x-3y) : (7x+3y)=?
(A) 51:76
(B) 6:13
(C) 51:75
(D) 51:76
(E) None of these
Rationale: Explanation:
x/y = 9/4 (Given)
(7x − 3y)/(7x + 3y)
7(x/y) − 3/7(x/y)+3
( on dividing Nr and Dr by y)
(7(9/4) − 3)/(7(9/4) + 3)
(63/4 − 3/1)/(63/4 + 3/1)
[(63 − 12)/4]/[(63 + 12)/4] = 51/75
(7x-3y) : (7x+3y) = 51:75
Answer: Option C
Answer: (C) 51:75
Question: The sum of three numbers is 294. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
(A) 20
(B) 30
(C) 38
(D) 90
(E) None of these
Rationale: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 294
or 49x = 294 or x = 6
⇒ Second number = 15x = 15 × 6 = 90
Answer D
Answer: (D) 90
Question: A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $204, what is the fewest number of $4 Frisbees that could have been sold?
(A) 24
(B) 12
(C) 8
(D) 4
(E) 2
Rationale: In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 60
3x + 4y = 204
x = 60 - y
3(60-y) + 4y = 204
180 - 3y + 4y = 204
y = 24
Answer: A
Answer: (A) 24
Question: There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly then what is the probability that neither blue nor green?
(A) 2/21
(B) 3/31
(C) 4/17
(D) 3/19
(E) probability=8/21
Rationale: Total number of balls = (8 + 7 + 6) = 21
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 8.
P(E) = 8/21.
Answer: (E) probability=8/21
Question: For an upcoming charity event, a male vocalist has agreed to sing 7 out of 9 “old songs” and 5 out of 8 “new songs.” How many ways can the singer make his selection?
(A) 25
(B) 50
(C) 150
(D) 480
(E) 161.28
Rationale: =9C7*8C5
=9*8/5*8*7/5
=161.28
Ans = E
Answer: (E) 161.28
Question: In a 1100 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy who runs at 4 m/s ?
(A) 100 sec.
(B) 55 sec
(C) 25 sec
(D) Data not sufficient
(E) None of these
Rationale: Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1100/5 = 220 sec.
Time taken by Baley to complete the race is D = 1000/4 = 275 sec.
Hence, D-B = 55 sec
ANSWER:B
Answer: (B) 55 sec
Question: Workers at a campaign office have 2000 fliers to send out. If they send out 1/4 of them in the morning and 1/5 of the remaining ones out during the afternoon, how many are left for the next day?
(A) 300
(B) 800
(C) 1100
(D) 1200
(E) 1180
Rationale: (1/4)*2000 = 500
Remaining = 2000-500 = 1500
(1/5) of remaining = (1/5)*1600 = 320
Remaining now = 1500-320 = 1180
Answer: Option E
Answer: (E) 1180
Question: A present value of a machine is $40000. Its value depletiation rate is 5% per annum then find the machine value after 2 years?
(A) $36540
(B) $36100
(C) $29580
(D) $31256
(E) $41250
Rationale: P= $40000
R = 5%
T = 2 years
Machine value after 3years = P/(1-R/100)^T
=40000*19/20 * 19/20 * 19/20
=$36100
Answer is B
Answer: (B) $36100
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 40, 55, 60, then the average marks of all the students is:
(A) 51.25
(B) 54.68
(C) 55
(D) 56
(E) None of these
Rationale: Explanation:
Required average = (55 × 40 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2200 + 3300 + 2700/160)
= 8200/160
= 51.25
Answer: A
Answer: (A) 51.25
Question: The sum of two numbers is 29 and the difference of their squares is 145. The difference between the number is
(A) 13
(B) 5
(C) 8
(D) 11
(E) 12
Rationale: Explanation:
Let the numbers be x and y.
We know that,
(x−y)=x2−y2/(x+y)
=145/29=5
Correct Option: B
Answer: (B) 5
Question: If H = 775 × 778 × 781, what is the remainder when H is divided by 14?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: H 775/14 leaves a remainder 5
778/14 leaves a remainder 8
781/14 leaves a remainder 11
5*8*11 =440
So the remainder will be the remainder of 440/14 which is 6
Ans A
Answer: (A) 6
Question: the sum of 3rd and 9th term of A.P is 8. find the sum of 1st 11 terms of A.P
(A) 33
(B) 22
(C) 44
(D) 55
(E) 66
Rationale: A.P. series is a, a+d, a+2d, a+3d, a+4d,..............nth terms
where a = first term
d = common difference
We have to given,
sum of 3rd and 9th terms = 8
(a+2d)+(a+8d) = 8
2a+10d = 8
a+5d = 4.............(1)
formula, Sum of 1st 11 terms of AP
S = n[ 2a+(n-1)d ]/2
=11[ 2a+(11-1)d ]/2
=11[a+5d]
=11[4] ( from eq. ...(1) )
S = 44
ANSWER:C
Answer: (C) 44
Question: What is the total number of prime numbers less than 55?
(A) 17
(B) 18
(C) 16
(D) 20
(E) 21
Rationale: Solution
Prime numbers less than 55 are	=16.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53
Their number is 16.
Answer C
Answer: (C) 16
Question: Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.58, b = 2.95, and c = 3.65, what is y – x?
(A) -0.1
(B) 0.2
(C) 0.05
(D) 0.1
(E) 0.2
Rationale: To find x, we first sum a, b, and c, then round to the tenths place. 5.58 + 2.95+ 3.65 = 12.18, which rounds to 12.2.
To find y, we first round a, b, and c to the tenths place and them sum them. so 5.5 + 2.9 + 3.6 = 12.0.
We are looking for y - x, which gives us 12.5 - 12.4 = 0.2, or answer choice B.
B
Answer: (B) 0.2
Question: An agency wants to buy furnitures of x% of a list of 10,000 furnitures in a catalogue. After a market price increase, the agency must reduce this selection by (x − 2)%. In terms of x, how many furnitures will the agency be able to buy?
(A) x*x – 2x
(B) (x)(102 – x)
(C) (100)(102 – x)
(D) (100)(98 – x)
(E) (x-2)/100
Rationale: Based on the answer choices and the question, this question begs the use of x=2 as a sample number.
Initial = 2%*10000 = 200
Reduction = 2-2=0%, so no math required here to calculate the reduction; just make sure that you can calculate 200 in your answer.
A. x*x – 2x = 0; No
B. (x)(102 – x) = 200; Winner!
C. (100)(102 – x) > 200; No
D. (100)(98 – x) > 200; No
E. (x-2)/100 = 0; No
B
Answer: (B) (x)(102 – x)
Question: There are 2 red chips and 4 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
(A) A)10
(B) B)12
(C) C)50
(D) D)60
(E) E)100
Rationale: Using anagram method:
6_5_4_3_2_1
R_R_B_B_B_B
so..
6!/Number of repeated letters (2!)(4!) = 10
ANS:E
Answer: (E) E)100
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
(A) 30 birds
(B) 22 birds
(C) 18 birds
(D) 38 birds
(E) 28 birds
Rationale: Let total number of shots =x
Shots fired by A =5x/8
Shots fired by B =3x/8
Killing shots by A
=(5x/8)×(1/3)=5x/24
Missing shots by B
=(3x/8)×(1/2)=3x/16
B has missed 27 times
⇒3x/16=27
⇒x=(27×16)/3=144
Hence, killing shots by A
=5x/24=(5×144)/24=30
i.e., A has killed 30 birds
Answer: A
Answer: (A) 30 birds
Question: What day of the week does May 28 2006 fall on
(A) Saturday
(B) Monday
(C) Sunday
(D) Thursday
(E) None of these
Rationale: Explanation :
28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6
Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148
148 days = 21 weeks + 1 day = 1 odd day
Total number of odd days = (0 + 6 + 1) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence May 28 2006 is Sunday. Answer : Option C
Answer: (C) Sunday
Question: Ajay, Bhavan and Chetan started a business together. Thrice the investment of Ajay, twice the investment of Bhavan and the investment of Chetan are equal. Find the ratio of their respective profits at the end of the year?
(A) 1:2:1
(B) 2:3:6
(C) 3:2:1
(D) 1:2:3
(E) 1:4:3
Rationale: Let the investments of Ajay, Bhavan and Chetan be Rs,a, Rs.b and Rs.c respectively.
3b = 2b = c.
a = c/3.
b = c/2.
Ratio of profits of Ajay, Bhavan and Chetan at the end of one year = Ratio of their respective investments
= 2:3:6.
ANSWER:B
Answer: (B) 2:3:6
Question: 125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 3:7
(B) 3:9
(C) 3:1
(D) 3:4
(E) 3:2
Rationale: Milk = 3/5 * 125 = 75 liters
Water = 50 liters
75 : (50+P) = 3:4
150 + 3P = 400 => P = 50
50 liters of water are to be added for the ratio become 3:4.
Answer:D
Answer: (D) 3:4
Question: Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 10 different shirts, 10 different pairs of jeans, and 8 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have?
(A) 30
(B) 90
(C) 240
(D) 480
(E) 800
Rationale: Total # of outfits = 10 * 10 * 8 = 800
Answer - E
Answer: (E) 800
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
(A) 8 days
(B) 5 days
(C) 4 days
(D) 6 days
(E) 2 days
Rationale: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B
= 1/4 + 1/12 = 1/3.
Total time required to complete the work
= 2 * 3 = 6 days.
Answer: D
Answer: (D) 6 days
Question: There are 7 red cups and 5 blue cups on a shelf. If 4 cups are selected at random from the shelf, what is the probability that all 4 cups selected are red cups?
(A) 1/99
(B) 5/99
(C) 7/99
(D) 11/99
(E) 17/99
Rationale: The number of ways of choosing 4 cups from the shelf is 12C4 = 495.
The number of ways of choosing 4 red cups is 7C4 = 35.
P(4 red cups) = 35/495=7/99.
The answer is C.
Answer: (C) 7/99
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
(A) 150 meter
(B) 178 meter
(C) 209 meter
(D) 279 meter
(E) 269 meter
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9
=150 meter
Answer:A
Answer: (A) 150 meter
Question: A train 90 meters long completely crosses a 200 meters long bridge in 36 seconds. What is the speed of the train is?
(A) 29
(B) 40
(C) 25
(D) 66
(E) 09
Rationale: S = (90 + 200)/36 = 290/36 * 18/5 = 29
Answer: A
Answer: (A) 29
Question: In a game of 80 points, A can give B 5 points and C 15 points. then how many points B can give C in a game of 60?
(A) 7 points
(B) 8 points
(C) 9 points
(D) 10 points
(E) 11 points
Rationale: In a game of 80 points,A give B 5 points and c 15 points means B=75,C=65
In 75 points B give 10 since 75-65=10
In 60 points B gives=60*10/75=8
so ans 8 points
ANSWER:B
Answer: (B) 8 points
Question: In 20 minutes, the minute hand gains over the hour hand by
(A) 16°
(B) 80°
(C) 88°
(D) 96°
(E) 110°
Rationale: In one hour, the hour hand moves 30°, which is 0.5° each minute.
In one hour, the minute hand moves 360°, which is 6° each minutes.
The minute hand gains 5.5° each minute.
In 20 minutes, the minute hand gains 20 * 5.5° = 110°.
The answer is E.
Answer: (E) 110°
Question: The length of a rectangle is halved, while its breadth is tripled. Watis the % change in area?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: Let original length = x and original breadth = y.
Original area = xy.
New length = x .
2
New breadth = 3y.
New area = x x 3y = 3 xy.
2 2
Increase % = 1 xy x 1 x 100 % = 50%.
2 xy
C
Answer: (C) 50%
Question: On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄2 of the total distance and again after she traveled 1⁄4 of the distance remaining between her first stop and her destination. She then drove the remaining 400 miles and arrived safely at her destination. What was the total distance, in miles, from Traci’s starting point to Seal Beach?
(A)  250
(B)  3200/3
(C)  3150/3
(D)  4002/3
(E)  550
Rationale: Let D = total distance
Traci traveled 1/2 = D/2
i.e. remaining distance = D/2
She traveled 1/4 th of D/2 = D/8
Thus:
D = (D/2) + (D/8) + 400
D = 3200/3
ANSWER: B
Answer: (B)  3200/3
Question: There is a family of six persons A, B, C, D, E and F. They are Lawyer, Doctor, Teacher, Salesman, Engineer and Accountant There are two married couples in the family. D, the Salesman is married to the Lady Teacher. The Doctor is married to the Lawyer. F, the Accountant is the son of B and brother of E. C, the Lawyer is the daughter-in-law of A. E is the unmarried Engineer. A is the grandmother of F. How is E related to F?
(A) Brother
(B) Sister
(C) Cousin
(D) Cannot be determined
(E) father
Rationale: Explanation:
C is the daughter-in-law of A who is the grandmother of F means C is the mother of F. But F is the son of B.
So. B is C's husband. But C, the lawyer is married to the Doctor So. B is the Doctor. F, the Accountant will be the son of B and C. E is the unmarried Engineer
So. the other mamed couple can be that of grandmother of F i.e, A and D. But D, the Salesman, is married to the Lady Teacher.
So. D, the Salesman, is the grandfather of F. father of B and the husband of A, the Lady Teacher.
Clearly, from the given data, the relation between E and F cannot be determined.
Answer: D)
Answer: (D) Cannot be determined
Question: Hillary and Eddy are climbing to the summit of Mt. Everest from a base camp 5,100 ft from the summit. When they depart for the summit at 06:00, Hillary climbs at a rate of 800 ft/hr with Eddy lagging behind at a slower rate of 500 ft/hr. If Hillary stops 1100 ft short of the summit and then descends at a rate of 1,000 ft/hr, at what time do Hillary and Eddy pass each other on her return trip?
(A) 14.0
(B) 9.0
(C) 10.0
(D) 11.0
(E) 12.0
Rationale: Solution:H stopped 800 ft before reaching the final point, time taken to reach 4000 ft= 4000/800= 5hrs.
this means she reached there at 11:00.
speed difference between them is 800-500=300 ft/hr
so by the time H stops they have 1500 ft of distance
so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft/hr and distance between them is 1500 ft so time taken to meet = 1 hr from 11:00
means 12:00 is the answer.
E
Answer: (E) 12.0
Question: Pipes A and B can fill a tank in 3 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in?
(A) 3 9/97 hrs
(B) 3 9/77 hrs
(C) 3 9/17 hrs
(D) 3 9/27 hrs
(E) 2 2/5 hrs
Rationale: Net part filled in 1 hour = 1/3 + 1/6 - 1/12
= 5/12
The tank will be full in 12/5 hrs, i.e., 2 2/5 hrs.
Answer:E
Answer: (E) 2 2/5 hrs
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1245, find the loss %?
(A) 17%
(B) 16%
(C) 19%
(D) 78%
(E) 28%
Rationale: 1500 ---- 255
100 ---- ? => 17%
Answer:A
Answer: (A) 17%
Question: If the annual rate of simple interest increases from 10% to 12 1/2 %, a man's yearly income increases by Rs. 1250. His principal in Rs. is?
(A) 29879
(B) 50000
(C) 72900
(D) 27992
(E) 89282
Rationale: Let the sum be Rs. x. Then,
(x * 25/2 * 1/100) - (x * 10 * 1)/100 = 1250
25x - 20x = 250000
x = 50000
Answer: B
Answer: (B) 50000
Question: Two pipes A and B can fill a cistern in 37 1/2minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after
(A) 5 min
(B) 9 min
(C) 10 min
(D) 15 min
(E) 17 min
Rationale: Explanation:
Part filled by pipe A in 1 minute = 2 7/5
Part filled by pipe B in 1 minute =1 4/5
Suppose pipe B is closed after x minutes. Then,
2 7/5 × 30 +1 4/5 × x =1
4/5 +x/45 =1
x=9
Answer: Option B
Answer: (B) 9 min
Question: Joey throws a dice 3 times and decides to invite the same number of guests for his birthday party as the sum of the outcomes of the throws. What’s the probability that he invites 12 guests?
(A) 1/6
(B) 1/16
(C) 1/18
(D) 1/36
(E) 25/216
Rationale: Total outcomes:
6^3.
Favorable outcomes:
{6 - 5 - 1} - 6 cases ({6 - 5 - 1}, {6 - 1 - 5} , {5 - 6 - 1}, {5 - 1 - 6}, {1 - 6 - 5}, {1 - 5 - 6});
{6 - 4 - 2} - 6 cases;
{6 - 3 - 3} - 3 cases;
{5 - 5 - 2} - 3 cases;
{5 - 4 - 3} - 6 cases;
{4 - 4 - 4} - 1 case.
6 + 6 + 3 + 3 + 6 + 1 = 25.
P = (favorable)/(total) = 25/6^3.
Answer: E.
Answer: (E) 25/216
Question: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
(A) 3
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
A
Answer: (A) 3
Question: The following sets each have a mean of 5 and the standard deviations are given in variable form.
Set I = {5, 5, 5, 5, 5, 5}, standard deviation = H
Set II = {1, 1, 1, 9, 9, 9}, standard deviation = J
Set III = {2, 3, 4, 6, 7, 8}, standard deviation = K
Rank these three standard deviations from least to greatest.
(A) K, J, H
(B) K, H, J
(C) H, J, K
(D) H, K, J
(E) J, H, K
Rationale: The answer should be D as the mean is least deviated in Set I followed by Set III and then Set II.
Answer: (D) H, K, J
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 6
(B) 5
(C) 4
(D) 7
(E) 8
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7.Answer: D
Answer: (D) 7
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 90. What is the largest among them?
(A) 21
(B) 24
(C) 27
(D) 33
(E) 45
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 90
3X = 81
X = 27
The numbers are 27, 30, 33
Therefore the largest number is 33
Answer D.
Answer: (D) 33
Question: A watch was sold at a loss of 16%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 700
(B) 882
(C) 799
(D) 778
(E) 901
Rationale: 84%
104%
--------
20% ---- 140
100% ---- ? => Rs.700
Answer: A
Answer: (A) 700
Question: P and Q had the same number of candies. P gave Q 22 candies so that now Q has five times as many candies as P has. How many candies does Q have now?
(A) 35
(B) 40
(C) 45
(D) 50
(E) 55
Rationale: Let P and Q be the number of candies they had at the start.
P = Q
5(P-22) = Q+22
5(Q-22) = Q+22
4Q = 132
Q = 33
Now person Q has 33+22 candies which is 55 candies.
The answer is E.
Answer: (E) 55
Question: if below equation are true
24$6=64
35$5=87
63$7=99
by using same logic what is the value of the below question
88$8=?
(A) 1621
(B) 1711
(C) 1611
(D) 1511
(E) 1311
Rationale: Correct Answer : C
the number on the right side is formed as (sum of digits of the 1st number)
no1/ no2
ex:
35$5=87 (3+5=8)(35/5=7)
63$7=99 (6+3=9)(63/7=9)
Answer: (C) 1611
Question: A, B and C can do a work in 18, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
(A) 9
(B) 16
(C) 17
(D) 18
(E) 11
Rationale: One days's work of A, B and C = 1/18 + 1/30 + 1/45
= (5 + 3 + 2)/90 = 1/9
A, B and C together can do the work in 9 days.
Answer:A
Answer: (A) 9
Question: In a full deck of 52 cards, there are 13 spades. A game is played whereby a card from is chosen at random from the deck. If the card is a spade, a winner is declared. If the card is not a spade, it is returned to the deck, the deck is reshuffled and another card is drawn. This process is repeated until a spade is drawn. What is the probability that one will pick the first spade on the second draw or later?
(A) 1/8
(B) 1/4
(C) 1/2
(D) 3/4
(E) 7/8
Rationale: Favorable case = the spade is picked in the third draw or later
Unfavorable case = The spade is picked in either first draw or in second draw
Probability = Favorable outcomes / Total out comes
Also probability = 1-(Unfavorable outcomes / Total out comes)
Unfavorable case: probability of spade picked in first draw = 13/52 =1/4
i.e., Favorable Probability = 1 - (1/4) = 3/4
Answer Option: D
Answer: (D) 3/4
Question: In a game of billiards, A can give B 10 points in 50 and he can give C 30 points in 50. How many points can B give C in a game of 100?
(A) 65
(B) 60
(C) 70
(D) 50
(E) 75
Rationale: A scores 50 while B score 40 and C scores 20.
The number of points that C scores when B scores 100 = (100 * 20)/40 = 50.
In a game of 100 points, B gives (100 - 50) = 50 points to C
Answer:D
Answer: (D) 50
Question: A person got Rs.55 more when he invested a certain sum at compound interest instead of simple interest for two years at 9% p.a. Find the sum?
(A) 6790
(B) 6890
(C) 6700
(D) 2667
(E) 2671
Rationale: P = (d * 1002) / R2
=> (55 * 100 * 100) / 9 * 9 = Rs.6790
Answer:A
Answer: (A) 6790
Question: Rs 70000 is divided into two parts One part is given to a person with 10% interest and another part is given to a person with 20 % interest. At the end of first year he gets profit 8000 Find money given by 10%?
(A) 30000
(B) 40000
(C) 50000
(D) 60000
(E) 70000
Rationale: let first parrt is x and second part is y then x+y=70000----------eq1
total profit=profit on x +profit on y
8000=(x*10*1)/100 + (y*20*1)/100
80000=x+2y-----------------------------------eq2
80000=70000+y
so y=10000 then x =70000-10000=60000
first part =60000
ANSWER:D
Answer: (D) 60000
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 1 hours?
(A) 1.6.
(B) 3.6.
(C) 4.2.
(D) 5.5.
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 4 carpenters in 1 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 1 =1.6 desks
A is the correct answer.
Answer: (A) 1.6.
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 12 years more than the present age of Anand. Find the present age of Anand?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 12
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 2) => 3a - 30 = a + 2
=> 2a = 32 => a = 16.
ANSWER:B
Answer: (B) 16
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
(A) 22
(B) 77
(C) 90
(D) 77
(E) 21
Rationale: SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs. 90.
Answer: C
Answer: (C) 90
Question: If the day after tomorrow is three days before tuesday, do you know which day is today?
(A) sunday
(B) monday
(C) saturday
(D) thursday
(E) wednesday
Rationale: Correct Answer : D
three days before tuesday is saturday, now saturday is day after tomorrow, so today is thursday
Answer: (D) thursday
Question: A and B are two positive number,if A is divisible by 2 but not by 5 and B is divisible by 5 but not by 2, what could be the value of A and B in the following:- [ the answer are given in the order (A,B) ]
(A) ( 10,10)
(B) (8,10)
(C) (10,8)
(D) (8,15)
(E) (15,8)
Rationale: In option (A) , (B) and (C) since all are divisible by 2 and 5 so they are wrong.
In (D),
A=8 ; divisible by 2 but not by 5
B=15 ; divisible by 5 but not by 2.
option (E) is just the opposite of (D)
answer: (D) ie (8,15)
Answer: (D) (8,15)