divelab/Sys2Bench huggingface dataset:
Question: Last year, for every 100 million vehicles that traveled on a certain highway, 80 vehicles were involved in accidents. If 4 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000)
Options:
A)1600
B)3200
C)800
D)400
E)200
Rationale: To solve we will set up a proportion. We know that “100 million vehicles is to 80 accidents as 4 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 4,000 million rather than 4 billion. Creating a proportion we have:
100/80 = 4,000/x
Cross multiplying gives us:
100x = 4,000 * 80
x = 40 * 80 = 3200
Answer : B
Answer: B
Question: In track last week, the boys ran sixteen laps. The girls ran four more
laps. Each lap is a quarter of a mile. How many miles did the girls run?
Options:
A)3 miles
B)2 miles
C)5 miles
D)9 miles
E)7 miles
Rationale: The girls ran 16 + 4 = 20 laps. 20 x ¼ = 20/4, which reduces to 5.
The girls ran 5 miles
correct answer C
Answer: C
Question: Two trains 140 m and 160 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)10.7
B)10.9
C)10.2
D)10.8
E)18.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5
= 10.8 sec.
Answer:D
Answer: D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 9 m wide at the top and 7 m wide at the bottom and the area of cross-section is 560 sq m, the depth of cannel is?
Options:
A)39
B)28
C)70
D)80
E)71
Rationale: 1/2 * d (9 + 7) = 560
d = 70
Answer: C
Answer: C
Question: The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP?
Options:
A)56%
B)68%
C)75%
D)85%
E)95%
Rationale: Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area of RR is less than the surface area of sphere PP
16k−4k=12k16k−4k=12k
Now,
=12k16k×100=12k16k×100
=75%=75%
Thus surface area of sphere RR is less than the surface area of sphere P by 75%
C
Answer: C
Question: On January 1, 2076, Lake Loser contains x liters of water. By Dec 31 of that same year, 2/7 of the x liters have evaporated. This pattern continues such that by the end of each subsequent year the lake has lost 2/7 of the water that it contained at the beginning of that year. During which year will the water in the lake be reduced to less than 1/4 of the original x liters?
Options:
A)2077
B)2078
C)2079
D)2080
E)2081
Rationale: The answer is D
here is the long explanation
This fraction problem contains anunspecifiedtotal (the x liters of water in the lake). Pick an easysmartnumber to make this problem easier. Usually, the smart number is the lowest common denominator of all the fractions in the problem. However, if you pick 28, you will quickly see that this yields some unwieldy computation.
The easiest number to work with in this problem is the number 4. Let's say there are 4 liters of water originally in the lake. The question then becomes: During which year is the lake reduced to less than 1 liter of water?
At the end of 2076, there are 4 × (5/7) or 20/7 liters of water in the lake. This is not less than 1.
At the end of 2077, there are (20/7) × (5/7) or 100/49 liters of water in the lake. This is not less than 1.
At the end of 2078, there are (100/49) × (5/7) or 500/343 liters of water in the lake. This is not less than 1.
At the end of 2079, there are (500/343) × (5/7) or 2500/2401 liters of water in the lake. This is not less than 1.
At the end of 2080, there are (2500/2401) × (5/7) or 12500/16807 liters of water in the lake. This is less than 1.
Notice that picking the number 4 is essential to minimizing the computation involved, since it is very easy to see when a fraction falls below 1 (when the numerator becomes less than the denominator.) The only moderately difficult computation involved is multiplying the denominator by 7 for each new year.
The correct answer is D.
Answer: D
Question: In a group of 6 boys and 4 girls are to be selected. In how many different ways can they be selected such that at least one boy should be there ?
Options:
A)209
B)200
C)210
D)225
E)221
Rationale: No of boys = 6
No of girls = 4
Therefore,
No of ways at least 1 boy can be selected = 6C4 * 4C0 + 6C3* 4C1 + 6C2*4C2 + 6C1 * 4C3
= 15 + 80 +90 + 24
= 209
Ans - A
Answer: A
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
Options:
A)1120 m2
B)1250 m2
C)1210 m2
D)1200 m2
E)1300 m2
Rationale: π (232 – 122) = 1210
ANSWER:C
Answer: C
Question: How many 4-digit positive integers are there, where each digit is positive, and no 4 adjacent digits are same?
Options:
A)1236
B)3024
C)4096
D)4608
E)6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
Fourth digit, 6 possibilities.
9*8*7*6 = 3024.
B
Answer: B
Question: According to the directions on the can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12 ounces cans of the concentrate are required to prepare 360 6 ounces servings of orange juice?
Options:
A)a) 45
B)b) 34
C)c) 50
D)d) 67
E)e) 100
Rationale: Its A.
Total juice rquired = 360*6 = 2160 ounce
12 ounce concentate makes = 12 * 4 = 48 ounce juice
Total cans required = 2160/48 = 45.
Answer A
Answer: A
Question: Jack and Jill are marathon runners. Jack can finish a marathon (42 km) in 7 hours and Jill can run a marathon in 4.2 hours.What is the ratio of their average running speed? (Jack: Jill)
Options:
A)14/15
B)15/14
C)5/5
D)5/4
E)Cannot be determined
Rationale: Average Speed of Jack =Distance/ Time
= 42 /7 = 6
Average Speed of Jill = 42/(4.2) = 10
Ratio of Average speed of Jack to Jill =6/10 = 3/5
Answer C
Answer: C
Question: If the sides of a square are multiplied by sqrt(5), the area of the original square is how many times as large as the area of the resultant square?
Options:
A)5%
B)20%
C)50%
D)100%
E)120%
Rationale: Let x be the original length of one side.
Then the original area is x^2.
The new square has sides of length sqrt(5)*x, so the area is 5x^2.
The area of the original square is 1/5 = 20% times the area of the new square.
The answer is B.
Answer: B
Question: A sum of Rs. 12500 amounts to Rs. 16000 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)7%
B)5%
C)6%
D)8%
E)14%
Rationale: S.I. = (16000 - 12500) = Rs. 3500/-
Rate = (100 * 3500) / (12500 * 4) = 7%
ANSWER:A
Answer: A
Question: A bonus of Rs.2800 is to be divided among 3 people such that Alex gets twice as much as David, who receives one-fourth as much as Peter. What amount did Peter get?
Options:
A)1600
B)1602
C)2768
D)2686
E)1297
Rationale: Explanation:
Let Peter’s share be x.
Hence, David gets x/4 and Alex gets x/2.
x + x/4 + x/2 = 2800
7x/4 = 2800
x = Rs.1600
ANSWER: A
Answer: A
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is:
Options:
A)2 : 3
B)3 : 2
C)3 : 4
D)4 : 3
E)1 : 2
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 --> 1/x + 4/y = 1/15 ------ (i)
Also, 200/x + 400/y = 25/3 --> 1/x + 2/y = 1/24 ----(ii)
Solving (i) and (ii), we get: x = 60 and y = 80.
--> Ratio of speeds = 60 : 80 = 3 : 4.
Answer : C.
Answer: C
Question: in a company the salary of 40 percentage of 400 employees is equal to 20 percentage of x employees, then what is x?
Options:
A)200
B)350
C)700
D)800
E)1,400
Rationale: 40/100(400) = 2/10(x)
X = 800..
Option D.
Answer: D
Question: A basketball team comprising of 5 players decides to get ice cream from a diner. What is the probability that Alex a member of the team will stand next to only person in the queue to get his ice cream?
Options:
A) 15%
B) 22%
C) 10%
D) 20%
E) 25%
Rationale: Possible standing position is 5! = 120
Alex Standing next to one person in the queue is 5 Combination 2
=5!/2!(5-2)!
=120/2(6)
=120/12
= 10
Answer = C
Answer: C
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
Options:
A)60 cm2
B)30 centimeter sqaure
C)45 cm2
D)15 cm2
E)None of these.
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2
14. The area of a square is 40
ANSWER:B
Answer: B
Question: A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 38 percent, what is the discount rate on mysteries?
Options:
A)18%
B)29.68%
C)19.68%
D)29%
E)68%
Rationale: Let B be the discount on biographies and M be the discount on mysteries
So., B + M = 0.38 -----(1)
And
(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19
--> 100(1-(1-B)) + 36(1-(1-M) = 19
100B + 36M = 19 ------(2)
Solving 12., we get M = 0.2968 = 29.68%
B
Answer: B
Question: In one hour, a boat goes 7 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Options:
A)3 km/hr
B)4 km/hr
C)5 km/hr
D)6 km/hr
E)8 km/hr
Rationale: Upstream relative speed is u + v=7km/hr
Downstream speed is u-v = 5
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =7+5
2u=12
Finally, u=6.
ANSWER : D
Answer: D
Question: Each of the following equations has at least one solution EXCEPT
Options:
A)–2^n = (–2)^-n
B)2^-n = (–2)^n
C)2^n = (–2)^-n
D)(–2)^n = –2^n
E)(–2)^-n = –2^-n
Rationale: a) –2^n = (–2)^-n
–2^n = 1/(–2)^n
–2^n * (–2)^n = 1, Keep it. Let's solve the other options..!!
b) 2^-n = (–2)^n
1/2^n = (–2)^n
1 = (–2)^n * (2^n)
For n=0, L.H.S = R.H.S
c) 2^n = (–2)^-n
2^n = 1/ (–2)^n
(2^n) * (–2)^n = 1
For n=0, L.H.S = R.H.S
d) (–2)^n = –2^n
(–2)^n / –2^n = 1
For n=1, L.H.S = R.H.S
e) (–2)^-n = –2^-n
1/ (–2)^n = 1/–2^n
For n=1, L.H.S = R.H.S answer is A
Answer: A
Question: A colony of bacteria in a petri dish grew by 150% from t0 to t1. The number of bacteria grew by 400% from t0 to t2. What was the percentage growth in the number of bacteria from t1 to t2?
Options:
A) 500%
B) 167%
C) 200%
D) 250%
E) 100%
Rationale: The bacteria grew by 150% for t0-t1, x+1.5x = 2.5x, and bacteria grew by 400% for t0-t2, x+4x = 5x. So, bacteria growth from t1-t2 = (5x-2.5x)/2.5x = 100%
Answer is E
Answer: E
Question: A train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
Options:
A)45 m
B)50 m
C)54 m
D)72 m
E)None of these
Rationale: Let actual speed of train = S m /sec
and length of train = L m.
Then, S - 2×5/18=L9
⇒ 9S = L + 5 ...… (i)
and S - 4 × 5⁄18 = L⁄10
⇒ 90S = 9L + 100 .....(ii)
By (i) & (ii), we get L = 50 m.
Answer B
Answer: B
Question: A patient was given a bottle of tablets by the doctor and he was asked to take five tablets in a gap of 5 minutes.
In how much time will he be able to take all the five tablets?
Options:
A)1 Hour.
B)2 Hour.
C)30 min
D)20 min
E)Cannot be determined
Rationale: Suppose he takes the first tablet at 8:00 pm. Then the second will be consumed by him at 8:05, third at 8:10, fourth at 8:15 and fifth at 8:20.
Time = 20 min
Answer D
Answer: D
Question: Some of 50%-intensity red paint is replaced with 25% solution of red paint such that the new paint intensity is 35%. What fraction of the original paint was replaced?
Options:
A)1/35
B)1/5
C)2/3
D)3/5
E)4/5
Rationale: 35% is 10%-points above 25% and 15%-points below 50%.
Thus the ratio of 25%-solution to 50%-solution is 3:2.
3/5 of the original paint was replaced.
The answer is D.
Answer: D
Question: Baker Donley is storing cake boxes in cartons that measure 25 inches by 42 inches by 60 inches. If the measurement of each cake box is 8 inches by 7 inches by 5 inches, then what is the maximum number of cake boxes that can be placed in each carton?
Options:
A)330
B)300
C)252
D)225
E)210
Rationale: Baker Donley is storing cake boxes in cartons The dimensions of the carton are 25x 42x 60and those of each cake box are 8x 7x 5.
To maximize number of boxes try and fit maximum into the base of the box. If you take the base as 25x 42and fit 5 x 6 boxes of 5x 7, then the total number of boxes is 5 x 6 x integer(60/8) = 5 x 6 x 7 = 210.
Alternatively you could try taking the base as 60x 42and fit 12 x 6 boxes of 5x 7, then the total number of boxes is 12 x 6 x integer(25/8) = 12 x 6 x 3 = 216. But since that is not an answer option, I go with (E) 210.
Answer: E
Question: Rohit invests a sum of money at compound interest which doubles itself in 3 years, find in how many years will it amount to four times itself ?
Options:
A)6
B)7
C)8
D)9
E)2
Rationale: Explanation:
Case (I) When Time (T) = 3 years, principle P becomes 2P.
Therefore, amount = 2P
A = P (1 + R/100)T
2P = P (1 + R/100)3
(1 + R/100)3 = 2
(1 + R/100) = 3√2 -------- (A)
(III) Find T for which P becomes 4P
When Time = X and Amount = 4P
4P = P (1 + R/100)X
(1 + R/100)X = 4
(1 + R/100) = 41/X --------- (B)
Equating (A) and (B) we get,
41/X = 3√2 = 21/3
22/X = 21/3
2/X = 1/3
X = 6 years
ANSWER: A
Answer: A
Question: If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
Options:
A)2:8
B)2:6
C)2:2
D)2:1
E)2:3
Rationale: 5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1
Answer:D
Answer: D
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 120 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)120y/x
B)120-y
C)120-x
D)120x/y
E)120x-y
Rationale: A wheel covers 2πr distance in one revolution. where r= diameter/2
First wheel covers d feet in 120 rev. => d= 120* 2π * (x/2)
Second wheel covers d feet in let's say P revolutions; => d = P* 2π * (y/2)
comparing both equations:-
=> p= (120∗2π∗x/2)/(2π∗y/2)
=> 120x/y
Answer :- D
Answer: D
Question: Jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 12 percent solution will be required?
Options:
A)18
B)20
C)24
D)33.75
E)42
Rationale: let a=amount of 4% acid and b= amount of 12% acid.
Now, The equation translates to,
0.04a + .12b = .05(a+b)
but a+b= 60
therefore .04a + .12b = .05(60)
=> 4a + 12b = 300
but b=60-a
therefore
4a+ 12(60-a) = 300
=> 16a = 420
hence a = 26.25.b= 60-26.25 = 33.75
Answer : D
Answer: D
Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 5t seconds, then what is the length of the platform?
Options:
A)L
B)2L
C)3L
D)4L
E)5L
Rationale: The train passes a pole in t seconds, so velocity v = L/t
(L+P)/v = 5t
(L+P) / (L/t) = 5t
P = 4L
The answer is D.
Answer: D
Question: If the average (arithmetic mean) of a and b is 210, and the average of b and c is 160, what is the value of a − c?
Options:
A)−220
B)−100
C)100
D)135
E)It cannot be determined from the information given
Rationale: Question: a - c = ?
(a + b)/ 2 =210 ===> a + b =420
(b + c)/2 = 160 ===> b + c = 320
(a + b) - (b + c) = 420 - 320 ===> a + b - b - c = 100 ===> a - c =100
Answer: C
Answer: C
Question: In a division, divident is 725, divisior is 36 and quotient is 20. Find the remainder.
Options:
A)A)4
B)B)3
C)C)2
D)D)5
E)E)6
Rationale: Explanation:
725 = 36 x 20 + r
725 = 720 + r
r = 725 - 720 = 5
Answer: Option D
Answer: D
Question: A sum fetched a total simple interest of 4020.75 at the rate of 9 %.p.a. in 5 years. What is the sum?
Options:
A)5768
B)8925
C)2345
D)6474
E)8935
Rationale: Principal = (100 x 4020.75)/(9 x 5)
= 402075/45
= 8935.
ANSWER E
Answer: E
Question: Find the value of log y(x4) if logx(y3) = 2
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: logx(y3) = 2 : given
x2 = y3 : rewrite in exponential form
x4 = y6 : square both sides
x4 = y6 : rewrite the above using the log base y
logy(x4) = logy(y6) = 6
correct answer C
Answer: C
Question: 4.2x4.2-1.9x1.9/2.3x6.1 is equal to:
Options:
A)2
B)1
C)3
D)4
E)8
Rationale: Given Expression
=(a2 - b2)/(a + b)(a - b)
=(a2 - b2)/(a2 - b2)
= 1.
Answer is B.
Answer: B
Question: In a 1000 m race, A beats B by 200 meters or 25 seconds. Find the speed of B?
Options:
A)8
B)9
C)7
D)5
E)2
Rationale: Since A beats B by 200 m or 25 seconds, i
t implies that B covers 200 m in 25 seconds.
Hence speed of B = 200/25 = 8 m/s.
Answer: A
Answer: A
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 20 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
Options:
A)230/(30+10A)
B)230/(30+60A)
C)230/38A
D)220/(30+10A)
E)220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-20) + (160-70)) in 60 minutes.
230 Kms in 60 minutes ==> 3.8km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: A
Question: A certain sum amounts to Rs.1600 in 4 years and Rs.1900 in 7 years. Find the rate % per annum?
Options:
A)9.33%
B)7.33%
C)5.33%
D)8.33%
E)6.33%
Rationale: 4 --- 1600
7 --- 1900
--------------
3 --- 300
N = 1 I = 100 R = ?
P = 1600 - 400= 1200
100 = (1200*1*R)/100
R = 8.33%
Answer: D
Answer: D
Question: A bag contains 20 black balls and 10 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)2/5
B)5/7
C)1/2
D)1/4
E)1/3
Rationale: Total number of balls = 20+10 = 30
no. of white balls = 10
probability of drawing a white ball = 10/30 = 1/3
Answer is E
Answer: E
Question: Points A, B, and, C have xy-coordinates (2,0), (8,12), and (14,0), respectively. Points X, Y, and Z have xy-coordinates (6,0), (8,4), and (10,0), respectively. What fraction Q of the area of triangle ABC is the area of triangle XYZ?
Options:
A) 1/9
B) 1/8
C) 1/6
D) 1/5
E) 1/3
Rationale: If you notice, both triangles ABC and XYZ have a side on X axis. we can take these sides as bases for each triangle, therefore
Area of ABC is 1/2*12*12 (Height of ABC is the y coordinate of the third point (8,12))
similarly Area of XYZ is 1/2*4*4
dividing area of XYZ with that of ABC gives Q=1/9.A
Answer: A
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
Options:
A)196
B)630
C)1260
D)2520
E)2860
Rationale: L.C.M. of 12, 18, 21 30 2 | 12 - 18 - 21 - 30
----------------------------
= 2 x 3 x 2 x 3 x 7 x 5 = 1260. 3 | 6 - 9 - 21 - 15
----------------------------
Required number = (1260 ÷ 2) | 2 - 3 - 7 - 5
= 630.
Answer: Option B
Answer: B
Question: There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
Options:
A)265
B)276
C)375
D)387
E)390
Rationale: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C
Answer: C
Question: If b is greater than 1, which of the following must be negative?
Options:
A)(2 - b)(b - 1)
B)(b - 1)/3b
C)(1 - b)^2
D)(2 - b)/(1 - b)
E)(1 - b^2)/b
Rationale: To be -ive, we should remember it should not be zero apart from being positive...
C will always be 0 or positive..
A and D will be zero at b=2..
B will always be positive..
left is E, where the numerator will always be negative and denominator, a positive..
ans E
Answer: E
Question: For a,f,d are the positive integers, and d|a means that “a is divisible by d”, if d|af, which of the following must be true?
Options:
A)d|a
B)d|f
C)d|2af
D)d|(a+f)
E)d|(a-f)
Rationale: d/a means a is divisible by d
d/af means af divisible by d.
all are integers so ,
if af is divisible by d,
1 a can be divisible by d
or
2 f can be divisble by d.
so the question stem asks must true.
so option a and b are could but not must.
option c is 2af divisible by d. if ab is divisible by d then 2af is divisible by d.
option d and e we can't predict.
so option C is correct.
Answer: C
Question: Find the value of 72519 x 9999 = m?
Options:
A)557842343
B)476686756
C)576763467
D)725117481
E)856443356
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: Each of the 59 members in Mount school class is required to sign up for a minimum of one and a maximum of three academic clubs. The three clubs to choose from are the poetry club, the history club, and the writing club. A total of 22 students sign up for the poetry club, 27 students for the history club, and 28 students for the writing club. If 6 students sign up for exactly two clubs, how many students sign up for all three clubs?
Options:
A)2
B)5
C)6
D)8
E)9
Rationale: Each of the 59 members in Mount school class is required to sign up for a minimum of one and a maximum of three academic clubs.Total = G1 + G2 + G3 - (# In exactly 2) - 2*(# in 3 sets)
59 = 22+27+28 - (6) - 2x
so, # In 3 sets = 6=C
Answer: C
Question: There are 10 stations on a railway line. The number of different journey tickets that are required by the authorities is :
Options:
A)90
B)92
C)91
D)None of these
E)Cannot be determined
Rationale: Explanation :
From a certain station, there will be a ticket for each of the other 9 stations.
Since, there are 10 stations on the railway line, the number of different journey tickets will be 10×9 i.e 90.
Answer : A
Answer: A
Question: Laura can paint 1/x of a certain room in 20 minutes. What fraction C of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)1/(3x)
B)3x/(x-3)
C)(x – 3)/(3x)
D)x/(x-3)
E)(x-3)/x
Rationale: Options with variables are often done by plugging in numbers.
Both working together can paint the room in 1 hr so if their individual rates were equal, each would take 2 hours alone.
2 hours is 120 mins so in 20 mins each would complete C=120/20 = 1/6th of the room alone.
So if x = 6 (Laura completes 1/6th of the room in 20 mins), the correct option will give 1/6. (Joseph will also paint 1/6th of the room if their rates are same)
If you put x = 6 in the options, only option (C) will give 1/6
Answer (C)
Answer: C