divelab/Sys2Bench huggingface dataset:
Question: If 0 < M < Y, M is an odd number and Y is a prime number, which of the following can be the value of M + Y ?
Options:
A)11.
B)13.
C)17.
D)10.
E)7.
Rationale: If m is odd ,implies m(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2m=1 since 0<M<Y therefore M+Y =3. But 3 is not an option
which implies y is odd,
Now M(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: D
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-4, 1), (1, 1), (1, -3) and (-4, -3)?
Options:
A)16
B)20
C)24
D)25
E)30
Rationale: Length of side 1= 4+1=5
Length of side 2= 3+1= 4
Area of rectangle= 5*4= 20
B is the answer
Answer: B
Question: A cistern is normally filled in 12 hrs,but takes 2 hrs longer to fill because of a leak on its bottom,if Cistern is full ,how much time citern would empty?
Options:
A)10 hours
B)84 hours
C)30 hours
D)40 hours
E)50 hours
Rationale: If leakage/hour=1/x, then 1/12 -1/x= 1/14, solving 1/x=1/84
So in 84 hours full cistern will be empty.
ANSWER:B
Answer: B
Question: By using the numbers 1, 2, 3, 5 and 7 only once, how many five digit numbers can be made that are divisible by 25?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: A number to be divisible by 25 must end with 00, 25, 50, or 75.
So, there are the following cases possible:
137-25 --> the first three digits can be arranged in 3=6 ways.
123-75 --> the first three digits can be arranged in 3=6 ways.
Total = 6 + 6 = 12.
Answer: C.
Answer: C
Question: what is the speed of a stream if a canoes rows upstream at 8km/hr and downstream at 10.5km/hr.
Options:
A)1.5 kmph
B)1.25 kmph
C)1.35 kmph
D)1.27 kmph
E)1.22 kmph
Rationale: Sol.
Speed of stream = 1/2(10.5 -8) kmph = 1.25 kmph.
Answer B
Answer: B
Question: The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 24 minutes is
Options:
A)17.2 km
B)7.2 km
C)7.6 km
D)17.6 km
E)27.2 km
Rationale: speed of a boat in still water = 15 km/hr
Speed of the current = 3 km/hr
Speed downstream = (15+3) = 18 km/hr
Distance travelled downstream in 24 minutes=(24/60)×18=(2×18)/5 = 7.2 km
Answer is B
Answer: B
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12 m
B)111.22 m
C)111.19 m
D)118.12 m
E)311.12 m
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.Answer:A
Answer: A
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)80
B)89
C)78
D)67
E)56
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer: Option B
Answer: B
Question: In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
Options:
A)1 kg
B)200 gms
C)800 gms
D)1.8 kg
E)None of these
Rationale: In 1 kg mixture quantity of iron = 200 gm
Let x gm sand should be added, then
10% of (1000 + x) = 200
\ x = 1000 gm = 1 kg
Answer A
Answer: A
Question: David and Rachel are getting married. The extended family wants to have its picture taken, but David's father is unwilling to stand next to Rachel's mother. How many options does the photographer have to arrange the 8 family members in a row for the picture?
Options:
A)9!
B)9×8!
C)6×7!
D)10!/2!
E)10!
Rationale: In how many ways David's father and Rachel's mother can stand together? Consider them as one unit: {F, M}. So, we'd have 9 units {F, M}, 1, 2, 3, 4, 5, 6, which can be arranged in 7! ways. David's father and Rachel's mother within their unit can be arranged in 2! ways. Therefore, David's father and Rachel's mother can stand together in 7!*2! ways.
Total - Restriction =
= 8! - 7!*2! =
= 7!(8 - 2!) =
= 6*7!.
Answer: C.
Answer: C
Question: A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze?
Options:
A)154 cm2
B)308 m2
C)150 m2
D)407 m2
E)None of these
Rationale: Area of the shaded portion
= 1⁄4 × π × (14)2 = 154 m2
Answer A
Answer: A
Question: Seven friends are planning to attend a concert. If another friend also goes with them, they will get a group discount on their tickets. If the new total price of the tickets with the group discount is the same as the original total price of the tickets without the group discount, how much is the discount?
Options:
A)8.5%
B)12.5%
C)16.5%
D)19.5%
E)21.5%
Rationale: Let x be the original price of one ticket.
The total original cost is 7x.
The new cost is 8y, where y is the discounted price of one ticket.
7x = 8y
y = 7x/8 = 0.875x which is a discount of 12.5%.
The answer is B.
Answer: B
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number H of employees who take the subway to work?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible H: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: D
Question: Mary is expected to pay back a total sum of $819200 to her bank as mortgage. If she is expected to make a payment which is double of the previous months amount, how long will it take her to fully repay the loan if her initial payment was $400.
Options:
A)13
B)15
C)12
D)10
E)11
Rationale: First payment--$400
Total amount to be repaid--$819200
First month payment--$400
Second month payment--$400*2=$800
Third month payment--$800*2=$1600
Fourth month payment--$1600*2=$3200
Fifth month payment--$3200*2=$6400
Sixth month payment--$6400*2=$12800
Seventh month payment--$25600*2=$51200
Eight month payment--$51200*2=$102400
Ninth month payment--$102400*2=$204800
Tenth month payment--$204800*2=$409600
Eleventh month payment--$409600*2=$819200
Answer is E
Answer: E
Question: What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
Options:
A)$788
B)$812
C)$864
D)$878
E)$912
Rationale: After one year: 1.2 * $500
After two years: (1.2)^2 * $500
After three years: (1.2)^3 * $500 = $864
The answer is C.
Answer: C
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
Options:
A)18/35
B)18/18
C)18/19
D)18/17
E)18/12
Rationale: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Answer: A
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
Options:
A)54.48
B)54.68
C)54.6
D)54.58
E)None of these
Rationale: Explanation:
(55×50)+(60×55)+(45×60) / 55+60+45
8750 / 160=54.68
Option B
Answer: B
Question: How many numbers amongst the numbers 7 to 56 are there which are exactly divisible by 8 but not by 6?
Options:
A)Nil
B)1
C)2
D)3
E)More than 3
Rationale: 8,16,24,32,40,48,56 are divisible by 8.
24,48 are divisible by 6 also.
So there are 5 numbers exactly divisible by 8 but not by 6
ANSWER:E
Answer: E
Question: The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?
Options:
A)1:96
B)1:92
C)1:98
D)1:94
E)1:99
Rationale: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.
(4x)(3x) = 6912
12x2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12x2 = 1 : 4x
= 1:96.
Answer:A
Answer: A
Question: The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)90, 10 kmph
B)35, 27 kmph
C)50, 60 kmph
D)45, 55 kmph
E)45, 65 kmph
Rationale: Speed of the boat in still water = (80+100)/2 = 90 kmph. Speed of the stream = (100-80)/2 = 10 kmph
ANSWER:A
Answer: A
Question: The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?
Options:
A)20%
B)18%
C)15%
D)12%
E)14%
Rationale: 100 * 100 = 10000
80 * 110 = 8800
10000------- 1200
100 ------- ? = 12%
ANSWER:D
Answer: D
Question: The ratio of numbers is 3:4 and their H.C.F is 8. Their L.C.M is:
Options:
A)12
B)96
C)24
D)48
E)98
Rationale: Let the numbers be 3x and 4x.
Then their H.C.F = x. So, x = 8.
So, the numbers are 24 and 32.
L.C.M of 24 and 32 = 96.
ANSWER:B
Answer: B
Question: If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={12,12,12...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
Options:
A)a) k(n+m+mn)+ k
B)b) (1+n+m+mn)(k+1)
C)c) k^2(mn+n/m)
D)d) kmn(k+m+n)
E)e) None of the above.
Rationale: a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
Mike
C
Answer: C
Question: A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Options:
A)220
B)277
C)298
D)100
E)271
Rationale: A can give B (5 min - 4 1/2 min) = 30 sec start.
The distance covered by B in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
A can give B 100m start.
Answer:D
Answer: D
Question: A password of a computer used four digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Options:
A)1/32
B)1/16
C)1/8
D)2/5
E)1/2
Rationale: We have four digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 * 5/10 =1/16 (B)
Answer: B
Question: If x is an even integer and y is an odd integer, which of the following is an even integer?
Options:
A)x+y
B)x+2y
C)3x+y
D)x+y^2
E)x+y+2
Rationale: Plug in an even integer for x; in this case 2
Plug in an odd integer for y; in this case 1
2+1 = 3 Odd
2+(2*1) = 4 Even
(3*2)+1 = 6 + 1 = 7 Odd
2+(1^2) = 2 + 1 = 3 Odd
2+1+2 = 5 Odd
Answer: B
Answer: B
Question: The sum of the present age of Henry and Jill is 48. What is their present ages if 9 years ago Henry was twice the age of Jill?
Options:
A)and 27
B)and 24
C)and 22
D)and 29
E)of these
Rationale: Let the age of Jill 9 years ago be x, age of Henry be 2x
x+9 + 2x+9 = 48
x = 10
Present ages will be 19 and 29
Answer : D
Answer: D
Question: Which number can we add to 722425 to get a number exactly divisible by 456?
Options:
A)312
B)335
C)347
D)361
E)383
Rationale: 722425 / 456 = 1584 with a remainder of 121.
We need to add 456 - 121 = 335
The answer is B.
Answer: B
Question: The mean of four integers L will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I, II, and III
Rationale: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....A
Answer: A
Question: In a class there are 10 boys and 25 girls. In how many ways can a boy and a girl be selected?
Options:
A)400
B)250
C)600
D)530
E)630
Rationale: Explanation:
We can select one boy from 10 boys in 10 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 10 * 25 ways i.e., = 250 ways.
Answer: Option B
Answer: B
Question: On a certain transatlantic crossing, 15 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
Options:
A)33 1/3%
B)40%
C)37.5%
D)60%
E)66 2/3%
Rationale: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 15 => X= 37.5.
Answer C
Answer: C
Question: Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?
Options:
A)4.1
B)3.6
C)2.6
D)5.0
E)5.5
Rationale: B
3.6
In this simple subtraction series, each number decreases by 0.4.
Answer: B
Question: If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?
Options:
A)–4
B)–3
C)–2
D)–1
E)0
Rationale: Just putting values, the LHS becomes
n=0 --> 11
n=-1 --> 11/10
n=-2 --> 11/100
n=-3 --> 11/1000
Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.
Answer is B.
Answer: B
Question: The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3 per metre approximately
Options:
A)4457
B)4567
C)4235
D)4547
E)4675
Rationale: Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.
Answer: Option A
Answer: A
Question: The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?
Options:
A)5100
B)5120
C)5130
D)5140
E)5160
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
8000 × 80/100 × 80/100 = 5120
B
Answer: B
Question: Statement: "In order to bring punctuality in our office, we must provide conveyance allowance to our employees."
Assumptions:
1)Conveyance allowance will not help in bringing punctuality.
2)Discipline and reward should always go hand in hand.
Options:
A)Only assumption I is implicit
B)Only assumption II is implicit
C)Either I or II is implicit
D)Neither I nor II is implicit
E)Both I and II are implicit
Rationale: Assumption I goes against the statement. So, it is not implicit. The allowance will serve as a reward to the employees and shall provoke them to come on time. So, II is implicit.
B)
Answer: B
Question: Steel company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?
Options:
A) 16
B) 64
C) 256
D) 576
E) 4096
Rationale: MAGOOSHOFFICIAL SOLUTION:
Steel company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.
N = 4*4*4*4 = 16*16 = 256
Answer = (C)
Answer: C
Question: If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?
Options:
A) 20 - x
B) 18 - x
C) x + 18
D) x + 2
E) x - 2
Rationale: Original Digits=xy i.e. Number=10x+y
After reversing the digits:
Digits=yx i.e. Number=10y+x
10y+x is 9 more than 10x+y
10x+y+18=10y+x
10x-x+18=10y-y
9x+18=9y
x+2=y
OR
y=x+2
Ans:D
Answer: D
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 15, how many more dollars, in terms of x, will it cost per person?
Options:
A) x/6
B) x/16
C) x/40
D) 3x/40
E) 3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is D.
Answer: D
Question: Reb normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Reb averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives?
Options:
A)135
B)105
C)95
D)75
E)45
Rationale: Reb normally drives to work in 45 minutes at an average speed of 40 miles per hour.
Use formula D = RT
Car:
T1: 45 min
R1: 40 mph
D1: [(40*45)/60] = 30 miles
Bike:
T1:?
R2: 12 - 16 mph
D2: 08*D1 = 24 miles
T1: [(24*60)/12] = 120 min (Only 12 mph speed yields an answer given in the choices)
Therefore, Deb has to leave 120 min - 45 min = 75 min early
ANSWER: D
Answer: D
Question: How many pieces of 0.40 meteres can be cut from a rod 47.5 meteres long
Options:
A)100
B)118
C)120
D)125
E)70
Rationale: Explanation:
We need so simple divide 47.5/0.40,
=(4750/40) = 118
Option B
Answer: B
Question: The average age of a class of 20 students is 18 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
Options:
A)40 years
B)41 years
C)42 years
D)43 years
E)44 years
Rationale: If age of the teacher was 18, average would not have changed.
Since average increased by 2,
Age of the teacher=18+22×1=40
ANSWER:A
Answer: A
Question: If 3x=9y=z, what is x+y, in terms of z?
Options:
A)z/2
B)2z
C)z/3
D)3z/5
E)4z/9
Rationale: 3x=9y=z
x = z/3
and y = z/9
x+y = z/3 + z/9 = 4z/9
Answer is E
Answer: E
Question: Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: B takes x hours
A takes x + 10 hours
rate of A = 660/x+10
rate of B = 660/x
thus, 660/x = (660/x+10)*1.10
x = 100
so B = 100
A = 110 sprockets per hour
660/110 = 6
ANSWER:A
Answer: A
Question: If a book is sold at 8% profit instead of 8% loss, it would have brought Rs 12 more. Find out the cost price of the book
Options:
A)Rs 75
B)Rs 72
C)Rs 60
D)Rs 70
E)Rs 80
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.08 X - 0.92X = 12
=> 0.16 X = 12 = 12/0.16 = Rs 75
ANSWER:A
Answer: A
Question: Two trains 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)11.16 sec
B)11.8 sec
C)27.7 sec
D)10.8 sec
E)17.8 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 170 = 310 m.
Required time = 310 * 9/250 =11.16 sec.
Answer: A
Answer: A
Question: A and B together can do a work In 2 days. A alone can do it in 12 days. What time B will take to do the work alone?
Options:
A)2.4 days
B)8 days
C)1.2 days
D)1.0 days
E)5 days
Rationale: Explanation:
A and B 1day's work = 1/2
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/2) - (1/12) = 2.4 Days
Answer: Option A
Answer: A
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y?
Options:
A)6
B)3
C)4
D)5
E)7
Rationale: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , x-y = 3+2 = 5
ANSWER:D
Answer: D
Question: A computer store offers employees a 15% discount off the retail price. If the store purchased a computer from the manufacturer for $500 dollars and marked up the price 15% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (15% off retail price) as opposed to the final retail price.
Options:
A)52.5
B)54.5
C)55.5
D)57.5
E)59.5
Rationale: Cost price=500
Profit=15% =15% of 500=75
selling price=CP+ Profit
SP=575
a Discount of 10% to employees means 10% off on 575
so 10% of 575= 57.5
Ans D
Answer: D
Question: A shop owner sells 40mtr of cloth and gains SP of 10 mtrs. Find the gain %?
Options:
A)33.33%
B)40%
C)50%
D)66.67%
E)70%
Rationale: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 40 m cloth) – (C.P. of 40 m cloth)
Selling price of 30 m cloth = Selling Price of 40 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 30 m cloth = Rs. 3000 and S.P. of 30 m cloth = Rs. Rs. 4000
Profit% = 10/30 × 100 = 33.33%
Profit of 33.33% was made by the merchant.
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)77
B)66
C)20
D)21
E)24
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: C
Question: Solve the given two equations and find the inequality of X and Y. (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2)
Options:
A)If x>y
B)If x>=y
C)If x<y
D)If x<=y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=4,-5
Y= -4,6
E
Answer: E
Question: In a group of 28 junior high school students, 5 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
Options:
A)7
B)13
C)9
D)12
E)10
Rationale: B
13
Add 1 + 10 + 4 to get 15.
Then subtract 21 from the total students ⇒ 28 – 15 = 13.
Answer is B
Answer: B
Question: A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 15 days before the project is completed, in how many days total will the project be completed?
Options:
A)18
B)21
C)24
D)27
E)30
Rationale: A's rate is 1/20 of the project per day.
B's rate is 1/30 of the project per day.
The combined rate is 1/12 of the project per day.
In the last 15 days, B can do 1/2 of the project.
Thus A and B must complete 1/2 of the project, which takes 6 days.
The total number of days is 6 + 15 = 21.
The answer is B.
Answer: B
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. What is the number of participants?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: Let n be the number of participants.
The number of games is nC2 = n*(n-1) / 2 = 171
n*(n-1) = 342 = 19*18 (trial and error)
The answer is E.
Answer: E