mathewhe/aqua_rat huggingface dataset:
Question: If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 25?
(A) 101
(B) 187
(C) 191
(D) 201
(E) 311
Rationale: ok, not sure if this is the best explanation, but here is my way of solving this :
tn +1 = tn + n,
t 3 = 14
so:
t 4 = t 3 + 3
t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4
....
so we get
t 25 = t 3 + 3 + 4 + 5 + 6....+ 24
the 3 + 4 + 5 + ... + 24 sequence is equal the sequence 1 + 2 + ... + 24, minus 1 + 2 at the beginning (so, minus 3)
and the 1 + 2 ... + 24 sequence is equal to n*(n+1)/2 with n being 24, so equal to 24 * 25 / 2 = 300
so :
t 20 = t 3 + 300 - 3
t 20 = 14 + 300 - 3 = 300 + 11 = 311, hence answer E
Answer: (E) 311
Question: The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 328
(B) 279
(C) 255
(D) 288
(E) 211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30 = 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.Answer: C
Answer: (C) 255
Question: If Aaron is now twice as old as Bailey was 5 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now?
(A) 3B
(B) 3B-1
(C) 3B-21
(D) 3B-11
(E) 3B-2
Rationale: B is Bailey's current age.
Let Aaron's current age be A.
given A = 2(B-5).
four years from now Aaron's age will be = 2(B-5) + 4 = 2B-6
four years from now Bailey's age will be = B+4
Sum of ages of Mason and Gunther's after 4 years = 2B-6+B+4 = 3B-2
Ans : E
Answer: (E) 3B-2
Question: Find the least number which when divided by 20,25,35 and 40 leaves remainders 14,19,29 and 34 respectively.
(A) 1394
(B) 1294
(C) 1194
(D) 1094
(E) None of them
Rationale: Here,(20-14) = 6,(25 – 19)=6,(35-29)=6 and (40-34)=6.
Therefore, Required number = (L.C.M. of 20,25,35,40) – 6 =1394.
Answer is A.
Answer: (A) 1394
Question: present ages of sameer and anand are in the ratio of 5:4 respectively. three years hence, the ratio of their ages will become 11:9 respectively . what anand's present age in years
(A) 27
(B) 24
(C) 40
(D) 32
(E) 35
Rationale: sameer and anand be 5x years and 4x years respectively
(5x+3)/(4x+3)=11/9
9(5x+3)= 11(4x+3), 45x+27=44x+33
45x-44x=33-27
x=6, therefore anand's present age : 4x=24 years
correct answer(B)
Answer: (B) 24
Question: Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 4 to 1, what is the ratio of US to British stamps?
(A) 5 : 1
(B) 10 : 5
(C) 15 : 2
(D) 20 : 2
(E) 25 : 2
Rationale: U/I = 5/2
I/B = 4/1
Since I is multiple of both 2 (as per first ratio) and 5 (as per second ratio) so let's assume that I = 10
i.e. Multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator
then, U : I : B = 20 : 8: 2
i.e. U : B = 20 : 2
Answer: Option D
Answer: (D) 20 : 2
Question: A wooden cube whose edge length is 6 inches is composed of smaller cubes with edge lengths of one inch. The outside surface of the large cube is painted red and then it is split up into its smaller cubes. If one cube is randomly selected from the small cubes, what is the probability that the cube will have at least one red face?
(A) 54.9%
(B) 58.7%
(C) 62.5%
(D) 66.3%
(E) 70.4%
Rationale: There are a total of 6*6*6 = 216 cubes.
All the exterior cubes will have at least one face painted red.
The interior is formed by 4*4*4 = 64 cubes.
The number of cubes with at least one side painted red is 216 - 64 = 152 cubes
The probability that a cube has at least one side painted red is 152/216 which is about 70.4%
The answer is E.
Answer: (E) 70.4%
Question: Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 2 km each. Then they turned left and ran for another 1.5 km.
What is the distance (in kilometers) between the the two twins when they stop?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: The distance between them is the hypotenuse of a right angle triangle with sides 3 km and 4 km.
hypotenuse = sqrt(3^2 + 4^2) = 5
The answer is A.
Answer: (A) 5
Question: A wheel rotates 10 times every minute and moves 10 cm during each rotation. How many metres does
the wheel move in one hour?
(A) 6 metre
(B) 60 metre
(C) 1500 metre
(D) 1200 metre
(E) 2200 metre
Rationale: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *10) cms = 6000 cms
In metres = 60 metre
Answer: B
Answer: (B) 60 metre
Question: A person travels equal distances with speeds of 4km/hr, 8km/hr, 12km/hr. and takes a total time of 11 minutes. Find the total distance ?
(A) 1km
(B) 500mts
(C) 600mts
(D) 2km
(E) 1200mts
Rationale: Let the each distance be x km
total distance = 3x
then total time,
(x/4)+(x/8)+(x/12) = 11/60
x=0.4
total distance = 3*0.4 = 1.2km = 1200meters
correct option is E
Answer: (E) 1200mts
Question: If x > y^3 > z^4, which of the following statements could be true?
I. x>y>z
II. x>z
III.y=z
(A) III only
(B) I,II only
(C) II only
(D) I only
(E) II,III only
Rationale: Answer : B
Answer: (B) I,II only
Question: A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat six customers, while the original tables each seat four customers. Altogether, the restaurant now has 40 tables and is capable of seating 206 customers. How many more new tables than original tables does the restaurant have?
(A) 6
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: If all the tables seated 4, the number of customers could be 4*40 = 160.
206-160 = 46, so 46/2 = 23 tables must be new tables seating 6 people.
The number of tables seating 4 people is 40-23 = 17.
The number of new tables is 23-17 = 6 more than the number of old tables.
The answer is A.
Answer: (A) 6
Question: what is the angle between the hands of a clock when time is 8:30?
(A) 65deg
(B) 75deg
(C) 45deg
(D) 15deg
(E) 30deg
Rationale: Angle between two hands =
30h - 11/2 m = 30*8 - 30*11/2 = 240 - 165 = 75deg
ANSWER:B
Answer: (B) 75deg
Question: If the price of an article went up by 20%, then by what percent should it be brought down to bring it back to its original price?
(A) 16 2/3%
(B) 20%
(C) 22 1/3%
(D) 15%
(E) None of these
Rationale: Let the price of the article be Rs. 100.
20% of 100 = 20.
New price = 100 + 20 = Rs. 120
Required percentage = (120 - 100)/120 * 100
= 20/120 * 100 = 50/3 = 16 2/3%.
ANSWER:A
Answer: (A) 16 2/3%
Question: In a camp,there is a meal for 120 men or 200 children.If 160 children have taken the meal,how many men will be catered to with the remaining meal ?
(A) 20
(B) 24
(C) 40
(D) 50
(E) 60
Rationale: Solution
There is a metal for 200 children. 160 children have taken the meal.
Remaining meal is to be catered to 40 children.
Now, 200 children = 120 men
40 children =( 120/200x40)men= 24 men. Answer B
Answer: (B) 24
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) Rs.1261
(B) Rs.9261
(C) Rs.9621
(D) Rs.9162
(E) Rs.9164
Rationale: A = 8000(21/20)3 = 9261
ANSWER:B
Answer: (B) Rs.9261
Question: If the perimeter and diagonal of a rectangle are 14 and 5 cms respectively, find its area.
(A) 12 cm2
(B) 16 cm2
(C) 20 cm2
(D) 24 cm
(E) None of these
Rationale: In a rectangle,
(Perimeter)2/4=(diagonal)2+2×area
⇒ (14)2/4=5(2)+2×area
49 = 25 + 2 × area
∴ Area = 49−25/2=24/2=12cm2
Answer A
Answer: (A) 12 cm2
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?
(A) 19 m
(B) 17 m
(C) 10 m
(D) 12 m
(E) 18 m
Rationale: Answer: Option B
Explanation:
Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.
Answer: Option B
Answer: (B) 17 m
Question: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent Q of the gasoline in the tank is brand Z?
(A) 50%
(B) 40%
(C) 37.5%
(D) 331⁄3%
(E) 25%
Rationale: Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) Q= 3/8 = 37.5%
Answer (C)
Answer: (C) 37.5%
Question: If a, b are integers and |a-b|=14, which of the following is the smallest possible value of ab?
(A) -16
(B) 0
(C) 16
(D) 7
(E) -49
Rationale: a=7, b=-7. Hence, the answer is E.
Answer: (E) -49
Question: The age of father 4 years ago was four times the age of his son. Five years hence, father's age will be twice that of his son. The ratio of their present ages is:
(A) 41 : 17
(B) 42 : 17
(C) 44 : 19
(D) 44 : 17
(E) 44 : 21
Rationale: Let the ages of father and son 4 years ago be 4x and x years respectively.
Then, (4x + 4) + 5 = 2[(x + 4) + 5]
4x + 9 = 2x + 18
x = 4.5.
Required ratio = (4x + 4) : (x + 4) = 22 : 8.5 = 44 : 17.
Answer: Option D
Answer: (D) 44 : 17
Question: Mrs. Rodger got a weekly raise of $155. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
(A) $204
(B) $231
(C) $156
(D) $155
(E) $200
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 155.
So after completing the 1st week she will get $ (x+155).
Similarly after completing the 2nd week she will get $ (x + 155) + $ 155.
= $ (x + 155 + 155)
= $ (x + 310)
So in this way end of every week her salary will increase by $ 155.
D
Answer: (D) $155
Question: When 242 is divided by a certain divisor the remainder obtained is 12. When 698 is divided by the same divisor the remainder obtained is 16. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 10. What is the value of the divisor?
(A) 11
(B) 18
(C) 13
(D) 23
(E) None of these
Rationale: let that divisor be x
since remainder is 12 or 16 it means divisor is greater than 16.
now 242-12=230 =kx (k is an integer and 234 is divisble by x)
similarly 698-16=682 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (230+682)+12+16
=x(k+l) + 28
when we divide this number by x then remainder will be equal to remainder of (28 divided by x) = 10 hence x = 28-10 = 18
hence B
Answer: (B) 18
Question: 10 women can complete a work in 5 days and 10 children take 10 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 2
Rationale: 1 women's 1 day work = 1/50
1 child's 1 day work = 1/100
(5 women + 10 children)'s 1 day work
= (5/50 + 10/100) = 1/5
5 women and 10 children will complete the work in 5 days.
B
Answer: (B) 5
Question: Molly is rolling a number cube with faces numbered 1 to 6 repeatedly. When she receives a 1, she will stop rolling the cube. What is the probability that Molly will roll the die less than 3 times before stopping?
(A) 11/180
(B) 125/216
(C) 25/216
(D) 11/216
(E) 27/128
Rationale: The probability that Molly will roll the die less than 4 times before stopping is the sum of the following:
The probability that Molly will roll the die once: P=1/6 (she gets 1 on the first roll);
The probability that Molly will roll the die twice: P=5/6*1/6 (not 1, 1);
P = 1/6 + 5/6*1/6 = 11/216.
Answer: D.
Answer: (D) 11/216
Question: Find at what time between 8 and 9 o'clock will the hands of a clock be in the same straight line but not together ?
(A) 120/11 min past 9
(B) 120/11 min past 8
(C) 120/11 min past 5
(D) 120/11 min past 3
(E) 120/11 min past 2
Rationale: In this type of problems the formulae is
x is replaced by the first interval of given time Here i.e 8
= min
Therefore the hands will be in the same straight line but not
together at min.past 8.
Answer: B
Answer: (B) 120/11 min past 8
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 5 cm
(B) 13√2 cm
(C) 12 cm
(D) 6 cm
(E) 8 cm
Rationale: Explanation:
4a = 48 4a = 20
a = 12 a = 5
a^2 = 144 a^2 = 25
Combined area = a^2 = 169 => a = 13
d = 13√2 cm
Answer : B
Answer: (B) 13√2 cm
Question: A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is
(A) 7 hrs 95 min
(B) 7 hrs 49 min
(C) 7 hrs 45 min
(D) 7 hrs 15 min
(E) 6 hrs 45 min
Rationale: Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
In fact, you can do all these calculations mentally and save a lot of time
which will be a real benefit for you.
Answer:C
Answer: (C) 7 hrs 45 min
Question: An advertising agency finds that, of its 105 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also, 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines. How many use all the three?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Total=105
Television=115
Radio=110
Magazine=130
All the three =105-115-110-130+85+75+95=5
ANSWER D
Answer: (D) 5
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 2% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
(A) 4 : 5
(B) 5 : 4
(C) 2 : 7
(D) Data inadequate
(E) None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 2% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.02x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.02x
or, 120 = 0.06x
x = 2000
Reqd ratio of population of males and females
2000/9000−2000=2000/7000=2:7
Answer C
Answer: (C) 2 : 7
Question: If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much percent should he reduce the quantity of gasoline that he buys?
(A) 6.66%
(B) 8%
(C) 10%
(D) 12%
(E) 12.5%
Rationale: Let price of original price of gasoline = 10$
and let original consumption of gasoline = 10
Amount spend on gasoline originally = 10*10 = 100$
the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline
Increased price of gasoline = 12.5$
Now Ron intends to spend on gasoline =1.15*100 = 115$
Consumption of gasoline needs to be = 115/12.5
= 1150/125
= 46/5 = 9.2
Reduction in consumption of gasoline = 10-9.2 = .8
% reduction in consumption of gasoline = .8/10 * 100%
= 8%
Answer B
Answer: (B) 8%
Question: P and Q started a business investing Rs. 48,000 and Rs. 24,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 2:6
(B) 2:3
(C) 2:1
(D) 17:9
(E) 17:4
Rationale: P:Q = 48000 : 24000
= 2:1.
Answer:C
Answer: (C) 2:1
Question: If p and q are positive integers, which of the following can never be the greatest common divisor of 48p and 18q?
(A) 48
(B) 48p
(C) 18q
(D) 6(p-q)
(E) 16q
Rationale: Greatest Common Factor of 48p and 18q = 6 or 6p or 6q ( A multiple of 6 )
Now, check the options , except (E) all are multiple of 6..
Hence ANSWER:E
Answer: (E) 16q
Question: On a trip covering 850 km, a bicyclist travels the first 400 km at 20 km per hour and the remainder of the distance at 15 km per hour. What is the average speed, in km per hour, for the entire trip?
(A) 16.0
(B) 16.5
(C) 17.0
(D) 17.5
(E) 18.0
Rationale: time 1 = 400 / 20 = 20 hours
time 2 = 450 / 15 = 30 hours
total time = 50 hours
average speed = 850 / 50 = 17 km/hr
The answer is C.
Answer: (C) 17.0
Question: The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 76 kg
(B) 76.5 kg
(C) 85 kg
(D) 90 kg
(E) NOne
Rationale: Sol.
Total weight increased
= (8 × 2.5) kg
= 20 kg.
Weight of new person
= (65 + 20) kg
= 85 kg.
Answer C
Answer: (C) 85 kg
Question: A ladder 25m long reaches a window of building 20m above the ground. Then the distance of the foot of the ladder from the building is?
(A) 35m
(B) 45m
(C) 30m
(D) 15m
(E) 25m
Rationale: let it forms a right angled triangle and follow c^2=a^2+b^2
then 25^2=20^2+b^2
b^2=625-400
b=15
ANSWER:D
Answer: (D) 15m
Question: Roja and Pooja start moving in the opposite directions from a pole. They are moving at the speeds of 2 km/hr and 3 km/hr respectively. After 4 hours what will be the distance between them?
(A) 11
(B) 20
(C) 77
(D) 26
(E) 12
Rationale: Distance = Relative Speed * Time
= (2 + 3) * 4 = 20 km
[ They are travelling in the opposite direction, relative speed = sum of the speeds].
Answer: B
Answer: (B) 20
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 588, what was his profit?
(A) s. 64
(B) s. 69
(C) s.108
(D) s.75
(E) s.90
Rationale: C.P. = Rs. (100/122.5)x588
= Rs. (1000/1225)x588
= Rs. 480
Profit = Rs. (588 - 480) = Rs. 108.
Answer:C
Answer: (C) s.108
Question: A rainstorm increased the amount of water stored in State J reservoirs from 180 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 60 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A)  90
(B)  114
(C)  125
(D) 130
(E)  144
Rationale: After the reservoir is filled to 200 gallons the amount of water is at 60% - which means that 40% of the reservoir is empty. To figure out what that 40% is approximate: 200 gallons /60 percent = x gallons /40 percent , therefore, x = 133.33 gallons , answer choices A,B,C,D are below 133.33 . We know that the reservoir must be short more than 133.33 gallons, therefore, the only possible choice is E.
Answer: (E)  144
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 29.16, the number of the member is the group is:
(A) 57
(B) 54
(C) 77
(D) 87
(E) 97
Rationale: Money collected =(29.16 x 100) paise = 29.16 paise
numbers of members = 2916 squareroot = 54
Answer B
Answer: (B) 54
Question: If 15% of 30% of 50% of a number is 90, then what is the number?
(A) 4000
(B) 3050
(C) 4400
(D) 4500
(E) None of these
Rationale: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 90
=> 3/20 * 3/10 * 1/2 * a = 90
=> a = 10 * 20 * 10 * 2 = 4000.
ANSWER:A
Answer: (A) 4000
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
(A) 32
(B) 75
(C) 12
(D) 51
(E) 47
Rationale: Number of ways in which one can travel from P to R
=3×4=12=3×4=12
Ans: C
Answer: (C) 12
Question: The average (arithmetic mean) of four different positive integers is 4. If the first of these integers in 3 times the second integer and the second integer is 6 less than the third integer, what is the least possible value of the fourth integer?
(A) 5
(B) 3
(C) 4
(D) 2
(E) 1
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 9
=> 5x + 2 + a = 36
=> 5x + a = 34
=> a = 34 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=6
This gives us a= 34 - 30 = 4
Therefore the minimum value that the fourth integer can have is 4.
Answer:C
Answer: (C) 4
Question: A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio of students per class?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 12
Rationale: Number of classes now : 120/x, where x is the number of students per class.
When it is increased by 1, Number of classes will be 120/(x+1).
We are told, 120/x - 120/(x+1) = 10 => Solving x = 3.
ANSWER:A
Answer: (A) 3
Question: 6^5 + 6^5 + 6^5 + 6^5 =
(A) 6^6
(B) 7^6
(C) 4^8
(D) 4^9
(E) 4^12
Rationale: Hi shakticnb,
Certain Quant questions on the GMAT are just about 'organizing' the information in a specific way. If you find yourself getting confused by a prompt, think about how you might change the way that the information is presented to you.
Here, for example, we're asked for....
6^5 + 6^5 + 6^5 + 6^5 =
Now, the GMAT doesn't really expect us to calculate this sum (but we could if we had to), but we are expected to find a way to organize this information... If, instead of all of those exponents, we had...
X + X + X + X =
What would the sum be?
Clearly, it would be 4(X) = 4X.....since we're just combining 'like' terms. Take that same idea with this prompt and you have...
6^5 + 6^5 + 6^5 + 6^5 =
6(6^5)
This can be re-written as...
(6^1)(6^5)
...and now we can use exponent rules; since we're MULTIPLYING 'bases' that are the same, we ADD the exponents...
(6^1)(6^5) = 6^6
Final Answer:
A
Answer: (A) 6^6
Question: On the first day of her vacation, Louisa traveled 240 miles. On the second day, traveling at the same average speed, she traveled 420 miles. If the 240-mile trip took 3 hours less than the 420-mile trip, what was the average speed, in miles per hour?
(A) 65
(B) 50
(C) 55
(D) 60
(E) 58
Rationale: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 240/t = 420/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 240/4 = 60
Answer: D
Answer: (D) 60
Question: One hour after Adrienne started walking the 60 miles from X to Y, John started walking from X to Y as well. Adrienne walks 3 miles per hour and John walks 1 mile per hour faster than Adrienne. How far from X will John be when he catches up to Adrienne?
(A) 12 miles
(B) 9 miles
(C) 10 miles
(D) 11 miles
(E) 18 miles
Rationale: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of John when he sets off. John walks at four miles/hour which means that every hour, John will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (John ) = r*t (adrienne)
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
A) 12 miles
Answer: (A) 12 miles
Question: 5358 x 55 = ?
(A) 272258
(B) 272358
(C) 294690
(D) 274258
(E) 274358
Rationale: 5358 x 51	= 5358 x (50 + 5)
= 5358 x 50 + 5358 x 5
= 267900 + 26790
= 294690.
C)
Answer: (C) 294690
Question: A student gets 50% in one subject, 60% in the other. To get an overall of 60% how much should get in third subject.
(A) 75%
(B) 70%
(C) 45%
(D) 55%
(E) 65%
Rationale: Let the 3rd subject % = x
50+60+x = 3*60
110+x =180
x = 180-110 =70
Answer :B
Answer: (B) 70%