mathewhe/aqua_rat huggingface dataset:
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 3, the speed of the leak is Vâ€™, When the height of the oil remaining is 9, what was the speed of the leak, in terms of Vâ€™?
(A) 9Vâ€™
(B) 4Vâ€™
(C) Vâ€™/2
(D) Vâ€™/4
(E) Vâ€™
Rationale: When h=3 v=V'
So V' = k.9
Hence k = V'/9
Now when h=9
v=(V'/9).9^2
v=V'.9
v=9V'
Ans : A
Answer: (A) 9Vâ€™
Question: What is the sum of all 3 digit nos formed by {1,3,5,7,9} with nos not repeated
(A) 33300
(B) 34500
(C) 38500
(D) 39800
(E) 45200
Rationale: Here 3 digit no. Can be formed in 5*4*3 = 60. Thus we hv to find the sum of 60 nos.
Now 60/5= 12 ; we hv 12 no's. starting with 1 ,12 no's. with 3,5,7,9....
So 12*100*(1+3+5+7+9)+12*10*(1+3+5+7+9)+12*1*(1+3+5+7+9)
=30000+3000+300
=33300
ANSWER:A
Answer: (A) 33300
Question: Four business people wish to invest in a new company. Each person is willing to pay one fourth of the total investment. After careful calculations, they realize that each of them would pay $6,200 less if they could find two more equal investors. How much is the total investment in the new business?
(A) $74,400
(B) $62,200
(C) $25,000
(D) $ 6,200
(E) $ 4,300
Rationale: Total Investment between 6: (x/6)
Total investment including 6200 less between 4 people(x-(6200*4))/4
Set both eq. equal to each other.
74,400
Answer A)
Answer: (A) $74,400
Question: For integers x and y, if 91x = 8y, which of the following must be true?
I. y > x
II. x is not a integer
III. The cube root of x is not an integer
(A) I only
(B) II only
(C) III only
(D) I and II
(E) None of these
Rationale: Statement 1: y>x
When y=x=0, equation holds but y is not greater than x
When x=-8 and y=-91, equation again holds but x>y
NOT TRUE
Statement 2: y/7 is an integer
Since x and y are integers, 91x and 8y must also be integers.
It is given that 91x=8y
or 13*7*x = 8 y
or 13x = 8y/7
To balance the equation, x must be an integer
NOT TRUE
Statement 3: The cube root of x is an integer
x can be equal to 2*2*2*3 and for this value of x,y will be 13*7*3
So, x may or may not be a cube root.
NOT TRUE
Answer:-E
Answer: (E) None of these
Question: In a car dealership, they buy cars for Rs.320000 and takes a profit of Rs. 25000. What is the % of profit dealership is making per car?
(A) 9.4%
(B) 11.6%
(C) 7.8%
(D) 10.2%
(E) 6.6%
Rationale: The profit % per car=(25000/320000)*100=7.8%
Answer:C
Answer: (C) 7.8%
Question: In a recent election, Geoff received 0.5 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,571 more votes to win the election, what is the value of x ?
(A) 50
(B) 54
(C) 56
(D) 60
(E) 63
Rationale: We are told that a candidate needs to receive more than x% of the vote.
We got that a candidate needs to receive more than 3,600 votes (3,601).
3,600 is 60% of total votes. Thus x=60%.
ANSWER:D
Answer: (D) 60
Question: The area of the largest triangle that can be inscribed in a semicircle pf rasius r Cm, is:
(A) r(power)3 Cm(power)2
(B) r(power)2 Cm(power)3
(C) r(power)3 Cm(power)3
(D) r(power)2 Cm(power)2
(E) None of them
Rationale: Area of the largest triangle = (1/2 × 2r × r) Cm(power)2
= r(power)2 Cm(power)2
Answer is D.
Answer: (D) r(power)2 Cm(power)2
Question: In a recent head-to-head run-off election, 15,000 absentee ballets were cast. 1/5 of the absentee ballets were thrown out and 1/4 of the remaining absentee ballets were cast for Candidate A. How many absentee votes did Candidate B receive?
(A) 2,000
(B) 3,000
(C) 6,000
(D) 8,000
(E) 9,000
Rationale: 4/5 * 3/4 (total absentee votes) = 3/5 (total votes)=3/5*15000=9000
Answer is E
Answer: (E) 9,000
Question: Find the 25% of Rs. 500.
(A) s. 50
(B) s. 70
(C) s. 100
(D) s. 125
(E) s. 60
Rationale: Explanation :
25% of 500
=> 25/100 *500 = Rs. 125
Answer : D
Answer: (D) s. 125
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
(A) 10 days
(B) 14 days
(C) 15 days
(D) 9 days
(E) 7 days
Rationale: Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days
ANSWER IS C
Answer: (C) 15 days
Question: A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 3hrs25 min
(B) 3hrs45 min
(C) 3hrs75 min
(D) 3hrs49 min
(E) 3hrs25 min
Rationale: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Answer: B
Answer: (B) 3hrs45 min
Question: ?% of 360 = 162
(A) 277
(B) 36
(C) 45
(D) 72
(E) None of these
Rationale: ?% of 360 = 162
or, ? = 162×100/360=45
Answer C
Answer: (C) 45
Question: A can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was?
(A) 10 days
(B) 12 days
(C) 16 days
(D) 18 days
(E) 20 days
Rationale: A and B did the work for some days.
After that , B completed the remaining work in 46 days .
In 46 days, word done by B =
1
80
x 46 =
23
45
Remaining work = 1 – 23/45
= 17/45
Remaining work is done by both A and B together =
17/45x 90 x 80/90 + 80
= 16 days
C
Answer: (C) 16 days
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 38 cm2
(B) 85 cm2
(C) 65 cm2
(D) 45 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2
Answer:E
Answer: (E) 35 cm2
Question: P is four times as fast as Q and working together, they can complete a work in 15 days. In how many days can Q alone complete the work?
(A) 5 1/4 days
(B) 8 3/4 days
(C) 16 1/4 days
(D) 25 days
(E) 18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 15 days, which means Q can do the work in 75 days.
Hence, P can do the work in 18 3/4 days.
ANSWER:B
Answer: (B) 8 3/4 days
Question: A certain experimental mathematics program was tried out in 2 classes in each of 26 elementary schools and involved 32 teachers. Each of the classes had 1 teacher and each of the teachers taught at least 1, but not more than 3, of the classes. If the number of teachers who taught 3 classes is n, then the least and greatest possible values of n, respectively, are
(A) 0 and 13
(B) 0 and 14
(C) 1 and 10
(D) 1 and 9
(E) 2 and 8
Rationale: One may notice that greatest possible values differ in each answer choice in contrast to the least values, which repeat.
To find out the greatest value you should count the total classes (26*2=52), then subtract the total #of teachers since we know from the question that each teacher taught at least one class (52-32=20). Thus we get a number of the available extra-classes for teachers, and all that we need is just to count how many teachers could take 2 more classes, which is 20/2 = 10. So the greatest possible value of the # of teachers who had 3 classes is 10.
Only answer C has this option.
Answer: (C) 1 and 10
Question: In a sequence, each term is obtained by adding 6 to the preceding one. If the sum of the first 10 terms is equal to 100, what is the result of the addition of the first 30 terms?
(A) 2100
(B) 2170
(C) 2200
(D) 2250
(E) 2400
Rationale: a is first term and d = 6 since the preceding number is always greater than the previous one..
Now 10th term is a+9(6).
Sum of n terms is n/2(first term + last term)and here we have to get sum of 10 terms , we get 10/2 ( a + a+54) = 100 ( given sum of 10 terms is 100)
=> 5(2a+54) = 100
=> 2a+54 = 20
=> a = -17
Now to get sum of first 30 terms , we need to get 30th term value i.e. -17+29(6) = 157.
Sum of first 30 terms = 30/2( -17 + 157) = 2100.
Hence option A is correct answer..
Answer: (A) 2100
Question: If each data point in a certain set Q is increased by a factor of 5, what happens with the set's standard deviation?
(A) Doesn't Change
(B) Decreases by Factor 5
(C) Increases by Factor 5
(D) Increases by 5
(E) Can't be determined
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 5, the standard deviation will increase proportionately, giving us answer choice C.
Answer: (C) Increases by Factor 5
Question: A, B, C, D and E are 5 consecutive points on a straight line. If BC = 2CD, DE = 7, AB = 5 and AC = 11, what is the length of AE?
(A) 19
(B) 21
(C) 23
(D) 25
(E) 27
Rationale: AC = 11 and AB = 5, so BC = 6.
BC = 2CD so CD = 3.
The length of AE is AB+BC+CD+DE = 5+6+3+7 = 21
The answer is B.
Answer: (B) 21
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.500 in 2 years?
(A) 221
(B) 287
(C) 453
(D) 288
(E) 171
Rationale: Explanation:
500 = P(21/20)2
P = 453.51
Answer:C
Answer: (C) 453
Question: Ratio between Rahul and Deepak is 4:3, After 4 Years Rahul age will be 32 years. What is Deepak present age.
(A) 14
(B) 15
(C) 20
(D) 21
(E) 24
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 4 = 32 => x = 7
So Deepak age is = 3(7) = 21
Option D
Answer: (D) 21
Question: The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 757
(B) 450
(C) 718
(D) 750
(E) 738
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 15 è x = 15 * 60 / 2
=450
Answer:B
Answer: (B) 450
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) Rs.250
(B) Rs.277
(C) Rs.297
(D) Rs.277
(E) Rs.299
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: (A) Rs.250
Question: There are 15 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?
(A) 105
(B) 110
(C) 115
(D) 120
(E) 125
Rationale: 15C2=105
The answer is A.
Answer: (A) 105
Question: If a,b are positive integers and a/b=80.75 which of the following could be the value of b?
(A) 1. 25
(B) 2. 26
(C) 3. 27
(D) 4. 24
(E) 5. 30
Rationale: Given a/b = 87.75.
this is 80 and 3/4 = 323/4
Since a and b are integers we know that whatever is the value of b, it must be divisible by 4 completely(to make a an integer)
from the options only D=24 is a multiple of 4 which is your answer.
Ans :D
Answer: (D) 4. 24
Question: 342
(A) 9
(B) 8
(C) 6
(D) 5
(E) 4
Rationale: One day's work of A and B = 1/9 + 1/8 = (2+1)/18
= 1/6 So, the time taken to complete the work is 6 days.
Answer: C
Answer: (C) 6
Question: In how many ways can the letters of word "EDUCATION" be arranged such that all the vowels as well as all the Consonants always appear together?
(A) 9!
(B) 5!*4!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: Since all the vowels and consonants have to be together there can only be there are 5! way to order the vowels and 4! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 5!4!2! (D)
Answer: (D) 5!*4!*2!
Question: How much is 80% of 40 is greater than 4/5 of 20?
(A) 12
(B) 27
(C) 18
(D) 16
(E) 81
Rationale: (80/100) * 40 â€“ (4/5) * 20
32 - 16 = 16
Answer:D
Answer: (D) 16
Question: In a group of 89 students, 36 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?
(A) 9
(B) 19
(C) 27
(D) 26
(E) 31
Rationale: Number of students taking history =H=36
Number of students taking statistics =S= 32
Total number of students =T= 89
Number of students taking History or Statistics or both =B= 59
Number of students taking neither history nor statistics =N= 89-59=30
LetXbe the number of students taking both history and statistics.
Then
T = H + S + N - X
or 89 = 36 + 32 +30 - X
or X = 9
Now,
Number of students taking only history will be
H-X
or 36-9 = 27
Answer:- C
Answer: (C) 27
Question: What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150o?
(A) 24 sq units
(B) 48 sq units
(C) 24 under root 3
(D) 48 under root 3
(E) Such a triangle does not exist
Rationale: Explanatory Answer
If two sides of a triangle and the included angle 'y' is known, then the area of the triangle = 1/2 * (Product of sides) * sin y
Substituting the values in the formula, we get 1/2 * 8 * 12 * sin 150o
= 1/2 * 8 * 12 * 1/2.
Note: Sin 150o = 1/2
Area = 24 sq units.
Choice A
Answer: (A) 24 sq units
Question: Several people are sitting around a round table playing a card game with a deck of 49 cards. Each person is dealt one card per deal, and the cards are dealt in a clockwise fashion. If Martin is dealt both the first card of the deck and the last card of the deck, which of the following could be the total number of people sitting at the table?
(A) 4
(B) 5
(C) 7
(D) 11
(E) 13
Rationale: Let n be the number of people at the table.
If Martin gets the first and the last card, it means Martin got one more card than the others.
Thus 49/n has a remainder of 1 and so 49-1 = 48 is a multiple of n.
The answer is A.
Answer: (A) 4
Question: At what time between 2 and 3 o'clock will the hands of a clock be together?
(A) 120/11 min. past 3
(B) 120/11 min. past 2
(C) 120/11 min. past 1
(D) 120/11 min. past 5
(E) 120/11 min. past 4
Rationale: At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min spaces apart.
To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min.
10 minutes will be gained in (60 x 10)/55 min. = 120/11 min.
The hands will coincide at 120/11 min. past 2.
Answer is B.
Answer: (B) 120/11 min. past 2
Question: Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 30hr. If all pipes are opened simultaneously, then the cistern will be filled in
(A) 6.67 hr
(B) 8 hr
(C) 8.5 hr
(D) 10 hr
(E) None of these
Rationale: Solution:
Work done by all the tanks working together in 1 hour.
1/10+1/12−1/30=3/20
Hence, tank will be filled in 20/3=6.67 hour
Option(A)
Answer: (A) 6.67 hr
Question: Today is Monday. After 51 days, it will be :
(A) Thursday
(B) Saturday
(C) Monday
(D) Sunday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 49 days, it will be Monday.
After 51 days, it will be Wednesday
Answer is E
Answer: (E) Wednesday
Question: In the quiet town ofNothintodothere are 700 inhabitants, 400 are unemployed and 300 are somnambulists. If half of the somnambulists are unemployed, how many are employed and are not somnambulists?
(A) 50.
(B) 100.
(C) 150.
(D) 200.
(E) 300.
Rationale: Total = 700
unemployed=400
employed=700-400=300
som=300
unemployed som = 300/2=150
employed som = 150
employed that are not som = 300-150=150
Answer : C
Answer: (C) 150.
Question: 9 friends went to a super market, and everyone decided to contribute equally to the total bill of $900. If one of the friends had a coupon for 10% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) 30
(B) 60
(C) 80
(D) 90
(E) 95
Rationale: At the non-discounted price, each friend would pay $100, as $900 divided by 9 friends is $100 per friend. But if the bill is 10% off, then each friend would pay 10% less. 10% of $100 is $10, so each friend saves $10 and pays the remaining $90
CORRECT OPTION:OPTION D
Answer: (D) 90
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $2,000 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $8,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
(A) 20%
(B) 25%
(C) 50%
(D) 60%
(E) 27%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 2000 : 8000 -----> 1 : 4
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 5) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/5) * 100 ---> 20%
Answer : A
Answer: (A) 20%
Question: What is the minimum percentage increase in the mean of set D {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
(A)  25%
(B)  50%
(C)  75%
(D)  100%
(E)  200%
Rationale: Mean of D is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of D, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: (D)  100%
Question: A five feet long staff casts a shadow 2 feet long. Can you find the height of a steeple whose shadow at the same hour, is 120 ft. long?
(A) 200 feet
(B) 220 feet
(C) 510 feet
(D) 400 feet
(E) 700 feet
Rationale: A
200 feet
Answer: (A) 200 feet
Question: Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?
(A) 29.25
(B) 29.28
(C) 29.29
(D) 29.12
(E) 29.19
Rationale: Average of 9 = x
9x = 8 * 3 + x * 2 x = 3.25
Total = 9 * 3.25
= 29.25
Answer:A
Answer: (A) 29.25
Question: At the end of year X, automobile installment credit accounted for 35% of all outstanding consumer installment credit. At that time automobile finance companies extended $40 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?
(A) 120
(B) 300
(C) 401.36
(D) 350.15
(E) 342.86
Rationale: System of Equations
a = (35/100) c
(1/3) a = 40 --> a = 120
Substitution
120 = (35/100) c
c = (100/35) 120
Answer
- 120/35 * 100
The Correct Answer is E.
- 342.86
Answer: (E) 342.86
Question: One ball is picked up randomly from a bag containing 8 yellow, 7 blue and 6 black balls. What is the probability that it is neither yellow nor black?
(A) 1/3
(B) 1/4
(C) 1/2
(D) 3/4
(E) 1/5
Rationale: Total number of balls, n(S) = 8 + 7 + 6 = 21
n(E) = Number of ways in which a ball can be selected which is neither yellow nor black
= 7 (∵ there are only 7 balls which are neither yellow nor black)
P(E) = n(E)/n(S)=7/21=1/3
ANSWER:A
Answer: (A) 1/3
Question: The average of 11 numbers is 10.9. If the average of first six is 10.1 and that of the last six is 11.4 the sixth number is?
(A) 9.5
(B) 10
(C) 10.5
(D) 9.1
(E) 12
Rationale: Explanation:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.1 = 60.6
6 to 11 = 6 * 11.4 = 68.4
60.6 + 68.4 = 129 – 119.9 = 9.1
6th number = 9.1
Option D
Answer: (D) 9.1
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 4 years?
(A) 20300
(B) 20400
(C) 20730
(D) 20500
(E) 20600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 120/100 Ã— 120/100 Ã— 120/100 Ã— 120/100= 20730
C
Answer: (C) 20730
Question: A is twice as good a workman as B and they took 10 days together to do the work B alone can do it in?
(A) 25 days
(B) 88 days
(C) 30 days
(D) 11 days
(E) 13 days
Rationale: WC = 2:1
2x + x = 1/10
x = 1/30 => 30 days
Answer: C
Answer: (C) 30 days
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is -.
(A) 1879
(B) 7899
(C) 4320
(D) 1680
(E) 1692
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!)
= 4320
Answer:C
Answer: (C) 4320
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.3, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
(A) $3.00
(B) $20.75
(C) $24.90
(D) $42.75
(E) $45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .3 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure at least 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .3 = 24.90 $
Answer C
Answer: (C) $24.90
Question: John.s car dealership contains m cars, 20% of which are minivans and 80% are sedans. Kevin's car dealership contains n cars, 40% of which are minivans are 60% are trucks. Larry's car dealership contains p cars, 50% of which are minivans and 50% of which are convertibles. If 25% of the m + n + p cars contained at the three dealerships are minivans, what is m in terms of n and p?
(A) n + 3p
(B) 3n + 5p
(C) 4n + 5p
(D) (n+5p)/2
(E) (4n+5p)/3
Rationale: For this question algebraic ways is the easiest: 0.2m+0.4n+0.5p=0.25(m+n+p)--> m=3n+5p
Answer: B.
Answer: (B) 3n + 5p
Question: A number, when 35 is subtracted from it, reduces to its 80 percent. What is four - fifth of that number ?
(A) 130
(B) 155
(C) 490
(D) 140
(E) 160
Rationale: Explanation:
x - 35 = 80x/100
=> x = 175
=> 4x/5 = 4x175/5 = 140.
Answer D
Answer: (D) 140
Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?
(A) 6/18
(B) 6/11
(C) 6/68
(D) 6/19
(E) 6/12
Rationale: Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20
Part filled by C in 3 minutes = 3/10
Required ratio = 3/10 * 20/11 = 6/11
Answer:B
Answer: (B) 6/11