mathewhe/aqua_rat huggingface dataset:
Question: A container has 3L of pure wine. 1L from the container is taken out and 2L water is added.The process is repeated several times. After 19 such operations, qty of wine in mixture is
(A) 2/7 L
(B) 3/7 L
(C) 6/19L
(D) 7/23L
(E) 8/25L
Rationale: First operation: 3L-1L=2=6/3L of wine left, total 4L;
#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;
#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;
#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;
....
At this point it's already possible to see the pattern: x=6/(n+2)
n=19 --> x=6/(19+2)=6/21=2/7L
Answer: A.
Answer: (A) 2/7 L
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 1/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) 7/16
(B) 7/15
(C) 10/21
(D) 17/35
(E) 1/10
Rationale: Let the total # of cups be 10.
# of small cups sold 3/5*10=6;
# of large cups sold 10-6=4;
Let the price of small cup be $6, then the price of larges cup would be 1/6*6=$1;
Revenue from small cups: 6*$6=$36;
Revenue from large cups cups: 4*$1=$4;
Fraction of total revenue from large cups: 4/(36+4)=1/10.
Answer: E.
Answer: (E) 1/10
Question: If it would take one machine 6 minutes to fill a large production order and another machine 8 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 2 1/60
(B) 3 3/7
(C) 5 5/11
(D) 5 1/2
(E) 11
Rationale: Since , Machine 1-M1 take 6 mins to fill the order
The work done by M1 in a min = 1/6
Machine 2- M2 take 8 mins to fill the same order
and work done by M2 in a min = 1/8
Total work done by M1 and M2 in a min = 1/6 + 1/8 = 7/24
Time needed for M1 and M2 to complete the order = 24/7 = 3 3/7
Answer B
Answer: (B) 3 3/7
Question: Mona and Donald fly to Rome for the weekend. They take cash only in notes of $10 and notes of €10. Mona carries three times the amount of euros Donald carries. She also carries as many dollars as Donald carries. The number of €10 notes they take is double the number of $10 notes they take. If Donald carries a total of 45 notes (of either $10 or €10,) then what is the total number of notes (of either $10 or €10,) they take?
(A) 70
(B) 80
(C) 150
(D) 120
(E) 140
Rationale: .let e10 =x no. d10 =y no. donald is having x+y notes mona carries 3x+y again x =2y or donald x+y =45
or 3y =45 y =15 ;x =30 , total notes they carry = 4x+2y = 120+30 =150
C
Answer: (C) 150
Question: A frog can climb up a well at 3 ft per min but due to slipperiness of the well, frog slips down 2 ft before it starts climbing the next minute. If the depth of the well is 57 ft, how much time will the frog take to reach the top?
(A) 29
(B) 27
(C) 55
(D) 17
(E) 10
Rationale: Explanation:
As per given, in 1 min,frog climbs up 3 ft and slips down by 2 ft.
So the frog climbs only 1 ft in 1 min
So after 54 mins,it would have climbed 54ft.
At the end of 55 mins it climbs up 3 ft to make it 57 ft and come out of the well.
Once it had reached the destination,it will not slip.
So the frog will take only 55 minutes to climb up the well.
Answer: C
Answer: (C) 55
Question: If xy = 5 and x^2 + y^2 = 20, then x/y + y/x =
(A) 2 2/5
(B) 3 1/7
(C) 5 1/3
(D) 4
(E) 60
Rationale: x/y+y/x=(x^2+y^2)/xy =substitute given we get 20/5=4 answer D
Answer: (D) 4
Question: If 20 men can build a wall 66 metres long in 6 days, what length of a similar can be built by 86 men in 8 days?
(A) 49.5m
(B) 46 m
(C) 49 m
(D) 46.5m
(E) 45 m
Rationale: Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)<=>x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer is C.
Answer: (C) 49 m
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?
(A) 150
(B) 882
(C) 277
(D) 261
(E) 281
Rationale: 5x + 12x + 13x = 300 => x = 10
a = 50, b = 120, c = 130
S = (50 + 120 + 130)/2 = 150
Answer: A
Answer: (A) 150
Question: If 10 percent of national ice cream sales are for strawberry flavored ice cream, 20 percent are chocolate, and 60 percent vanilla, what fraction of of total ice cream sales are for other flavors?
(A) 4/5
(B) 3/5
(C) 3/10
(D) 1/5
(E) 1/10
Rationale: 100%-(10%+20%+60%)=10% of sales are for other flavors --> 10% = 10/100 = 1/10.
Answer: E.
Answer: (E) 1/10
Question: If m : n = 3 : 4 and n : o = 8 : 9, then m : o is :
(A) 1 :3
(B) 3 :2
(C) 2 : 3
(D) 1 : 2
(E) 2 : 1
Rationale: m/n = m/n * n/o
=3/4 * 8/9
= 2/3.
So m : o = 2 : 3
ANSWER:C
Answer: (C) 2 : 3
Question: The average score of a cricketer for ten matches is 38.9 runs. If the average for first six matches is 42, then average for last four matches is
(A) 33.25
(B) 32.25
(C) 34.25
(D) 34.5
(E) 35.5
Rationale: Explanation:
=(38.9×10)−(42×6)/4
=(1216−750)4=34.25
Answer: Option C
Answer: (C) 34.25
Question: A salesperson receives a base salary of $1200 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 210 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $2,100
(D) $2,500
(E) $3,000
Rationale: Ans : 1200+ 7.5 % * 150 * (210-50) = $ 3000
Answer E
Answer: (E) $3,000
Question: Fresh fruit contains 68% water and dry fruit contains 20% water.How much dry fruit can be obtained from 100 kg of fresh fruits ?
(A) 30 kg
(B) 40 kg
(C) 50 kg
(D) 60 kg
(E) 70 kg
Rationale: The fruit content in both the fresh fruit and dry fruit is the same.
given,fresh fruit has 68% water.so remaining 32%(100-68) is fruit content.weight of fresh fruits is 100kg
dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.
fruit % in freshfruit = fruit% in dryfruit
32/100 * 100 = 80/100 * y
we get y = 40 kg
fruit pulp = 40 kg
so with water total amount = 40*100/80 = 50 kg
ANSWER:C
Answer: (C) 50 kg
Question: Of the sixteen participants in a certain competition, half are male, and half of the males are younger than 18 years of age. If half of the female competitors are also younger than 18 years of age, into how many distinct groups of 4 competitors could the participants be divided if each group must contain two males under 18 years of age and 2 females over 18 years of age?
(A) 3
(B) 4
(C) 36
(D) 9
(E) 20
Rationale: M under 18 - 4
F above 18 - 4
How many distinct groups can be formed now: 4c2 * 4c2 = 36
Answer : C
Answer: (C) 36
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
(A) 4
(B) 7
(C) 9
(D) 13
(E) 15
Rationale: Solution
Required number
= H.C.F of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F of 48, 92 and 140
= 4.
Answer A
Answer: (A) 4
Question: The mean of 50 observations was 36. It was found later that an observation 45 was wrongly taken as 23. The corrected new mean is
(A) 35.24
(B) 36.14
(C) 36.24
(D) 36.44
(E) None
Rationale: Solution
Correct sum = (36x50+45-23)
= 1822.
âˆ´ Correct mean = 1822 / 50
= 36.44.
Answer D
Answer: (D) 36.44
Question: If the product of the integers w, x, y and z is 68, and if 0< w < x < y < z, what is the value of w + z?
(A) 10
(B) 5
(C) 16
(D) 18
(E) 21
Rationale: 24= 1* 2* 3* 4
So w = 1, x = 2, y = 3, z = 4
w + z = 1+ 4= 5
Answer - B
Answer: (B) 5
Question: A certain truck uses 18 gallons of diesel fuel in traveling 220 miles. In order for the truck to travel the same distance using 10 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
(A) 8
(B) 9
(C) 12
(D) 15
(E) 7
Rationale: There are two sets 18G1 gallons and 10G2 gallons details given.
18 gallons covering 220 miles
Then 1 G1 is used to cover 15 miles.
Now for 10 G2 covering 220 miles.
then 1 G2 is used to cover 22 miles.
There must 22 - 15 = 7miles per gallon increment is needed for 10 gallons to improve the mileage to cover 220 miles.
IMO E is correct answer.
Answer: (E) 7
Question: The ratio of the number of boys and girls in a school is 3:2 Out of these 10% the boys and 25% of girls are scholarship holders. % of students who are not scholarship holders.?
(A) 84%
(B) 86%
(C) 88%
(D) 82%
(E) 74%
Rationale: let the boys are 3x and girls are 2x
so,no.of boys not holding scholorship is 3x-(30x/100)=27x/10
and no.of girls not holding scholorship is 2x-(50x/100)=3x/2
the total is (27x/10)+(3x/2)=42x/10
% of students not scholorship holders are (42x/10)*100/5x=84%
ANSWER:A
Answer: (A) 84%
Question: In the xy-plane, the line y = k is the perpendicular bisector of the line segment PQ and the line x = b is the perpendicular bisector of the line segment RQ. If the coordinates of the point R are (-b, -k), then what are the coordinates of the point P?
(A) (-5b, -5k)
(B) (-3b, -3k)
(C) (2b, 2k)
(D) (3b, 3k)
(E) (5b, 5k)
Rationale: firstly the Question tells us that RQ and PQ are perpendicular at Q..
Now the coordinates of the point R are (-b, -k), so R is at a distance of 2b from line x and at dist of 2k from line Y..
as line X bisect RQ .... length of RQ =4b and coord (3b,-k)..
as line Y bisect PQ .... length of PQ =4k and coord (3b,3k).ans D
Answer: (D) (3b, 3k)
Question: If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 10 percent decrease in y would result in which of the following changes in z?
(A) decrease of 4.5%
(B) decrease of 14.5%
(C) increase of 4.5%
(D) increase of 21.5%
(E) increase of 35.5%
Rationale: After the changes, z = 1.5x*(0.9y)^2 = (1.5*0.81)xy^2 = 1.215*z
The answer is D.
Answer: (D) increase of 21.5%
Question: Can you find the next letter in the series ?
S - T - I - L - N - T - F - Y - ?
(A) A
(B) B
(C) C
(D) D
(E) E
Rationale: C
The answer is C.
These are letter of the question asked in reverse order.
Answer: (C) C
Question: A rectangular field has a length 10 meters more than it is width. If the area of the field is 200, what is the length (in meters) of the rectangular field?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: area = l * w = (L) * (L-10) = 200
trial and error:
19*9 = 171 (too low)
20*10 = 200
The length is 20 meters.
The answer is A.
Answer: (A) 20
Question: If c > 1 and d = 2^(c −1), then 4^c =
(A) 16d^2
(B) 4d^2
(C) d^2
(D) d^2/4
(E) d^2/16
Rationale: If c > 1 and d = 2^(c −1), then 4^c
Given c>1, so let's assume c=2
d=2^(c-1) = 2^(2-1) = 2, so d=2
hence, 4^c = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16d^2 --> clearly > 16
B) 4d^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) d^2 --> clearly < 16
D) d^2/4 --> clearly < 16
E) d^2/16 --> clearly < 16
Ans. B) 4d^2
Answer: (B) 4d^2
Question: Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 40% of Charlie's weight. Charlie weighs 180% of Mary's weight. Which of these 5 people weighs the highest?
(A) Mary
(B) Mike
(C) Michelle
(D) Alan
(E) Charlie
Rationale: Mary < Michelle < Mike
Alan < Charlie
Let x be Mary's weight.
Mike's weight is 2x and Charlie's weight is 1.8x.
The answer is B.
Answer: (B) Mike
Question: One week a certain van rental lot had a total of 20 vans, all of which were on the lot Monday morning. If 50 percent of the vans that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different vans that could have been rented out during the week?
(A)  16
(B)  18
(C)  20
(D)  8
(E)  4
Rationale: A) 16 vans rented means 4 were left and 8 were returned - 12 vans - good
Answer is (B)
Answer: (B)  18
Question: Roy is now 8 years older than Julia and half of that amount older than Kelly. If in 4 years, Roy will be twice as old as Julia, then in 4 years what would be Roy’s age multiplied by Kelly’s age?
(A) 172
(B) 180
(C) 192
(D) 200
(E) 216
Rationale: R = J+8 = K+4
R+4 = 2(J+4)
(J+8)+4 = 2J+8
J = 4
R = 12
K = 8
In 4 years (R+4)(K+4) = 16*12 = 192
The answer is C.
Answer: (C) 192
Question: how many words formed ACCIDENT without changing relative order of vowels??
(A) 360
(B) 370
(C) 380
(D) 390
(E) 400
Rationale: Vowels: AIE = 1, since order of vowels must not be changed, so 3! should not be multiplied.
Rest: CCDNT = here we have 5 terms, with 1 common term 'C'.
So according to me ans should be :
(5+1)!/2!
= 6!/2!
=360
ANSWER:A
Answer: (A) 360
Question: The difference between two parallel sides of a trapezium is 4 cm. perpendicular distance between them is 10 cm. If the area of the trapezium is 250cm2 find the lengths of the parallel side
(A) 27, 23
(B) 25, 25
(C) 24, 26
(D) 23, 29
(E) 24, 45
Rationale: Explanation:
Let the two parallel sides of the trapezium be a cm and b cm.
Then, a-b = 4 ------ (1)
And, (1/2) x (a+b) x 10 = 475 =>(a+b) =((250 x 2)/10) => a + b = 50------- (2)
Solving 1 and 2, we get: a=27,b=23
So, the two parallel sides are 27 cm and 23 cm.
Answer: Option A
Answer: (A) 27, 23
Question: A pump can fill a tank with water in 10 hours. Because of a leak, it took 20 hours to fill the tank. The leak can drain all the water in ?
(A) 20hr
(B) 10hr
(C) 30hr
(D) 14hr
(E) 16hr
Rationale: Work done by the leak in 1 hour = 1/10 - 1/20 = 1/20
Leak will empty the tank in 20 hours
Answer is A
Answer: (A) 20hr
Question: A and B have the same number of marbles when they start playing. After some time A gains 20 marbles and later he loses 2/3rds of what he had. Now B has 4 times as many marbles as A has. What are the initial number of marbles that each of them had?
(A) 80
(B) 90
(C) 100
(D) 110
(E) 120
Rationale: 100
ANSWER:C
Answer: (C) 100
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 6 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 2
(B) 4
(C) 12
(D) 6
(E) 160
Rationale: Actual miles/gallon is = 480/40 = 12 miles/gallon.
Current engine miles/gallon is 6 miles/gallon.
Additional 6 miles/gallon is required to match the actual mileage.
IMO option D.
Answer: (D) 6
Question: How many positive integers G less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72
Rationale: 210 is the answer when 2, 3, 5 and 7 are multiplied. 210 can also be arrive using 5,6 and 7 and 1, 5, 6 and 7.
So sum of arrangements of 2357, 567 and 1567. This translates to 4! +3! + 4!, this equals to 24 + 6 + 24 = 54, D is the answer.
Answer: (D) 54
Question: With both inlets open, a water tank will be filled with water in 52 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
(A) 9,000
(B) 10,500
(C) 11,750
(D) 17,500
(E) 19,500
Rationale: The work Done by Inlet A and B together in 1 min = 1/52
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/52)- (1/120) = 1/92
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/92)- (1/120) = 50 Cubic meter
= 19,500 Cubic Meter
Answer: option E
Answer: (E) 19,500
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 125/129
(B) 125/121
(C) 125/126
(D) 125/122
(E) 125/124
Rationale: Explanation:
Required probability = 1 - 1/126 = 125/126
Answer: C
Answer: (C) 125/126
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 60 = x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A) 1
Answer: (A) 1
Question: Julie has $2000 saved in her bank account after this summer. She made money babysitting and delivering newspapers which she added to her previous savings. Julie babysat for 30 hours at $10/hr, she delivered papers for 40 hours at $7/hr. What % of her bank account was savings she had before this summer?
(A) 41 %
(B) 51 %
(C) 61 %
(D) 71 %
(E) 81 %
Rationale: Total amount in the bank account minus new earnings = 2000 - (10 x 30 + 7 x 40)
= 2000 - (580)
= 1420
Now, we need to calculate 1420 is what percent of 2000.
=> 1420/2000 * 100 = 71 %
D
Answer: (D) 71 %
Question: Rakesh's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation :
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quotations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer : A
Answer: (A) 5
Question: 90 people are attending a newspaper conference. 45 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
(A) 18
(B) 16
(C) 12
(D) 10
(E) 6
Rationale: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=90;
{Writers}=45;
{Editors}>38;
{Both}=x;
{Neither}=2x;
90=45+{Editors}-x+2x --> x=45-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=45-39=6.
Answer: E.
Answer: (E) 6
Question: The ratio E, by volume of soap to alcohol to water in a 76 litre solution is 2: 50: 100 . The solution is then altered by adding more soap, alcohol and water.After this alteration the ratio, by volume of soap to water in the solution doubles whereas the ratio, by volume of soap to water remains the same as before. What COULD BE the resulting volume.
(A) 79 litres
(B) 78 litres
(C) 77 litres
(D) 152 liters
(E) 304 litres
Rationale: I guess it should be
the ratio E, by volume ofsoaptowaterin the solutiondoubleswhereas the ratio, by volume ofalocoholtowaterremains thesameas before
2:50: 100 => 1 : 25 : 50. If we add all the parts, we get 76 liters
So we have 1 liters of Soap, 25 liters of Alcohol and 50 liters of Water.
Now as per the Question, Soap : Water doubles but alcohol to water remains the same.
So Soap becomes 2 liters, Alcohol remains 25 liters and Water remains at 50 liters.
Hence 77 liters - Option C)
Answer: (C) 77 litres
Question: The relationship between quantities m and n is expressed by the equation 15m = 5(n - 42). If the difference between the two chosen values of n is 30, what is the difference in the corresponding values of m?
(A) 30/11
(B) 42/11
(C) 60/11
(D) 150/11
(E) 10
Rationale: Another Simple way
15m=5(n-42)
Assume n = 42 to make one side equal to 0
then 15m=0
and m = 0
Repeat it by assuming n as 42+30 i.e 72
15m= 5(72-42)
15m=150
m=150/15
diff = 10 - 0 = 10
Answer : E
Answer: (E) 10
Question: A loan has a variable interest rate that fluctuates between 6% and 8% of the base payment per month. If base payments remain at $400 each month and an additional monthly surcharge of 2% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
(A) $435.32
(B) $436.48
(C) $438.16
(D) $440.64
(E) $442.32
Rationale: The maximum interest in one month is 8%*$400=$32.
The combined payment (base plus interest) is $400 + $32 = $432.
The greatest possible payment is: 1.02*$432=$440.64.
The answer is D.
Answer: (D) $440.64
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 54 sec. The length of each train is?
(A) 50
(B) 26
(C) 75
(D) 28
(E) 21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/54 = 25/9 => x = 75.
Answer: C
Answer: (C) 75
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)
and Rupesh + 6 = | (Ravi + 6) ...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12
Question: Which one of the following is not a prime number?
(A) 21
(B) 34
(C) 67
(D) 91
(E) 55
Rationale: D
91 is divisible by 7. So, it is not a prime number.
Answer: (D) 91
Question: A work can be finished in 15 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
(A) 4:3
(B) 3:4
(C) 2:3
(D) 3:2
(E) 5:4
Rationale: Work done by 20 women in 1 day = 1/15
Work done by 1 woman in 1 day = 1/(15Ã—20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15Ã—16)
Ratio of the capacity of a man and woman =1/(15Ã—16) : 1/(15Ã—20) = 1/16 : 1/20
= 1/4 :1/5 = 5:4
Answer is E.
Answer: (E) 5:4
Question: A honey bee flies for 10 seconds, from a daisy to a rose. It immediately continues to a poppy, flying for 6 additional seconds. The distance the bee passed, flying from the daisy to the rose is 6 meters longer than the distance it passed flying from the rose to the poppy. The bee flies to the poppy at 3 meters per second faster than her speed flying to the rose. The bee flies how many meters per second from the daisy to the rose?
(A) 3
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Let the speed be 's' and let the distance between rose and poppy be 'x'
The problem boils down to:
Rose to Poppy: s+3=x/6 ------- 1
Daisy to Rose: s=(x+6)/10------ 2
so from 1 we can re write x as x=6s+18
substitute the value of x in 2 gives us s=3 m/s
A
Answer: (A) 3
Question: There are 4 copies of 5 different pens. In how many ways can they be arranged on a shelf?
(A) 20!/4!
(B) 20!/5(4!)
(C) 20!/(4!)^5
(D) 20!
(E) 5!
Rationale: There are 4 copies of 5 different pens.20!/((4!)^5)
Answer - C
Answer: (C) 20!/(4!)^5
Question: The sum of the squares of the first 15 positive integers (1^2 + 2^2 + 3^2 + . . . + 15^2) is equal to 1290. What is the sum of the squares of the second 15 positive integers (16^2 + 17^2 + 18^2 + . . . + 30^2) ?
(A)  2480
(B)  3490
(C)  6785
(D)  8265
(E)  9255
Rationale: You'll never need a formula for the sums of squares on the actual GMAT. You don't need to use that formula here, though it's not all that straightforward to solve without one. Two different approaches:
16^2 + 17^2 + 18^2 + ... + 30^2 = (15 + 1)^2 + (15 + 2)^2 + (15 + 3)^2 + ... + (15 + 15)^2
Now we can expand each square; they are all in the (x + y)^2 = x^2 + 2xy + y^2 pattern.
= (15^2 + 2*15 + 1^2) + (15^2 + 4*15 + 2^2) + (15^2 + 6*15 + 3^2) + ... + (15^2 + 30*15 + 15^2)
Now we have fifteen 15^2 terms, so adding these gives 15*15^2 = 15^3 = 3375. We also have the entire sum 1^2 + 2^2 + ... + 15^2, which we know is equal to 1240. Finally adding the middle terms, we have:
2*15 + 4*15 + 6*15 + ... + 30*15 = 15(2 + 4 + 6 + .... + 30) = 15*2*(1 + 2 + 3 + ... + 15) = 15*2*8*15 = 3600
So the sum must be 3375 + 1240 + 3600 = 8215
Alternatively, we can use a different factoring pattern. We want to find the value of 30^2 + 29^2 + ... + 17^2 + 16^2. Well if we subtract 15^2 + 14^2 + .... + 2^2 + 1^2 from this, the answer will be 1240 less than what we want to find. So if we can find the value of
30^2 + 29^2 + ... + 17^2 + 16^2 - (15^2 + 14^2 + .... + 2^2 + 1^2)
then we can add 1240 to get the answer. Now grouping the terms above to get differences of squares, we have
= (30^2 - 15^2) + (29^2 - 14^2) + ... + (16^2 - 1^2)
and factoring each of these using x^2 - y^2 = (x + y)(x - y), we have
= 45*15 + 43*15 + 41*15 + ... + 17*15 = 15(45 + 43 + 41 + ... + 17)
In brackets we have an equally spaced sum with fifteen terms, which we can evaluate using the familiar formula. So the above equals
15*15*62/2 = 6975
and adding back the 1290, we get the answer of 8265. (ANS D)
Answer: (D)  8265
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
11 * 13 * 15 =?
(A) 89
(B) 49
(C) 206
(D) 38
(E) 55
Rationale: C
206
(15 * 13) + 11 = 206
Answer: (C) 206