mathewhe/aqua_rat huggingface dataset:
Question: The total circumference of two circles is 49. If the first circle has a circumference that is exactly twice the circumference of the second circle, then what is the approximate sum of their two radii?
(A) 7.8
(B) 6.0
(C) 6.7
(D) 9.7
(E) 18.0
Rationale: Let r= Radius of smaller circle. Let R = Radius of larger circle
Therefore:
2πr + 2πR = 49
where 2r = R
Thus:
2πr + 4πr = 49
6πr = 49
r = approx 2.6
πR + 2Rπ = 49
3πR = 49
R = approx 5.2
r + R = approx 7.8
Answer :A
Answer: (A) 7.8
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 30, and 40 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
(A)  4/11
(B)  1/2
(C)  15/22
(D)  120/7
(E)  11/4
Rationale: P1 takes 12 hrs
Rate for P2P3 together = 1/30 + 1/40 = 7/120
Therefore they take 120/7
Ratio = 120/7 = D
Answer: (D)  120/7
Question: A total of Y tourists were transported by bus to a certain museum. If there were Z tourists on each bus, which of the following expresses the number of buses used?
(A)  YZ
(B)  Y/Z
(C)  Z/Y
(D)  Y-Z
(E)  Z^2
Rationale: IMHO (B)Y/Z as well !
Number of buses used = Total number of tourists / Number of tourists per bus => Y/Z
PS : In case of any doubt , plug in some numbers
Total number of tourists transported by bus = 500
Number of tourists per bus = 10
No of buses required = 500/10
Answer: (B)  Y/Z
Question: A certain airline's fleet consisted of 80 type A planes at the beginning of 1980. At the end of each year, starting with 1980, the airline retired 3 of the TYPE A planes and acquired 4 new type B plans. How many years did it take before the number of type A planes left in the airline's fleet was less than 50 percent of the fleet?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Let x be the number of years.
4x > 80 - 3x
7x > 80
x > 11 + 3/7
The answer is D.
Answer: (D) 12
Question: 2. Seven movie addicts- Guna, Isha, Leela, Madhu, Rinku, Viji and Yamini attend a film festival. Three films are shown, one directed by Rajkumar Hirani ,one by S.Shankar,and one by Mani Ratnam. Each of the film buffs sees only one of the three films. The films are shown only once, one film at a time. The following restrictions must apply :- Exactly twice as many of the film buffs sees the S.shankar film as see the Rajkumar Hirani film.- Guna and Rinku do not see the same film as each other.- Isha and Madhu do not see same film as each other.- Viji and Yamini see the same film as each other.- Leela sees the S.Shankar film.- Guna sees either the Rajkumar Hirani film or the Mani Ratnam film.Which one of the following could be an accurate matching of the film buffs to films ?(A) Guna: the S.Shankar film; Isha: the Mani Ratnam film; Madhu: the S.Shankar film(B) Guna: the Mani Ratnam film; Isha: the Rajkumar Hirani film; Viji: the Rajkumar Hirani film(C) Isha : the S.Shankar film; Rinku: the Mani Ratnam film; Viji: the Rajkumar Hirani film(D) Madhu: the Mani Ratnam film; Rinku: the Mani Ratnam film; Viji: the Mani Ratnam film
(A) A
(B) B
(C) C
(D) D
(E) NONE
Rationale: Explanation:
Guna × Rinku
Isha × Madhu
(Viji + Yamini)
Leela - Film: Shankar
Guna = RKH/Mani Ratnam
The following options are possible:
RKH	Shankar	Mani Ratnam
1	2	4
2	4	1
We will take options and check them.
Option A: Guna should not watch Shankar's Film. So ruled out
Option B:
RKH	Shankar	Mani Ratnam
Isha	_	Guna
Viji	_	_
Now Yamini also watch RKH. Which is not possible.
Option C:
RKH	Shankar	Mani Ratnam
Viji	Isha	Rinku
Yamini	Leela	_
As Guna should not be watching Shankar's movie she should watch Mani ratnam's which is not possible.
Option D:
RKH	Shankar	Mani Ratnam
Guna	Leela	Madhu
_	Isha	Rinku
_	_	Viji and Yamini
Answer:B
Answer: (B) B
Question: If xy is an integer, which of the following must also be an integer?
I. x/y
II. x
III. y/x
(A) I alone
(B) II alone
(C) I and II
(D) I and III
(E) None of the above
Rationale: Lets take X = 3 and Y = 7
Then XY = 21 which is an integer.
But X/Y = 3/7 --> Not an integer.
Y/X = 7/3 --> Not an integer.
X alone is 3. which is an integer.
Hence B.
Answer: (B) II alone
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be
(A) 45 min
(B) 60 min
(C) 55 min
(D) 70 min
(E) 80 min
Rationale: Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Answer : B.
Answer: (B) 60 min
Question: If 7 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 3:2
(B) 2:3
(C) 3:3
(D) 1:2
(E) 6:1
Rationale: B
2:3
7M + 2B = 4(1M + 1B)
7M + 2B = 4M + 4B
3M = 2B
The required ratio of work done by a man and a boy = 2:3
Answer: (B) 2:3
Question: The speed of a boat in still water is 55kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) kmph
(B) kmph
(C) kmph
(D) kmph
(E) kmph
Rationale: Speed downstream = 55 + 20 =75 kmph
Speed upstream = 55 - 20 = 35 kmph
Answer:B
Answer: (B) kmph
Question: A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn, meeting the circumference of the semicircle at D. Given that AC=2cm and CD=6cm, the area of the semicircle in square cm will be ?
(A) 30pi
(B) 40pi
(C) 50pi
(D) 60pi
(E) 70pi
Rationale: let O be center of circle and radius be x.
C can be anywhere on AB.Let us suppose that C is somewhere between A and O.
AC=2cm....so CO=(x-2)
DO=x,CD=6cm
CDO form a right angled triangle with right angle at C.
Using Pythagoras theorem,
x^2=6^2+(x-2)^2
4x=40
x=10cm
area=[pi(x)^2]/2
area=50pi
ANSWER:C
Answer: (C) 50pi
Question: In how many ways a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
(A) A)12540
(B) B)11450
(C) C)11760
(D) D)13250
(E) E)12450
Rationale: Required number of ways = 8C5*10C5 = 8C3*10C4 = 11760
Answer is C
Answer: (C) C)11760
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 768 as interest at the end of the loan period, what was the rate of interest?
(A) 3.6
(B) 6
(C) 8
(D) Cannot be determined
(E) None of these
Rationale: let rate = R% and time = R years
Then ( 1200 x R x R /100) = 768
=> 12R2= 768
=> R2= 64
=> R= 8
Answer C
Answer: (C) 8
Question: Looking at a portrait of a man, Harsh said, "His mother is the wife of my father's son. Brothers and sisters I have none." At whose portrait was Harsh looking ?
(A) His son
(B) His cousin
(C) His uncle
(D) His nephew
(E) His Sister
Rationale: Explanation:
Since Harsh has no brother or sister, so he is his father's only son. Now, wife of my father's son — my wife.
So, Harsh's wife is the man's mother or the man is Harsh's son.
Answer: A) His son
Answer: (A) His son
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 100 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
(A) 100 % decrease
(B) 60% decrease
(C) 30% decrease
(D) 40% increase
(E) 50% increase
Rationale: Let's say here is the formula of how A and B affects the reaction speed:
rate = A/B
After the concentration B is increased by 100%, the percentage of B
become 2B, to keep 'rate' the same, need to have 2A being doubled.
Which means A increased by 100%.
Answer : A
Answer: (A) 100 % decrease
Question: In a friendship gang Mala has 5 gang, in how many ways can he invite one or more of the gang to his house?
(A) 31
(B) 12
(C) 58
(D) 74
(E) 36
Rationale: mala can select one or more than one of his 8 gang.
=> Required number of ways = 2^5 – 1= 31.
A
Answer: (A) 31
Question: A 12 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point?
(A) 1/6
(B) 2/3
(C) 3/10
(D) 1/3
(E) 2/5
Rationale: A square with an area of 4 has a perimeter of 8.
For the area to be >4, the longer piece must be >8.
The wire must be cut within 4 meters from either end.
The probability of this is 8/12 = 2/3.
The answer is B.
Answer: (B) 2/3
Question: A laborer is engaged for 30 days on the condition that he receives Rs.25 for each day he works and is fined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was he absent?
(A) 22
(B) 38
(C) 19
(D) 10
(E) 28
Rationale: Explanation:
30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
Answer:D
Answer: (D) 10
Question: In a certain diving competition, 5 judges score each dive on a scale from 1 to 10. The point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty. If a dive with a degree of difficulty of 3.2 received scores of 7.5, 8.1, 9.0, 6.0, and 8.5, what was the point value of the dive?
(A) 68.8
(B) 73.6
(C) 75.2
(D) 77.12
(E) 81.6
Rationale: Degree of difficulty of dive = 3.2
Scores are 6.0 , 7.5 , 8.1 , 8.5 and 9.0
We can drop 6.0 and 9.0
Sum of the remaining scores = (7.5+8.1+8.5)= 24
Point of value of the dive = 24.1*3.2 =77.12
Answer D
Answer: (D) 77.12
Question: List L: ABC, BCA, CAB
In list L above, there are 7 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
(A) 47
(B) 114
(C) 152
(D) 161
(E) 488
Rationale: Let's try to sum the 3 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
E
Answer: (E) 488
Question: (32^32^32)/9 will leave a remainder?????
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 32^32^32=(2^5)^32^32=2^5120.
2^5120/9
=((2^3)^1706*2^2)/9
=((9-1)^1706*2^2)/9
=(-1)^1706*4
=4
ANSWER:C
Answer: (C) 4
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 15. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 354
Rationale: Clearly, the numbers are (23 x 13) and (23 x 15).
Larger number = (23 x 15) = 345.
Answer: Option D
Answer: (D) 345
Question: The food in a camp lasts for 40 men for 50 days. If ten more men join, how many days will the food last?
(A) 20days
(B) 30days
(C) 40days
(D) 50days
(E) 60days
Rationale: one man can consume the same food in 40*50 = 2000 days.
10 more men join, the total number of men = 50
The number of days the food will last = 2000/50 = 40 days.
Answer: C
Answer: (C) 40days
Question: There are 8 girls and 8 boys. If they are to be seated in a row, what is the probability that no two girls sit together?
(A) A)1/16!
(B) B)6!5!/16!
(C) C)6!6!/16!
(D) D)2∗8!8!/16!
(E) E)6!7!/12!
Rationale: If girls are alternate, then only no 2 girls can be together.
So among 16 places, girls can be seated in 8 alternate places in 8! ways.
And boys can be seated in the remaining 8 places in 8! ways.
Therefore total number of ways = 8! * 8!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*8! * 8!
Also total number of ways to fill 16 places = 16!
Hence probability =2∗8!8!/16!
Answer:D
Answer: (D) D)2∗8!8!/16!
Question: Rajesh can finish 1/6 of his home work in one hour. Seema can finish 3/7 of
her homework in 70 minutes and Ramya can finish 3/4 of her homework in
three and a half hours. If all of them start their home work at 12.00 PM and can
go to play as soon as they all finish their homework. When can they start to
play, if they take a break at 3.30 PM for 30 minutes?
(A) 4:30pm
(B) 5:10pm
(C) 6:30pm
(D) 5:30pm
(E) 3:30pm
Rationale: rajesh can finish his work in 6 hr,
ramya can finish her work in 2.7 hr
seema can finish in 3.5 hr
so 6:30pm they can go to play
ANSWER:C
Answer: (C) 6:30pm
Question: Out of 7 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) A)3/7
(B) B)5/4
(C) C)5/7
(D) D)5/6
(E) E)5/3
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - ⁶C₃/¹⁰C₃
= 1 - (6 * 5 * 4)/(7 * 6 * 5)
= 3/7
Answer:A
Answer: (A) A)3/7
Question: A code is to be made by arranging 8 letters. four of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?
(A) 42
(B) 210
(C) 420
(D) 840
(E) 10080
Rationale: we have 8 letters out of which 2 are of one kind, 2 are of another kind..
so total ways = 8!/2!2!=420
ans E
Answer: (E) 10080
Question: A car moves at 102 km/hr. What is the speed of the car in meters per second ?
(A) 20 2/9m sec
(B) 28 1/3m sec
(C) 24 1/9m sec
(D) 26 2/3m sec
(E) 28 2/9m sec
Rationale: Explanation:
Speed=(102∗5/18)m/sec
=85/3 m/sec
=28 1/3msec
Option B
Answer: (B) 28 1/3m sec
Question: x percent of y percent of z is decreased by y percent. What is the result?
(A) (100xyz - xy^2z) / 1000000
(B) (xz - y) / 100
(C) (xz - y) / 10,000
(D) (xyz - 2y) / 100
(E) (xyz - 2y) / 10,000
Rationale: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH
Answer B. (xz - y) / 100 = (1,000 - 50)/100 = 950/100 = 9.5 NOT a match
Answer C. (xz - y) / 10,000 = 950/10,000 = .095 NOT a match
Answer D. (xyz - 2y) / 100 = (50,000 - 100)/100 = 49,900/100 = 499 NOT a match
Answer E. (xyz - 2y) / 10,000 = 49,900/10,000 = 4.99 NOT a match
A
Answer: (A) (100xyz - xy^2z) / 1000000
Question: Ram and Krishna start from A and B respectively at the same time and travel towards each other at constant speeds of 30m/m and 40 m/m respectively along the same route. Ram meets Krishna at point C on the road after 10 minutes. Find the total distance between A to B.
(A) 700 meters
(B) 1000 meters
(C) 700 kilometers
(D) 555 meters
(E) 750 meters
Rationale: Vr=30 m/m, Vk= 40m/m;
t-time for Meet.
distance A-C = 30*10=300 m
distance B-C = 40*10=400 m
therefore distance A-C = 300+400=700 m.
option A
Answer: (A) 700 meters
Question: A hall 36m long and 15m broad is to be paved with stones, each measuring 4dm by 5 dm. The number of stones required is:
(A) 180
(B) 2700
(C) 18
(D) 18000
(E) 1.8
Rationale: Area of the hall= 3600*1500
Area of each stone= (40*50)
Therefore, number of stones= (3600*1500/ 40*50)= 2700
ANSWER:B
Answer: (B) 2700
Question: The market value of a certain machine decreased by 10 percent of its purchase price each year. If the machine was purchased in 1982 for its market value of $8,000, what was its market value two years later?
(A)  $8,000
(B)  $5,600
(C)  $3,200
(D)  $6,400
(E)  $800
Rationale: D
Market value in 1982= $ 8000
Market value in 1983 = $ 8000- ($ 8000 x 10/100) = 8000-800= $ 7200
Market value in 1984 = Market value in 1983 - (10 % of $8000)= 7200-800 = $6400
Answer: (D)  $6,400
Question: On her annual road trip to visit her family in Seal Beach, California, Traci stopped to rest after she traveled 1⁄3 of the total distance and again after she traveled 1⁄2 of the distance remaining between her first stop and her destination. She then drove the remaining 100 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)  300
(C)  350
(D)  400
(E)  550
Rationale: Let D = total distance
Traci traveled 1/3 = D/3
i.e. remaining distance = 2D/3
She traveled 1/2 th of 2D/3 = D/3
Thus:
D = (D/3) + (D/3) + 100
D = 300
ANSWER: B
Answer: (B)  300
Question: In a mixture of 45 litres the ratio of milk to water is 4:1. Additional 21 litres of water is added to the mixture. Find the ratio of milk to water in the resulting mixture.
(A) 2/1
(B) 4/1
(C) 6/5
(D) 3/4
(E) 3/2
Rationale: Given that Milk/Water=4x/x and 4x+x=45 --> x=9.
Thus Milk=4x=36 liters and Water=x=9 liters.
New ratio = 36/(9+21) = 36/30 = 6/5.
Answer: C.
Answer: (C) 6/5
Question: In how many different number of ways a combination of 3 persons can be selected from 4 men and 2 women?
(A) 200
(B) 220
(C) 240
(D) 260
(E) 280
Rationale: 6C3 × 5C2
6C3
= 6!/(3! . 3!)
= (6 × 5 × 4)/(3 × 2)
= 5 × 4 = 20.
5C2
= 5!/(3! . 2!)
= 5 × 2 = 10
= 20 × 10 = 200.
A)
Answer: (A) 200
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 34 per kg. His profit percent is:
(A) No profit, no loss
(B) 5%
(C) 19%
(D) 10%
(E) None of these
Rationale: Explanation :
C.P. of 56 kg rice = (26 * 20 + 30 * 36) Rs. = (520 + 1080) Rs. = 1600 Rs.
S.P. of 56 kg rice = (56 * 34) Rs. = 1904 Rs.
Profit % = (1904−1600/1600∗100)% = 19%
Answer : C
Answer: (C) 19%
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Y that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
(A) 3/5
(B) 2/3
(C) 7/10
(D) 3/4
(E) 4/5
Rationale: X(1+10/100) + Y(1-15/100) = X+Y
this gives 2X = 3Y
or X/Y = 3/2
So, fraction invested in X = 3/5
ANSWER:A
Answer: (A) 3/5
Question: The probabilities of solving a question by 3students A, B & C are 1/2,1/3 &1/4, respectively. The probability that the problem will be solved is?
(A) 1/3
(B) 3/4
(C) 3/5
(D) 3/7
(E) 4/7
Rationale: Sol. First, we find the probability of not solving the problem x PTO x = (1 — D x - D x - D
1 2 3 1 =iXiX71=4;
1 3 Required probability 3/4
B
Answer: (B) 3/4
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
(A) 50
(B) 267
(C) 26
(D) 87
(E) 62
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer:A
Answer: (A) 50
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
(A) 22 Yrs
(B) 25 Yrs
(C) 26 Yrs
(D) 32 Yrs
(E) 34 Yrs
Rationale: Sol. Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 yANSWER B
Answer: (B) 25 Yrs
Question: Three consecutive even numbers are such that thrice the first number exceeds double the third number by three. What is the third number?
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15
Rationale: Let the three numbers be x, x+2, and x+4.
3x = 2(x+4) + 3
x = 11 and then the third number is x+4 = 15.
The answer is E.
Answer: (E) 15
Question: Pipes A and B can fill a tank in 5 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) 3 9/19 hrs
Rationale: Net part filled in 1 hour = 1/5 + 1/6 - 1/12
= 17/60
The tank will be full in 60/17 hrs, i.e., 3 9/17 hrs.
Answer:C
Answer: (C) 3 9/17 hrs
Question: In what time will a train 250 metres long cross an electric pole, if its speed be 162 km/hr?
(A) 4 sec
(B) 5 sec
(C) 5.55 sec
(D) 6.55sec
(E) 4.55 sec
Rationale: Solution
Speed	= (162 x 5 /18) m/sec
= 45 m / sec
Time taken	= (250 /45) sec
= 5.55 sec.
Answer C
Answer: (C) 5.55 sec
Question: At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the men are married?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 3/5
(E) 2/7
Rationale: --------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married man/total man, so 20/30=2/3
C
Answer: (C) 2/3
Question: A manâ€™s current age is (2/5) of the age of his father. After 10 years, he will be (1/2) of the age of his father. What is the age of father at now?
(A) 40
(B) 45
(C) 38
(D) 50
(E) 39
Rationale: Let, fatherâ€™s current age is A years.
Then, Manâ€™s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 10 ]= (1/2)(A + 10)
2(2A + 50) = 5(A + 10)
A = 50
D
Answer: (D) 50
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 65 km
(B) 88 km
(C) 55 km
(D) 66 km
(E) 20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer: E
Answer: (E) 20 km
Question: When 52416 is divided by 312, the quotient is 168. what will be the quotient when 52.416 is divided by 0.12510168?
(A) 5
(B) 6
(C) 10
(D) 3
(E) 8
Rationale: for the 1st no. there are 2 digits after decimal
for the 2nd no. there are 9 digits after decimal
total no. of decimals = 11
req. no. of digits=(n-1)=(11-1)=10
ANSWER :C
Answer: (C) 10
Question: If (a-b) is 6 more than (c+d) and (a+b) is 3 less than (c-d), then (a-c)
(A) 0.5
(B) 1
(C) 1.5
(D) 2
(E) 2.5
Rationale: (a-b)-(c-d)=6 and (c-d)-(a+b)=3
(a-c)-(b+d)=6 and (c-a)-(b+d)=3
(b+d)= (a-c)-6 and (b+d)=3-(c-a)
2(a-c)=3
(a-c)=1.5
ANSWER C 1.5
Answer: (C) 1.5
Question: James took a 3-hour bike ride. In the second hour he traveled 30 miles, which was 20 percent farther than he traveled the first hour. If he traveled 25 percent farther in the third hour than he did in the second hour, how many miles did jose travel during the entire ride?
(A) 54.0
(B) 54.9
(C) 92.5
(D) 57.0
(E) 63.0
Rationale: Let the distance travelled in the first hour be x. Thus, 1.2x = 30 , x = 25. Now, the distance travelled in the 3rd hour = 30+1/4âˆ—30= 37.5 The only option ending with a 0.5 in the decimal place is C.
ANSWER:C
Answer: (C) 92.5
Question: If 3 people can do 3 times of a particular work in 3 days, then how many days would it take 6 people to do 6 times of that particular work?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 9
Rationale: 3 people can do the work one time in one day.
1 person can do 1/3 of the work in one day.
6 people can do 6/3 of the work in one day.
6 people can do 6 times the work in 3 days.
The answer is C.
Answer: (C) 3
Question: Mary is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of waffle. The pattern repeats after she leaves the morsel of waffle. If Mary drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
(A) waffle − wheat − wheat
(B) wheat − wheat − white
(C) white − waffle − wheat
(D) white − white − white
(E) white − white − waffle
Rationale: In a single round Mary drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: (A) waffle − wheat − wheat