divelab/Sys2Bench huggingface dataset:
Question: W is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in W?
I. 9
II. 15
III. 27
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: Ans: C
W->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: C
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 910 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1110
B)B)1045
C)C)1055
D)D)1060
E)E)1075
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 10 kg of mangoes = 55 × 10 = 550.
Total cost he has to pay = 560 + 550 = 1110.
A)
Answer: A
Question: Find the surface area of a 8 cm x 6 cm x 2 cm brick.
Options:
A)112 cu cm
B)136 cu cm
C)164 cu cm
D)180 cu cm
E)152 cu cm
Rationale: Sol.
Surface area = [2(8 x 6 + 6 x 2 + 8 x 2)]
= (2 x 76)
= 152 cu cm
Answer E
Answer: E
Question: A large box contains 17 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Options:
A)250
B)350
C)425
D)550
E)650
Rationale: The number of chocolate bars is equal to
17 * 25 = 425
correct answer C
Answer: C
Question: If you multiply all the numbers on your mobile phone except 0 and 9, what is the answer?
Options:
A)25869
B)48586
C)40320
D)58964
E)45698
Rationale: We have to multiply 1 to 8 to find the answer.
Therefore 1*2*3*4*5*6*7*8=40320
Answer is C
Answer: C
Question: Jamboree and GMAT Club Contest Starts
QUESTION #40:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
Options:
A) 660
B) 600
C) 500
D) 300
E) 240
Rationale: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option A is correct!
Answer: A
Question: Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work?
Options:
A)20 days
B)23 days
C)26 days
D)21 days
E)28 days
Rationale: A
20 days
(5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 * 8)/4 = 20 days.
Answer: A
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
Options:
A)8
B)12
C)6
D)14
E)None of these
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
ANSWER:B
Answer: B
Question: R-R-R-G-G-G-Y-Y-Y-B-R-R-R-G-G-G-Y-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
Options:
A)65
B)66
C)67
D)68
E)69
Rationale: The repeated pattern R-R-R-G-G-G-Y-Y-Y-B has 10 beads.
But the missing section includes R-R-R-G-G-G-Y-Y-Y at the end.
Thus the number of beads in the missing section has the form 10k + 9.
The answer is E.
Answer: E
Question: The average weight of 12 person's increases by 4 kg when a new person comes in place of one of them weighing 58 kg. What is the weight of the new person?
Options:
A)85
B)80
C)95
D)90
E)106
Rationale: Total increase in weight =12 × 4 = 48
If x is the weight of the new person, total increase in weight = x−58
=> 48 = x - 58
=> x = 48+58 = 106
ANSWER:E
Answer: E
Question: {1/(4-√15)} =
Options:
A)a. 16+16√15
B)b. 31- 8√15
C)c. 31+ 8√15
D)d. 32- 4√15
E)e. 4 + √15
Rationale: = 1 / (4 - root15)
Multiply numeratordenominator by (4+ root15)
= (4 + root15) / (16-15) = (4 + root15)
Answer = E
Answer: E
Question: The total marks obtained by a student in Mathematics and Physics is 50 and his score in Chemistry is 20 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together.
Options:
A)40
B)26
C)27
D)35
E)22
Rationale: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.
Given , M + C = 50 and C - P = 20 M + C / 2 = [(M + P) + (C - P)] / 2 = (50 + 20) / 2 = 35.Answer:D
Answer: D
Question: Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 32% chemical A, what percent of the mixture is Solution X?
Options:
A)85%
B)80%
C)75%
D)70%
E)65%
Rationale: The volume of the mixture be X+Y.
0.3X +0.4Y=0.32(X+Y)
X=4Y
X/(X+Y)=4/5=80%.
The answer is B.
Answer: B
Question: In an examination, a student scores 5 marks for every correct answer and loses 2 marks for every wrong answer. If he attempts all 100 questions and secures 290 marks, the number of questions he attempts correctly, is:
Options:
A)60
B)80
C)70
D)45
E)50
Rationale: Let the number of correct answers be x.
Number of incorrect answers = (100 â€“ x).
5x â€“ 2(100 â€“ x) = 290 or 7x = 490 or x = 70.
ANSWER:C
Answer: C
Question: Suppose you flip a fair coin four times. What is the probability that, in four flips, you get at least one head?
Options:
A)13/16
B)7/16
C)15/16
D)21/16
E)19/16
Rationale: Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads
probability of flipping either a head or a tail = 1/2
probability of flipping 3 tails in a row (1/2)^4
probability of flipping at least 1 head = 1 - (1/2)^4 = 15/16
Answer : C
Answer: C
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)22.7 kmph
B)12.7 kmph
C)27.6 kmph
D)12.5 kmph
E)22.1 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.Answer: D
Answer: D
Question: A certain collage has total of 300 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Options:
A)100
B)80
C)75
D)60
E)55
Rationale: Answer E
300 = 225 + 20 + x => x = 55
= 3/4 * 300 in 4 subjects + 20 min for 5th subject + x = 300
Answer: E
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options:
A)3377
B)1800
C)2776
D)1881
E)1882
Rationale: Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
Machines	6	:	10 :: 270 : x
Time (in minutes)	1	:	4
6 x 1 x x = 10 x 4 x 270
x =	(10 x 4 x 270)
(6)
x = 1800.
View Answer
Answer: B
Answer: B
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2234
B)4350
C)4560
D)5132
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
Options:
A)20%
B)29%
C)70%
D)27%
E)28%
Rationale: SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: A
Answer: A
Question: If a train, travelling at a speed of 160 kmph, crosses a pole in 9 sec, then the length of train is?
Options:
A)281
B)125
C)288
D)266
E)400
Rationale: D = 160 * 5/18 * 9
= 400 m
Answer: E
Answer: E
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 30 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Options:
A)22%
B)24percent
C)25%
D)28%
E)27%
Rationale: Total sales =800
Commission = (20/100)*500+ (30/100)*300
=100 + 90
=190
%Commission = (190/800)*100=23.7~ 24%
Answer is B
Answer: B
Question: What is the small positive two digit no. divisible by 3 and such that the sum of its digits is 9?
Options:
A)10
B)12
C)14
D)18
E)21
Rationale: Let xy be the whole number with x and y the two digits that make up the number. The number is divisible by 3 may be written as follows
10 x + y = 3 k
The sum of x and y is equal to 9.
x + y = 9
Solve the above equation for y
y = 9 - x Substitute y = 9 - x in the equation 10 x + y = 3 k to obtain.
10 x + 9 - x = 3 k
Solve for x
x = (k - 3) / 3
x is a positive integer smaller than 10
Let k = 1, 2, 3, ... and select the first value that gives x as an integer. k = 6 gives x = 1
Find y using the equation y = 9 - x = 8
The number we are looking for is 18 and the answer is D. It is divisible by 3 and the sum of its digits is equal to 9 and it is the smallest and positive whole number with such properties.
Answer: D
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1500, then his salary per month in rupees is:
Options:
A)4000
B)6000
C)8000
D)10000
E)None of these
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 1500, Salary = 10000 Rs.
Answer:D
Answer: D
Question: Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $20.00 each, what was Company C’s gross profit?
Options:
A) $7,250
B) $8,500
C) $8,100
D) $8,250
E) $8,600
Rationale: Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900
Revenue : 500 * 20 = $10000
Profit: 10000 - 1900 = $ 8100
Option C is correct
Answer: C
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
Options:
A)38008
B)38000
C)38005
D)38001
E)38002
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: B
Question: Some pens are divided among A, B, C and D. A gets twice the number of pens that B gets. C gets the same number of pens as D gets. If A gets 25 pens more than D and the ratio of the number of pens that B and C get is 2 : 3, then find the number of pens that D gets ?
Options:
A)56 pens
B)76 pens
C)75 pens
D)98 pens
E)45 pens
Rationale: Let the number of pens that A, B, C and D get be a, b, c and d respectively.
a : b = 2 : 1
a = c + 25
b : c = 2 : 3
a : b : c : d = 4 : 2 : 3 : 3
a,d get 4p, 3p pens
=> 4p - 3p = 25 (given)
p = 25
=> D gets 3p = 3 * 25 = 75 pens.
Answer:C
Answer: C
Question: A certain industrial loom weaves 0.129 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
Options:
A)114
B)115
C)116
D)117
E)118
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.129 : 15 :: 1 : x
=>0.129*x=15
=>x=15/0.129
=>x=116
ANSWER:C
Answer: C
Question: In a sports club with 30 members, 18 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Let x play both badminton and tennis so 18-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(18-x)+(19-x)+x+2=30
39-2x+x=30
39-x=30
x=9
So 9 members play both badminton and tennis.
C
Answer: C
Question: Two pipes function simultaneously the reservoir will be filled in 12 hours. One pipe fills reservoir 10 hours faster than the other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)12
B)99
C)20
D)88
E)21
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
Answer: C
Answer: C
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)Rs.2520
B)Rs.3120
C)Rs.3320
D)Rs.2760
E)None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
ANSWER:B
Answer: B
Question: In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is ?
Options:
A)11
B)82
C)10
D)28
E)23
Rationale: Explanation:
Total employees = \inline \frac{(25-10)\times 20}{10}=30
Hence number of educated employees = 30-20 = 10
Answer: C
Answer: C
Question: Find the fraction which has the same ratio to 2/13 that 5/34 has to 7/48?
Options:
A)240/1576
B)240/1542
C)240/1547
D)240/1528
E)240/1529
Rationale: P : 2/13 = 5/34 : 7/48
As the product of the means is equal to the product of the extremes.
P*7/48 = 2/13 * 5/34
P*7/48 = 10/442
P = 480/3094 => P = 240/1547
Answer: C
Answer: C
Question: If the average of q, b, c, 14 and 15 is 12. What is the average value of q, b, c and 29
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: q+b+c+14+15 = 12*5 = 60
=>q+b+c = 60-29 = 31
q+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: D
Question: Amit and Ian paint a wall in alternating shifts. First Amit paints alone, then Ian paints alone, then Amit paints alone, etc. During each of his shifts, Amit paints 1/2 of the remaining unpainted area of the wall, while Ian paints 1/3 of the remaining unpainted area of the wall during each of his shifts. If Amit goes first, what fraction of the wall's area will remain unpainted after Amit has completed his 5th shift?
Options:
A)1/27
B)1/54
C)1/81
D)1/162
E)1/216
Rationale: Fraction of area unpainted after FIRST shift of Amit = 1-(1/2) = 1/2
Fraction of area unpainted after FIRST shift of Ian = (1/2)-(1/3)(1/2) = (2/3)(1/2)
Fraction of area unpainted after SECOND shift of Amit = (1/2)(2/3)(1/2)
Fraction of area unpainted after SECOND shift of Ian = (2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after THIRD shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FORTH shift of Ian = (2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)
Fraction of area unpainted after FIFTH shift of Amit = (1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)(2/3)(1/2)=1/162
Answer: option D
Answer: D
Question: Average of first five multiples of 2 is
Options:
A)9
B)6
C)13
D)15
E)16
Rationale: Explanation:
Average=2(1+2+3+4+5)5=6
Answer: Option B
Answer: B
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
Options:
A)6
B)8
C)9
D)10
E)12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: B
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
Options:
A)227
B)268
C)245
D)299
E)271
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer:C:
Answer: C
Question: A bag contains 15 purple jellybeans, 10 green jellybeans, and 10 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be green?
Options:
A)15%
B)29%
C)25%
D)30%
E)35%
Rationale: Probability of green beans = 10 / (15 + 10 + 10) = 10/35 = 29%
Answer is B
Answer: B
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Options:
A)Rs. 24800
B)Rs. 28400
C)Rs. 24400
D)Rs. 28800
E)None of these
Rationale: Explanation:
Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
ANSWER IS D
Answer: D
Question: For the symbol, m”n=n^2−m for all values of m and n. What is the value of 3”3?
Options:
A)6
B)3
C)2
D)1
E)0
Rationale: 3”3= 9 - 3=6
Answer: A
Answer: A
Question: In a garment industry, 12 men working 9 hours per day complete a piece of work in 10 days. To complete the same work in 12 days, working 15 hours a day, the number of men required is:
Options:
A)4
B)5
C)6
D)7
E)9
Rationale: Explanation :
Let the required number of men be x.
Less days, More men (Indirect Proportion)
More working hrs per day, Less men (Indirect Proportion)
Days 8 : 10
Working Hrs 15 : 9 :: 12 : x
=> 12 x 15 x x = 10 x 8 x 12
=> x = 10 x 9 x 12 / (12 x 15)
=> x = 7
Answer : D
Answer: D
Question: Half of 1 percent written as decimal is
Options:
A)5
B)0.5
C)0.05
D)0.005
E)None of these
Rationale: Explanation:
It will be 1/2(1%) = 1/2(1/100) = 1/200 = 0.005
Option D
Answer: D
Question: If 20 typists can type 40 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
Options:
A)63
B)72
C)144
D)180
E)400
Rationale: 20 typists can type 40 letters, so 30 typists can type = 40*30/20
40*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 40*30*60/20*20= 180
D is the answer
Answer: D
Question: In a game of 60 points; A can give B 10 points and C 15 points. Then how many points B can give C in a game of 40 ?
Options:
A)can give C 1 points
B)can give C 4 points
C)can give C 2 points
D)can give C 6 points
E)can give C 8 points
Rationale: A: B = 60 : 50, A : C = 60 : 45.
B/C = ( B/ A * A/C) = (50 / 60 * 60 / 45) = 10/9 = 40 /36
Therefore ,In a game of 40, B can give C 4 points.
Answer is B.
Answer: B
Question: How many two letter words are formed using the letters of the word RAM?
Options:
A)22
B)6
C)8
D)10
E)12
Rationale: Explanation:
The number of letters in the given word is three.
The number of two letter words that can be formed using these four letters is Ã¢Â´PÃ¢â€šÆ’ = 3 * 2 = 6.
Answer: B
Answer: B
Question: Count each 7 which is not immediately preceded by 5 but is immediately followed by either 2 or 3.
How many such 7's are there ?
5 7 2 6 5 7 3 8 3 7 3 2 5 7 2 7 3 4 8 2 6 7 8
Options:
A)2
B)4
C)3
D)5
E)None
Rationale: Answer: A . 2
Answer: A
Question: What is the 8th digit to the right of the decimal point in the decimal expansion of 1/37?
Options:
A) 0
B) 2
C) 4
D) 7
E) 9
Rationale: 1/37=0.027027... So, we have a repeating cycle of 027. Every third digit (2nd, 4th, 6th, ...) to the right of the decimal point is alternating by 2,0,7, thus 8th digit to the right of the decimal point is 2.
Answer: B.
Answer: B
Question: If the average (arithmetic mean) of the four numbers K, 2K + 2, 3K – 5 and 5K + 1 is 63, what is the value of K?
Options:
A) 11
B) 15 3/4
C) 22
D) 23
E) 23 1/11
Rationale: K + 2K +2 + 3K - 5 + 5K +1 = 11K -2
(11K -2)/4 = 63
11K = 63 * 4 +2 = 252 +2 = 254
K = 254 / 11 = 23 1/11
Answer E.
Answer: E
Question: In a series of consecutive odd numbers, 27 is the seventh smallest number and 25 is the tenth largest number. What is the range of the series?
Options:
A) 32
B) 30
C) 29
D)28
E) 14
Rationale: Imp:All are consecutive odd numbers.
27 is the 8th smallest ,there are 6 numbers smaller then 27 ,smallest number :27-12=15
25 is the 10th largest ,so there are 9 numbers larger then 25, largest number:25+18=43
Range:43-15=28
Ans : D
Answer: D
Question: Insert the missing number.
2, 4, 12, 48, 240, (....)
Options:
A)3388
B)1440
C)398
D)278
E)2771
Rationale: Explanation:
Go on multiplying the given numbers by 2, 3, 4, 5, 6.
So, the correct next number is 1440.
Answer: B) 1440
Answer: B
Question: Bongani and Jane are friends. Bongani takes Jane's physics test paper and will not tell her what her mark is. He knows that Jane hates maths so he decides to tease her. Bongani says: “I have 2 marks more than you do and the sum of both our marks is equal to 14. What are our marks?”
Options:
A)j=6,b=8
B)j=3,b=5
C)j=8,b=2
D)j=1,b=3
E)j=5,b=5
Rationale: We have two unknown quantities, Bongani's mark and Jane's mark. Let Bongani's mark be b and Jane's mark be j.
Set up a system of equations
Bongani has 2 more marks than Jane.
b=j+2............(1)
Both marks add up to 14.
b+j=14............(2)
Use equation (1) to express b in terms of j
b=j+2
Substitute into equation (2)
b+j=14
(j+2)+j=14
Rearrange and solve for j
2j=14−2
=12
∴j=6
Substitute the value for j back into equation (1) and solve for b
b=j+2
=6+2
=8
Bongani got 8 for his test and Jane got 6.
Answer is A.
Answer: A
Question: Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?
Options:
A)20
B)34
C)38
D)40
E)46
Rationale: We have that X/24 - (60-X)/2R = 40
Also X/R - (60-X)/2R = 120
So we get that 2x - 60 = 80R
3x - 60 = 240R
Get rid of R
120 = 3x
x = 40
Hence answer is D
Answer: D
Question: Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 6 hours and machine Y produces k bottles in 12 hours. How many hours does it take machines X and Y , working simultaneously , to produce 12k bottles?
Options:
A) 8
B) 12
C) 15
D) 48
E) 24
Rationale: x rate = k/6
y rate = k/12
k/6 + k/12 = 12k / T
solving T = 48
Answer D
Answer: D
Question: Sarah operated her lemonade stand Monday through Friday over a two week period and made a total profit of 200 dollars. On hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days. Each cup she sold had a total cost of 75 cents and Sarah did not incur any other costs. If every day she sold exactly 32 cups and 4 of the days were hot, then what was the price of 1 cup on a hot day?
Options:
A)$ 1.56
B)$ 1.88
C)$ 2.25
D)$ 2.50
E)$ 3.25
Rationale: 6 regular days --> sales = 6*32*x = 192x;
4 hot days --> sales = 4*32*(1.25x) = 160x;
Total sales = 192x+160x = 352x.
Total cost = 10*32*0.75 = 240.
Profit = 352x - 240 = 200 --> x=1.25.
1.25x=~1.56.
Answer: A.
Answer: A