divelab/Sys2Bench huggingface dataset:
Question: The value of x is to be randomly selected from the integers from 1 to 7, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
Options:
A)1/5
B)2/7
C)1/7
D)3/7
E)7/10
Rationale: y will only be negative for x=2.
(We can check the values from 1 to 7 to be certain.)
P(y is negative) = 1/7
The answer is C.
Answer: C
Question: Louie takes out a three-month loan of $1000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
Options:
A)333
B)383
C)402
D)433
E)483
Rationale: Let say she pays $X per month.
interest for month 1 = 1000*10/100
= 100
interest for month 2 = (1000+100 -X)*10/100
= (1100 - X)*10/100
= 110 - X/10
interest for month 3 = (1100 -X + 110 - X/10 - X)*10/100
= 121 - 21/100 X
Total interest = 3X-1000
So 3X-1000 = 100 + 110 - X/10 + 121 - 21/100 X
=>331X = 133100
=>X = 402.11
ANSWER:C
Answer: C
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (2, b), (a, 4), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
Options:
A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2
Rationale: b=2k+1...(1)
b+1=ak+1...(2)
4=ak+1...(3)
Taking (2) and (3)
4=b+1
b=3
Taking (1)
3=2k+1
k=1
Answer : B
Answer: B
Question: A person can row at 9 kmph and still water. He takes 3 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?
Options:
A)16 km
B)87 km
C)89 km
D)67 km
E)20 km
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 3.5
=> x/10 + x/8 = 7/2 => (4x + 5x)/40 = 7/2 => x
= 16 km.
Answer:A
Answer: A
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)45
B)49
C)20
D)82
E)13
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Answer: C
Question: In a shop X number of kinds of fruits are there and 40 number of kinds of vegetables are there, then 1% of vegetable is equal to 20% of fruits then how many kinds of fruits are there
Options:
A)20
B)35
C)70
D)90
E)1,40
Rationale: 1/100(400) = 2/10(x)
X = 20..
Option A.
Answer: A
Question: The width of a rectangular hall is ½ of its length. If the area of the hall is 200 sq.m, what is the difference between its length and breadth?
Options:
A)8m
B)10m
C)12m
D)15m
E)17m
Rationale: Let the length of the hall be x m
Breadth of the hall = 1x/2 m
Area of the hall = Length * Breadth
200 = x * 1x/2
x² = 400
x =20
Difference between the length and breadth of the hall = x - 1x/2 = x/2
=20/2 = 10m
ANSWER:B
Answer: B
Question: A chemical lab is scheduled to go through two air ventilation systems, a basic system and a more advanced system that takes forty minutes and 1.5 hours respectively to fully ventilate the room. If both ventilation systems were to operate at the same time with their respective constant rates, how many hours would it take to fully ventilate the chemical lab?
Options:
A)2/7
B)3/10
C)5/11
D)6/13
E)7/15
Rationale: The rate of the basic system is 1 room/ (2/3 of an hour) = 3/2 rooms per hour
The rate of the advanced system is 1/1.5 = 2/3 of a room per hour
The combined rate is 13/6 rooms per hour.
The time to ventilate one room is 6/13 of an hour.
The answer is D.
Answer: D
Question: If n is an integer and 102n^2 is less than or equal to 8100, what is the greatest possible value of n?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: 102 * n^2 <=8100
n^2 <=8100/102 which will be less than 81 since 8100/100 = 81 which is the square of 9
Next closest value of n where n^2<=81 is 8
Ans B
Answer: B
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 23 gallons of gasoline?
Options:
A)190
B)284.6
C)300
D)280
E)312
Rationale: so 12.2 * 23 = 280..
IMO option D is correct answer..
Answer: D
Question: Vasya wrote down several consecutive integers. Which of the following could not be the percentage of even numbers among them?
Options:
A) 40
B) 45
C) 48
D) 50
E) 60
Rationale: what you have to check is if the (answer given: 100-answer given) is either equal or two consecutive values..
reason for this is that there are only three possiblities of numbers of odd numbers in consecutive integers
1) equal to number of even numbers
2)one more than number of even numbers
3)one more than number of even numbers
(A) 40:60=2:3possible
(B) 45:55=9:11not possible
(C) 48:52=12:13possible
(D) 50:50=1:1possible
(E) 60:40=3:2possible
ans A
Answer: A
Question: Jar X is 1/4 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
Options:
A)2/5
B)1/4
C)1/3
D)1/2
E)2/3
Rationale: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/4+P/4=P/2
The answer is D.
Answer: D
Question: Two goods trains each 2000 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)228
B)278
C)192
D)27
E)21
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 2000 + 2000 = 4000 m.
Required time = 4000 * 6/125 = 192 sec.
Answer:C
Answer: C
Question: If r and t are positive integers, rt + r + t cannot be
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Let rt + t + r = x
Add 1 on both sides:
rt + t + r + 1 = x + 1
t(r + 1) + r + 1 = x + 1
(r + 1)(t + 1) = x + 1
Minimum value of (r + 1) = 2
Minimum value of (t + 1) = 2
Hence x + 1 cannot be prime
Substitute x from the given options: 6 + 1 = 7 --> prime --> rt + t + r cannot be 6
Answer: B
Answer: B
Question: A certain ski shop sells pairs of gloves in 10 different colors. If one pair of each color is dropped in a bag and a store clerk reaches in to draw two individual gloves simultaneously and at random, what is the probability that she draws two gloves of the same color?
Options:
A)1/144
B)1/143
C)1/24
D)1/23
E)1/19
Rationale: there are 10 different colours sothere are 10 pairs of gloves dropped..
first can be any of 20..so 20/20..
second has to be its pair, which will be just one out of remaining 19.. 1/19..
overall prob=20/20*1/19= 1/19..
E
Answer: E
Question: In State X, all vehicle license plates have 2 letters from the 26 letters of the alphabet followed by 3 one digit numbers. How many different license plates can State X have if repetition of letters and numbers is allowed?
Options:
A)23,400
B)60,840
C)67,600
D)608,400
E)676,000
Rationale: Two alphabets, 3 digits.
Ways of selecting 3 digits = 10X10X10 = 1000
Ways of selecting two alphabets = 26X26
In total total ways of selecting 5 vacancies = 676000
ANSWER:E
Answer: E
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
Options:
A)5760 lr
B)6000 lr
C)6500 lr
D)4000 lr
E)4500 lr
Rationale: 1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
ANSWER A
Answer: A
Question: A person walking at a constant rate of 6 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour. the cyclist stops to wait for the person 10 minutes after passing her, while the person continues to walk at her constant rate, how many minutes must the cyclist wait until the person catches up?
Options:
A)15min
B)11min
C)20min
D)40min
E)1hour
Rationale: After passing the person the cyclist travels for 10 minutes at a rate of 10 miles/hour.
In those 10 mins the cyclist travels a distance of 5/3 miles.
In those 10 mins the person travels a distance of 1 miles.
So the person still has to cover 2/3 miles to meet the waiting cyclist.
The person will need 1/9 hours or 11 mins to cover the remaining 2/3 miles.
The answer is B
Answer: B
Question: A focus group is currently made up of x men and y women. If 3 men and 7 women are added to the group, and if one person is selected at random from the larger focus group, then what is the probability that a man is selected?
Options:
A)x/(x + 7)
B)x/(x + y)
C)(y + 3)/(x + y + 7)
D)(y + 4)/(x + y + 10)
E)(x + 3)/(x + y + 10)
Rationale: x men
y women
x+3+y+7 is the total
=x+y+10
x+3 is the number of men
so (x + 3)/(x + y + 10)
E. (x + 3)/(x + y + 10)
Answer: E
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 35 grams of protein daily, how many grams of food X are in the mixture.
Options:
A)100
B)140
C)150
D)160
E)200
Rationale: Let x be the amount of food X.
0.1x + 0.15(300-x) = 35
0.05x = 10
x = 200
The answer is E.
Answer: E
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)80%
B)70%
C)60%
D)50%
E)40%
Rationale: Explanation:
Let C.P. = Rs. 100. Then, profit = Rs. 320, S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125.
New S.P. = Rs. 420
Profit = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: B
Answer: B
Question: Look at this series: 28, 25, 30, 27, 32, 29, ... What number should come next?
Options:
A)32
B)34
C)30
D)31
E)36
Rationale: Explanation:
In this simple alternating subtraction and addition series; 3 is subtracted, then 5 is added, and so on.
Answer: Option B
Answer: B
Question: If the area of a circle is 81pi square feet, find its circumference.
Options:
A)48
B)38
C)51
D)92
E)18
Rationale: The area is given by pi
pi × r × r = 81 pi
r × r = 81 ; hence r = 81 feet
The circumference is given by
2 × pi × r = 2 × pi × 9 = 18 pi feet
correct answer is E) 18
Answer: E
Question: On June 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months. If the stock continues to decrease at the same rate for the rest of the year, how many fewer bicycles will be in stock on october 1 than were in stock on January 1?
Options:
A) 8
B) 12
C) 20
D) 32
E) 36
Rationale: Jan 1 = C
Feb 1 = C - 4
March 1 = C - 8
April 1 = C - 12
May 1 = C - 16
June 1 = C - 20
July 1 = C - 24
Aug 1 = C - 28
Sept 1 = C - 32
Oct 1 = C - 36
Difference between stock on October 1 than were in stock on January 1 will be -
C - ( C - 36 )= 36
Hence answer will be (E)
Answer: E
Question: 0.35 represents what percent of 7?
Options:
A)0.05%
B)0.5%
C)5%
D)500%
E)5000%
Rationale: One more method
0.35 represents what percent of 7?
Divide by 7
0.05 represents what percent of 1?
Answer = 0.05*100 = 5% = C
Answer: C
Question: How many integers between 5000 and 6000 that have distinct digits and increase from left to right ?
Options:
A)10
B)48
C)60
D)20
E)600
Rationale: Since the numbers must be distinct and increasing from left to right,
The only arrangements we could come-up with are:
545_ --> 4
546_ --> 3
547_ --> 2
548_ --> 1
556_ --> 3
557_ --> 2
558_ --> 1
567_ --> 2
568_ --> 1
578_ --> 1
Number of integers =20
D
Answer: D
Question: 3 and 9 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 5th term?
Options:
A)3*3^2
B)3* 3^13 - 5 * 3^11
C)3^13
D)8 * 3^6
E)3^12 - 3^10
Rationale: Common ratio = 9/3 =3
7th term = 3*3^7
5th term = 3*3^5
Difference = 3 * (3^7 - 3^5) = 3 * 3^5 *(3^2 - 1)
= 3 * 3^5 * 8
= 8 * 3^6....
D
Answer: D
Question: How many positive integers t less than 30 have no common prime factor with 30?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: t=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: D
Question: An order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2. Subsequently, the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter. Find the ratio of the areas of the carpets in both the cases.
Options:
A)4 : 3
B)8 : 7
C)4 : 1
D)6 : 5
E)None of these
Rationale: Let the length and breadth of the carpet in the first case be 3x units and 2x units respectively.
Let the dimensions of the carpet in the second case be 7y, 3y units respectively.
From the data,.
2(3x + 2x) = 2(7y + 3y)
=> 5x = 10y
=> x = 2y
Required ratio of the areas of the carpet in both the cases
= 3x * 2x : 7y : 3y
= 6x2 : 21y2
= 6 * (2y)2 : 21y2
= 6 * 4y2 : 21y2
= 8 : 7
ANSWER:B
Answer: B
Question: There were totally 100 men.83 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 100-(100-83)-(100-75)-(100-85)-(100-70)
= 100-17-25-15-30=100-87=13
ANSWER:C
Answer: C
Question: There are 15 slate rocks, 20 pumice rocks, and 10 granite rocks randomly distributed in a certain field. If 2 rocks are to be chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
Options:
A)1/3
B)7/22
C)1/9
D)7/66
E)2/45
Rationale: Total No of Rocks = 45
Probability of choosing 1st Slate Rock = 15/45
Probability of choosing 2nd Slate Rock = 14/44 (Without replacement)
So combined probability = 15/45*14/44 = 7/66
So, ANSWER D.
Answer: D
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
Options:
A)350
B)288
C)277
D)2912
E)321
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.Answer: B
Answer: B
Question: A boy has six trousers and 9 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)186 ways
B)78 ways
C)56 ways
D)54 ways
E)189 ways
Rationale: The boy can select one trouser in six ways.
The boy can select one shirt in 9 ways.
The number of ways in which he can select one trouser and one shirt is 6 * 9 = 54 ways.
Answer:D
Answer: D
Question: A baseball player hit the following number of home runs in consecutive years: 35, 38, 39, 43, and 44. If the player had hit 3 additional home runs in the last year, which of the following statements best describes the change in the mean and the median of the home runs?
Options:
A) The mean and the median will remain unchanged.
B) The mean will remain unchanged but the median will increase.
C) The mean will increase but the median will remain unchanged.
D) The mean and the median will increase by the same amount.
E) The mean and the median will increase by different amounts.
Rationale: Old set = {35, 38, 39, 43, 44}.
New set = {35, 38, 39, 43, 47} --> the median (middle term) will remain the same and the mean will increase.
Answer: C.
Answer: C
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 76. Find their present ages.
Options:
A)20,35,45
B)8,20,28
C)16,28,36
D)16,28,46
E)None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 76
20K = 100
K = 5
Therefore, then present ages are 20,35,45.
ANSWER:A
Answer: A
Question: Bipin is 6 times old as Alok. Bipin's age will be twice of Chandan's age after 10 years. If Chandan's 7th birthday was celebrated 3 years ago, what is Alok's present age ?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: let the present ages of bipin, alok, chandan are b,a,c respectively
given conditions are
1)b=6a
2)(b+10)=2*(c+10)
3)chandans present age=c=10 years
therefore b=30
so a=5
ANSWER:D
Answer: D
Question: At a school, three-fifths of the male students and two-thirds of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?
Options:
A)11/25
B)14/25
C)16/25
D)18/25
E)21/25
Rationale: Let x be the number of students in the school.
The number of males who speak a foreign language is (3/5)(2/5)x = (6/25)x
The number of females who speak a foreign language is (2/3)(3/5)x = (2/5)x
The total number of students who speak a foreign language is (6/25)x + (2/5)x = (16/25)x
The answer is C.
Answer: C
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
Options:
A)3
B)7
C)8
D)6
E)2
Rationale: S = (1 + 2 + 3)/2
= 3
Answer:A
Answer: A
Question: The sum of the two numbers is 16 and their product is 35. What is the sum of the reciprocals of these numbers?
Options:
A)16/35
B)1/35
C)35/8
D)7/32
E)None of these
Rationale: Let the numbers be a and b. Then, a+b=16 and ab =35.
a+b/ab=16/35; (1/b+1/a)=16/35
Sum of reciprocals of given numbers=16/35.
Correct Option: A
Answer: A
Question: Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is?
Options:
A)33
B)76
C)85
D)22
E)99
Rationale: Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F of 551 and 1073 = 29;
First number = 551/29 = 19
Third number = 1073/29 = 37.
Required sum = 19 + 29 + 37 = 85.
Answer:C
Answer: C
Question: In a certain circle there are 10 points. What is the number of the triangles connecting 5 points of the 10 points?
Options:
A)80
B)96
C)108
D)120
E)252
Rationale: IMO : E
HERE we have to select 5 points out of 10 points. Order is not important
So the answer will be 10c5 = 252
Answer E
Answer: E
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 110?
Options:
A)35
B)77
C)25
D)18
E)12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (110 - 75) = 35 points to C.
Answer:A
Answer: A
Question: If the price of 23 balls is 276, then what will the price of 12 balls?
Options:
A)144
B)148
C)156
D)186
E)None of these
Rationale: Explanation :
Less balls, Less Price (Direct Proportion)
So, let the price be Rs. x
then,
23:12::276:x
=>x=276*12/23
=>x=144
So price of 12 balls will be Rs. 144
Answer : A
Answer: A
Question: As a treat for her two children, a mother runs to the freezer in which she has three cherry ice pops, three orange ice pops, and four lemon ice pops. She chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one being jealous of the other and getting even more upset. What is the probability that she has to return to the freezer to make sure that they each receive the same flavor?
Options:
A)2/5
B)3/7
C)7/12
D)11/15
E)17/25
Rationale: P(2 cherry) = 3/10 * 2/9 = 6/90
P(2 orange) = 3/10 * 2/9 = 6/90
P(2 lemon) = 4/10 * 3/9 = 12/90
P(2 of the same flavor) = 24/90
P(2 different flavors) = 1 - 24/90 = 66/90 = 11/15
The answer is D.
Answer: D
Question: which one is odd?
4377
3954
9862
8454
9831
Options:
A)4377
B)3954
C)9862
D)8454
E)None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9862 is 25
Answer: C
Question: In a box of 8 pencils, a total of 2 are defective. If a customer buys 3 pencils selected at random from the box, what is the probability that neither pencils will be defective?
Options:
A)1/12
B)5/14
C)2/13
D)2/15
E)1/17
Rationale: First, there are 6C3 ways you can select 3 good pencils from 4 good ones.
Second, there are 8C3 ways you select 3 pencils from 6 ones in the box.
Then, the probability that neither pen will be defective is: 6C3/8C3=20/56 = 5/14
Answer is B
Answer: B
Question: There are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
Options:
A)25
B)32
C)35
D)30
E)45
Rationale: Explanation:
HCF (408, 192) = 24
The number of boys or girls that can be placed in a section = 24.
Thus the total number of sections is given by
408/24+192/24 =17+8 = 25
Answer: A
Answer: A
Question: A tourist purchased a total of $1,400 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
Options:
A)$1,430
B)$1,310
C)$1,290
D)$1,170
E)$1,150
Rationale: since total cashed checks = 7 ans $10 check cashed = one less or more than $50 checks
Therefore either $10 checks = 3 and $50 checks = 4 OR $10 checks = 4 and $50 checks = 3
using this information 1st option gives us the maximum cashed value therefore if we negate this value from total value we will get minimum value of which checks have lost
Therfore 1400 - 230 = 1170 hence answer is D
Answer: D
Question: The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 150 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?
Options:
A)90
B)120
C)160
D)360
E)600
Rationale: If we exclude those cases and take the question at face value, then it seems straightforward.
Group #1 = (didn't like, didn't understand) = 150
Group #2 = (likeunderstood) = 3/4
(1/4)N = 150
N = 600
Answer =(E)
Answer: E
Question: A fair 2 sided coin is flipped 8 times. What is the probability that tails will be the result at least twice, but not more than 8 times?
Options:
A)5/8
B)3/4
C)7/8
D)157/64
E)143/128
Rationale: at least twice, but not more than 8 timesmeans exactly 2 times, 3 times, 4 times, 5 times, 6 times, 7 times, 8 times
The probability of getting exactly k results out of n flips is nCk/2^n
8C2/2^8+8C3/2^8+8C4/2^8+8C5/2^8+8C6/2^8+8C7/2^8=143/128
Option: E
Answer: E
Question: A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes William can make using this recipe?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.
Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.
Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.
answer is A
Answer: A
Question: In an intercollegiate competition that lasted for 3 days, 150 students took part on day 1, 110 on day 2 and 140 on day 3. If 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days, how many students took part only on day 2?
Options:
A)50
B)35
C)45
D)25
E)60
Rationale: Day 1&2 = 75; Only Day 1&2 (75 -15) = 60,
Day 2&3 = 25; Only Day 2&3 (25 -15) = 10,
Only Day 2 = 110 - (60+10+15) = 25
Answer:D
Answer: D