divelab/Sys2Bench huggingface dataset:
Question: A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
Options:
A)22 days
B)4 days
C)13 days
D)6 days
E)9 days
Rationale: (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12).
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Answer is D.
Answer: D
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 7 boys when a boy gets any no. of prizes?
Options:
A)55
B)58
C)343
D)354
E)200
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (7 x 7 x 7) ways = 73 ways = 343 ways Or nr ways = 73 ways = 343 ways
Answer: C
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/10
II. 1/9
III. 1/11
Options:
A)None
B)I only
C)III only
D)II and III only
E)I, II, and III
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us B as the only possible answer.
Answer: B
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 16 times smaller, from source B alone?
Options:
A)6 hours and 40 minutes
B)15 minutes
C)12 minutes
D)10 minutes
E)25 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=40 times smaller or400/16=25 u
B will take 25/60 hrs or 25 minutes.
Ans E
Answer: E
Question: Eight carpenters can individually complete a particular task in 3, 4, 5, and 7 hours, respectively. What is the maximum fraction of the task that can be completed in forty-five minutes if seven of the carpenters work together at their respective rates ?
Options:
A)11/15
B)3/5
C)11/30
D)329/480
E)5/9
Rationale: Farmer A, B, C, and D
A's rate: 1/3 job/hour
B's rate: 1/4 job/hour
C's rate: 1/5 job/hour
D's rate: 1/7 job/hour
By intuition we know that the three fastest farmers are A B and C.
As such
(1/3 + 1/4 + 1/5)*(7/8) = ?
47/80 or (D)
Answer: D
Question: One pipe can fill a pool three times faster than a second pipe. When both pipes are opened, they fill the pool in seven hours. How long would it take to fill the pool if only the faster pipe is used?
Options:
A)3.6 hr
B)4.7 hr
C)5.1 hr
D)9.3 hr
E)9.7 hr
Rationale: fast pipe + slow pipe = together
One pipe fills the pool three times faster than the other pipe so,
hourly fill rates:
1/x + 1/3x = 1/7
Let x = number of hours it would take the fast pipe to fill the pool thus,
x=9.3 hours
Answer: D
Answer: D
Question: Of a certain group of 100 people, 40 graduated from High School M, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School M, did not graduate from College Y, and do not live in City Z ?
Options:
A) 5
B) 15
C) 35
D) 65
E) 85
Rationale: 1. m+y+z+my+yz+mz+myz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Answer: C
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 5650 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
Options:
A)2160
B)2350
C)2000
D)2300
E)None of these
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+5650 = 21150
Exp in % = 100-10 = 90%, 21150 = 90%
Saving = 10 % = 21150 X 10/90 = Rs. 2350
Answer : B
Answer: B
Question: 1,1,3,2,1,5,3,4,10,4,2,?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: 1+1+1=3
2+1+2=5
3+4+3=10
4+2+4=10
ANSWER:A
Answer: A
Question: Dave has no fashion sense, and will wear any combination of garments regardless of whether someone thinks they “match.” Every day Dave chooses an outfit consisting of one of each of the following garments: jacket, tie, shirt, pants, boxers, right sock, left sock, right shoe, left shoe. If Dave has more than one of each of the listed garments, and can make 7200 different outfits, then for how many garments does Dave have exactly five choices?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 7200 = 72*100 = 72*5^2*2^2
Dave has exactly 5 choices for two garments.
The answer is C.
Answer: C
Question: What is the least common multiple of 12, 18, and 24?
Options:
A)72
B)120
C)240
D)360
E)720
Rationale: Let us first write the numbers in the form of prime factors:
12 = 2^2 * 3^1
18 = 2^1 * 3^2
24 = 2 * 17^1
The LCM would be the largest powers of the prime numbers from all these three numbers.
Hence LCM = 72
Option A
Answer: A
Question: The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N.
Options:
A)797
B)197
C)597
D)997
E)297
Rationale: According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 15* 13 + 2 = 197 correc answer B
Answer: B
Question: P alone can complete a piece of work in 6 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
Options:
A)4(3/4)
B)7
C)4
D)5
E)4(1/2)
Rationale: Option E
Explanation:
Work done by P alone in one day = 1/6th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/6 of the total) = 1/18 of the total.
Work done by P and Q, working together in one day = 1/6 + 1/18 = 4/18 = 2/9 of the total
They would take 9/2 days = 4 (1/2) days to complete the work working together.
Answer: E
Question: How many positive factors of 42 are not factors of 56?
Options:
A)1
B)2
C)3
D)four
E)5
Rationale: 42=2*3*7.
So, total number of factors for 42 = 2*2 *2 = 8
factors for 42 = 1,2,3,6,7,14,21 and 42
56=2*2*2*7
So, total number of factors for 56 = 4*2 = 8
factors of 56 = 1,2,4,7,8,14,28 and 56.
Factors same in 42 and 56 are 1,2,7 and 14.
Hence, answer will be D.
Answer: D
Question: A dog takes 5 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 5 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options:
A)25 : 10
B)25 : 8
C)25 : 9
D)8 : 25
E)24 : 8
Rationale: Explanation:
Dog : Hare = (5*5) leaps of hare : 8 leaps of hare = 25 : 8
Answer: B
Answer: B
Question: If integer k is equal to the sum of all even multiples of 15 between 390 and 615, what is the greatest prime factor of k?
Options:
A)5
B)7
C)8
D)13
E)17
Rationale: if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600.
using arithmetic progression to find n : 600 = 390 + (n - 1) 30
210+ 30 = 30n
240 = 3n => n = 8
the sum would be: 8* mean
mean = [600 + 390] / 2 = 495
8*495
C
Answer: C
Question: A certain list of 100 data has an average (arithmetic mean) of 8 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 106 data with standard deviation less than d?
Options:
A)-8 and 0
B)0 and 0
C)0 and 8
D)0 and 16
E)8 and 8
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 8 and 8 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: E
Question: If 6 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)3:2
B)2:2
C)3:4
D)1:2
E)6:1
Rationale: B
2:2
6M + 2B = 4(1M + 1B)
6M + 2B = 4M + 4B
2M = 2B
The required ratio of work done by a man and a boy = 2:2
Answer: B
Question: How long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250m in length?
Options:
A)28.8 sec
B)16.8 sec
C)15.2 sec
D)25.4 sec
E)16.2 sec
Rationale: D = 150 + 250 = 400 m
S = 50 * 5/18 = 125/9
T = 400 * 125/9 = 28.8 sec
ANSWER:A
Answer: A
Question: In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 7th Rd and 8th Ave in the shortest possible time, how many different routes could he take?
Options:
A)156
B)180
C)225
D)252
E)281
Rationale: Bills needs to walk 5 blocks north and 5 blocks east.
One possible solution is NNNNNEEEEE.
There are 10C5 = 252 possible solutions.
The answer is D.
Answer: D
Question: How many integers are divisible by 5 between 10! and 10! + 20 inclusive?
Options:
A)5
B)7
C)8
D)9
E)10
Rationale: A - 7
10! is divisible by 5
There are 4 numbers between 10! and 10!+20 that are divisible by 5.
Hence 5
Answer: A
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio F of men to women?
Options:
A) 5:2
B) 5:1
C) 4:3
D) 4:1
E) 3:1
Rationale: (A)F= 184 x 5 + 170 x 2 = 1260.A
Answer: A
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 35 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
Options:
A)1/4
B)21/26
C)2/3
D)7/8
E)8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .35/40)/ (.65/60) = 21/26 B is the answer
Answer: B
Question: The average of first 17 even numbers is?
Options:
A)10
B)11
C)18
D)20
E)24
Rationale: Sum of 17 even numbers = 17 * 18 = 306
Average = 306/17 = 18
ANSWER:C
Answer: C
Question: Which of the following equivalent to (1/216)^2?
Options:
A)(0.01)^3
B)(0.02)^3
C)(0.03)^3
D)(0.04)^3
E)(0.05)^3
Rationale: (1/36)^2 = (1/6^3)^2 = (1/6)^6 = (1/36)^3 = (0.02)^3
Answer: Option B
Answer: B
Question: On the coordinate plane , points P and U are defined by the coordinates (-1,0) and (3,3), respectively, and are connected to form a chord of a circle which also lies on the plane. If the area of the circle is (25/4) π , what are the coordinates of the center of the circle ?
Options:
A) (1.5,1)
B) (2,-5)
C) (0,0)
D) (1,1.5)
E) (2,2)
Rationale: Although it took me 3 mins to solve this question using all those equations, later I thought this question can be solved easily using options.
One property to keep in mind - A line passing through the centre of the circle bisects the chord (or passes from the mid point of the chord).
Now mid point of chord here is (-1+3)/2, (3+0)/2 i.e. (1,1.5) now luckily we have this in our Ans. choice. so definitely this is the ans. It also indictaes that PU is the diameter of the circle.
There can be a case when PU is not a diameter but in that case also the y-coordinate will remain same as it is the midpoint of the chord and we are moving up in the st. line to locate the centre of the circle.
If ans choices are all distinct (y cordinates) ONLY CHECK FOR Y CORDINATE and mark the ans=D
Answer: D
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 180 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)63
B)30
C)38
D)42
E)48
Rationale: For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
180 / 20 = 9 sandwiches in one part
For bologna we have 7 parts so:
7 * 9= 63
Answer is A
Answer: A
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)100
B)150
C)120
D)130
E)140
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
ANSWER C
Answer: C
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 10'o clock.
Options:
A)60sec
B)62sec
C)66sec
D)64sec
E)54sec
Rationale: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
.
.
9'o clock 8 *6=48sec
10'o clock 9 *6=54sec
So, 54sec at 10'o clock.
ANSWER:E
Answer: E
Question: If one length of a square is tripled, and the original parameter is 4y. What is the new length of one of the sides?
Options:
A)12y/3
B)2y/2
C)6y/3
D)12y/4
E)4y/3
Rationale: If the original parameter is 4y, each length of the square is 4y/4. If the parameter is tripled, then each length becomes 3(4y)/4. This is 12y/4. Answer option D.
Answer: D
Question: The number 94 can be written as the sum of the squares of 4 different positive integers in two ways. Of the following, which can be the sum of these 4 integers?
Options:
A)9
B)14
C)15
D)18
E)20
Rationale: The only possible sum for 4 different squares of an integer with total sum number is 95 are :
48 + 36 + 9 + 1 = 95 which are the square from numbers :8, 6, 3, 1 (total sum number is 16)
or
80 + 9 + 4 + 1 = 95 which are the square from numbers : 9, 3, 2, 1 (total sum number is 14)
hence the answer is (B)
Answer: B
Question: A man spends Rs. 1800 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Options:
A)2050
B)2150
C)2250
D)2350
E)2450
Rationale: Explanation:
Total expenditure for the first 3 months = 3 Ã— 1800 = 5400
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 5400 + 6200 + 9000 + 5200 = Rs. 25800
So, Average monthly income = 25800/12 = Rs. 2150
Answer B
Answer: B
Question: If log 27 = 1.434, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.956
D)0.958
E)0.987
Rationale: log 27 = 1.434
log (33 ) = 1.434
3 log 3 = 1.434
log 3 = 0.478
log 9 = log(32 ) = 2 log 3 = (2 x 0.478) = 0.956.
Answer: Option C
Answer: C
Question: If a fair coin is flipped three times in a row, what is the probability that there will be at least one head and one tail?
Options:
A)3/4
B)11/12
C)15/16
D)31/32
E)63/64
Rationale: The number of possible outcomes is 2^3 = 8
There is one way to get no heads and one way to get no tails.
Thus there are 6 outcomes with at least one head and one tail.
P(at least one head and one tail) = 6/8 = 3/4
The answer is A.
Answer: A
Question: A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?
Options:
A)6 and 1 kmph
B)8 and 2 kmph
C)8 and 1 kmph
D)9 and 1 kmph
E)2 and 1 kmph
Rationale: Explanation:
Downstream speed = 72km/8hrs = 9 kmph
upstream speed = 84km/12hrs = 7 kmph
speed of boat = avg of downstream and upstream speeds
speed of boat = (9+7)/2kmph = 8 kmph.
current speed = half of the difference of downstream and upstream speeds
currend speed = (9-7)/2kmph = 1 kmph
Answer: C
Answer: C
Question: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?
Options:
A)22 1/8 %
B)22 9/2 %
C)22 1/7 %
D)22 1/2 %
E)21 1/2 %
Rationale: 9 = (1*40*R)/100
R = 22 1/2 %
Answer:D
Answer: D
Question: The height of the wall is 6 times its width and lenght of the wall is 7 times its height .if the volume of the wall be 16128 cu.m.its width is
Options:
A)4m
B)5m
C)6m
D)7m
E)8m
Rationale: Explanation:
Let width = x
Then, height=6x and length=42x
42x × 6x × x = 16128
x = 4
Answer: A
Answer: A
Question: The value of a machine is Rs 6,250. It decreases by 20% during the first , 40% during the second year and 30% during the third year. What will be the value of the machine after 3 years?
Options:
A)Rs 2,100
B)Rs 2,200
C)Rs 2,152
D)Rs 2,252
E)none of these
Rationale: Here A = 6250, x = - 20, y = - 40 and z = - 30
Therefore value of the machine after 3 years
= A ( 1 + x/100) ( 1 + y/100) ( 1 + z/100)
= 6250 ( 1 - 20/100) ( 1 - 40/100) ( 1 - 30/100)
= (6250 x 80 x 60 x 70) / (100 x 100 x 100)
= Rs 2,100
ANSWER:A
Answer: A
Question: Solve the equation for x : 6x - 27 + 3x = 4 + 9 - x
Options:
A)4
B)5
C)7
D)9
E)3
Rationale: A
4
9 x + x = 13 + 27
10 x = 40 => x = 4
Answer: A
Question: In a fraction, if 1 is added to both the numerator at the denominator, the fraction becomes 1/2. If numerator is subtracted from the denominator, the fraction becomes 3/4. Find the fraction.
Options:
A)3/7
B)4/7
C)5/7
D)6/7
E)8/7
Rationale: Let fraction be a/b, where a and b are integers.
"If 1 is added to both the numerator and denominator, the fraction becomes 1/2"
(a+1)/(b+1) = 1/2
2(a+1) = b+1
2a + 2 = b + 1
2a - b = -1
"If numerator is subtracted from the denominator, the fraction becomes 3/4"
a/(b-a) = 3/4
4a = 3(b-a)
4a = 3b - 3a
4a + 3a - 3b = 0
7a - 3b = 0
Now we just need to solve system of linear equations:
2a - b = -1 . . . [1]
7a - 3b = 0 . . . [2]
From [1], we get:
b = 2a + 1
Substituting in this value of b into [2], we get
7a - 3(2a+1) = 0
7a - 6a - 3 = 0
a - 3 = 0
a = 3
b = 2(3)+1
b = 7
So original fraction is a/b = 3/7
ANSWER:A
Answer: A
Question: Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 10 = f(x – 2) ?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 2(3x-5)-10 = 3(x-2) - 5
3x = 9
x = 3
The answer is C.
Answer: C
Question: Can you get total of 720 by using six zeros 0,0,0,0,0,0 and any maths operators.
Options:
A)650
B)550
C)700
D)720
E)500
Rationale: D
720
(0!+0!+0!+0!+0!+0!)!
=(1+1+1+1+1+1)!
=(5)!
=6! is 6*5*4*3*2*1=720
Answer: D
Question: A four-digit code can consist of the digits 0 ~ 9 except that it does not contain the digits 1, 2, and 4 at all. If repeated digits are allowed, what is the probability that it has at least one even digit?
Options:
A)145/401
B)845/901
C)1145/1401
D)2145/2401
E)3145/3401
Rationale: P(no even digits) = 4/7*4/7*4/7*4/7 = 256/2401
P(at least one even digit) = 1 - 256/2401 = 2145/2401
The answer is D.
Answer: D
Question: A certain car traveled twice as many miles from Town A to Town B as it did from Town B to Town C. From Town A to Town B, the car averaged 10 miles per gallon, and from Town B to Town C, the car averaged 12 miles per gallon. What is the average miles per gallon that the car achieved on its trip from Town A through Town B to Town C?
Options:
A)11.5
B)9.5
C)13.5
D)10.6
E)14.5
Rationale: step 1) took LCM of 10 and 12.. came as 30. just multiplied by 10...(to make easy calculation)
step 2) 300 distance between B to C... do 300/12 hence 25 gallons used
step 3) twice distance.. hence 300*2= 600... do as above.. 600/10= 60 gallons used
step 4) total gallons.. 25+60=85 gallons
step ) total miles= 300+600= 900 miles
hence.. average of whole journey = 900/85 which comes to 10.6
Answer : D
Answer: D
Question: An average age of A, B and C is 45. If the averageage of A and B be 40 and that of B and C be 43, then the weight of B is
Options:
A)25
B)29
C)31
D)35
E)36
Rationale: Let A, B, C represent their respective age's. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31.
B's age= 31
C
Answer: C
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1456?
Options:
A)1000
B)2217
C)2889
D)2777
E)1300
Rationale: 1456 = P [1 + (5*12/5)/100]
P= 1300
Answer: E
Answer: E
Question: Annie has 100 cards numbered 1 through 100. If she deals seven cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?
Options:
A)95!/100!
B)(94! X 7!)/100!
C)(95! X 5!)/100!
D)(96! X 5!)/100!
E)(97! X 4!)/100!
Rationale: Alex to get 7 consecutive cards in ascending order, to have 7 consecutive at the end is good enough.
There are 94 consecutive numbers in 100: {1, 2, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7, 8}, ..., {94, 95, 96, 97, 98, 99, 100};
Total ways to pick 7 cards out of 100 is {7!*94!}{100!}.
Answer: B.
Answer: B
Question: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0018)?
Options:
A)16.82
B)19.82
C)17.82
D)20
E)22
Rationale: You get 10^2 (100-1) (.0018)
we know 18/10000 = .0018
10^2 (99) * (18/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(18/100).
0.99*18 = 17.82
Answer : C
Answer: C
Question: Find the option to replace the question mark in the series below
5 ? 15 75 525 4725
Options:
A)2
B)6
C)7
D)5
E)8
Rationale: ol: 5 x 1 = 5
5 x 3 = 15
15 x 5 = 75
75 x 7 = 525
525 x 9 = 4725
So ? = 5
Answer:D
Answer: D
Question: If one and a half women, drink one and a half tea in one and a half minutes.
How many tea can 9 women drink in 3 minutes ?
Options:
A)11
B)8
C)37
D)15
E)18
Rationale: E
18
Explanation:
More minutes implies more tea.
More women implies more tea.
The time become twice (3 minutes / 1.5 minutes).
women become six times (9 / 1.5).
Number of tea = 2 * 6 * Original(1.5)
Answer: E
Question: A shop sells bicycles and tricycles. In total there are 10 cycles (cycles include both bicycles and tricycles) and 21 wheels. Determine how many of each there are, if a bicycle has two wheels and a tricycle has three wheels.
Options:
A)b=9,t=1
B)b=7,t=3
C)b=6,t=2
D)b=2,t=5
E)b=6,t=4
Rationale: Let b be the number of bicycles and let t be the number of tricycles.
Set up the equations
b+t=10............(1)
2b+3t=21............(2)
Rearrange equation (1) and substitute into equation (2)
2b+30-3b=21
-b=-9
b=9
Calculate the number of tricycles t
t=10−b
=10−9
=1
There are 1 tricycles and 9 bicycles.
Answer is A.
Answer: A
Question: Which of the following are roots of an equation (x^-2)+(3x^-1)-10=0
Options:
A)1/5 and -1/2
B)-1/5 and 1/2
C)1/5 and 1/2
D)-1/5 and -1/2
E)-5/2 and -1/2
Rationale: Given: (x^-2) + (3x^-1) - 10 = 0
Rewrite as: 1/(x²) + 3/x - 10 = 0
Remove fractions by multiplying both sides by x² to get: 1 + 3x - 10x² = 0
Rearrange to get: 10x² - 3x - 1 = 0
Factor to get: (5x + 1)(2x - 1) = 0
So, EITHER 5x + 1 OR 2x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 2x - 1 = 0, then x = 1/2
So, the roots (solutions) are -1/5 and 1/2
The answer is B.
Answer: B
Question: S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 50, what is the greatest possible value of S minus T?
Options:
A)40
B)42
C)44
D)45
E)48
Rationale: A two-digit integer "ab" can be expressed algebraically as 10a+b.
S-T=(10a+b)-(10b+a)=9(a-b)<50.
The greatest multiple of 9 which is less than 50 is 45.
The answer is D.
Answer: D