divelab/Sys2Bench huggingface dataset:
Question: Varma can read a book in m minutes. What part of the book can he read in 7 minutes?(m>7)
Options:
A)(k - 8)/k
B)k/8
C)8 + k
D)k-8
E)7/m
Rationale: Option E
Explanation:
Part of the book he can read in 1 minute = 1/3
Part of the book he can read in 7 minutes =7/3.
Answer: E
Question: If positive integer k is divided by 12, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
Options:
A)None
B)I
C)II
D)III
E)I and II only
Rationale: k = 12m+2 = 2(6m+1)
I. k + m = 2(6m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: A
Question: If a class of 10 students has six men, how many ways can the men and women be arranged in a circle so that no two men sit next to each other?
Options:
A)5!4!
B)6!5!
C)4!4!
D)10!
E)10!/5!
Rationale: for no two men to sit together, either all are in even or odd position
fix one at any one position then rest five can be fixed in 5! ways...
also rest six position of women can be fixed in 6!..
total ways 6!5!
B
Answer: B
Question: Find the remainder when 4*4! + 5*5! + 6*6! +...................+ 19*19! is divided by 64.
Options:
A)22
B)27
C)40
D)28
E)11
Rationale: 8*8! and its subsequent terms are exactly divisible by 64. As highest power of 2 in 64 is 6 and highest power of 2 in 8! is 7 which is greater than 6. So we have to find the remaidner when 4*4! + 5*5! + 6*6! + 7*7! is divided by 64 which is 40.
Elitmus model questions
Answer:C
Answer: C
Question: G is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of G, and y is the minimum value of the sum of k distinct members of G, what is x + y?
Options:
A) kn
B) kn + k^2
C) kn + 2k^2
D) 2kn – k^2
E) 2kn
Rationale: Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so G, the set of the first n positive odd numbers would be: G={1, 3, 5};
Say k=1, so X, the maximum value of the sum of K distinct members of G would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of G would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
Answer: E
Question: A worker is paid Rs.20/- for a full days work. He works 1,1/3,2/3,1/8.3/4 days in a week. What is the total amount paid for that worker ?
Options:
A)56.5 rupees
B)58.5 rupees
C)57.5 rupees
D)59.5 rupees
E)55.5 rupees
Rationale: the total days worked=1+0.333+0.667+0.125+0.75=2.875 days
amount for 2.875 days is(2.875*20) 57.5 rupees
ANSWER:C
Answer: C
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)80%
B)20%
C)28%
D)90%
E)30%
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: B
Question: There are 15 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)267
C)261
D)211
E)272
Rationale: The total number of stations = 17
From 17 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 17P₂ ways.
17P₂ = 17* 16= 272.
Answer: E
Answer: E
Question: A person spent Rs. 8,596 from his salary on food and ?7,640 on house rent. After that he was left with 28% of his monthly salary. What is his monthly salary ?
Options:
A)Rs. 21,560
B)Rs. 22,500
C)Rs. 22,550
D)Rs. 23,550
E)None of these
Rationale: Explanation :
Total money spent on food and 16236 Which is 100 - 28 = 72% of his monthly salary
∴ His salary = 16236x100/72 = 22550
Answer : Option C
Answer: C
Question: The average age of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 2 students?
Options:
A)133 years
B)177 years
C)119 years
D)212 years
E)None
Rationale: Solution
Sum of the ages of 14 students	= (16 x 35) - (14 x 21)
= 560 - 294.
= 266.
∴ Required average	= 266 / 2
= 133 years.
Answer A
Answer: A
Question: The ratio of radius of a circle and the side of a square is 2 : 11. Find the ratio of their areas:
Options:
A)2 : 1
B)4 : 7
C)8 : 77
D)4 : 121
E)None
Rationale: radius/side = 2/11
⇒ area of circle/area of square= 4/121
Answer: D
Answer: D
Question: A big container is 35% full with water. If 48 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container in liters?
Options:
A)80
B)90
C)100
D)110
E)120
Rationale: 48 liters is 40% of the capacity C.
48 = 0.4C
C = 48/0.4 = 120 liters.
The answer is E.
Answer: E
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 16!
Options:
A)8
B)10
C)6
D)14
E)16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
---- count 3's =6 so answer is 6
Answer: C
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 10 pencils and 5 charts have been brought to the meeting, how many people are present?
Options:
A)5
B)7
C)8
D)9
E)10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 10
Total charts are 11 so A + 2B = 5
Add both: 3A + 3B = 15 so A + B = 5
Total number of people = 5
A
Answer: A
Question: A train covers a distance of 12 km in 10 min. If it takes 15 sec to pass a telegraph post, then the length of the train is?
Options:
A)100
B)300
C)120
D)400
E)150
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 15 = 300 m.
Answer: Option B
Answer: B
Question: If you add all the numbers on your mobile phone except 9, what is the answer?
Options:
A)45
B)28
C)65
D)36
E)42
Rationale: We have to add 0 to 8 to find the answer.
Therefore 0+1+2+3+4+5+6+7+8=36
Answer is D
Answer: D
Question: If x^2 = 191, which of the following is closest to a potential value of x?
Options:
A)-127
B)-11
C)12
D)14
E)131
Rationale: Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √191 => +- 14 (approx)
this value is closer to 14
Hence D is correct.
Answer: D
Question: There are 21 balls in a jar. You take out 3 red balls without putting them back inside, and now the probability of pulling out a red ball is 1/3. How many blue balls were there in the beginning?
Options:
A)12.
B)9.
C)8.
D)7.
E)6.
Rationale: 9= 3 blue balls + 18 / 3
Answer: B
Answer: B
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 25, what is the value of r-p?
Options:
A)20
B)10
C)30
D)40
E)5
Rationale: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=50 ----eq2
Subtracting eq1 from eq2 we get: r-p=30
Hence, the correct answer is C
Answer: C
Question: If Sn is the sum of the first n terms of a certain sequence and if Sn = n(n+7) for all positive integers n, what is the third term of the sequence?
Options:
A)3
B)4
C)6
D)8
E)12
Rationale: Tn = nth term
T1 = 1st term
T2 = 2nd term
and so on...
Sn = Sum of first n terms of the sequence
Sn = 1st term + 2nd term + 3rd term + ... + nth term
Sn = T1 + T2 + T3 + ....Tn
You are given here thatSn is the SUM of first n terms...So you have
Sn = T1 + T2 + T3 + ....Tn = n(n+1)
So S1 = T1
S2 = T1 + T2
S3 = T1 + T2 + T3
and so on
S1 = T1 = 1*(1+1) = 2
S2 = T1 + T2 = 2 + T2 = 2*(2+1) = 6
So T2 = 4
S3 = T1 + T2 + T3 = 2 + 4 + T3 = 3*(3+1) = 12
So T3 = 12
(This is what we wanted)
The third term is 12.
E
Answer: E
Question: P can complete a piece of work in 18 days & B can do the same piece of work in 15 days. They started working together but after 3 days P left & Q alone completed the remaining work. The whole work was completed in how many days?
Options:
A)12days
B)12.5 days
C)13 days
D)14.5 days
E)15 days
Rationale: Both together worked for 3 days.
In 3 days , P can do = 3 x
1
18
=
1
6
th work
In 3 days, Q can do = 3 x
1
15
=
1
5
th work
In 3 days , work finished =
1
6
+
1
5
=
11
30
Balance work =
19
30
Balance work finished by Q => Time taken by Q to finish the balance work =
19
30
x 15 = 9.5 days
The whole work was completed in 9.5 + 3 = 12.5 days
B
Answer: B
Question: A can work three times as fast as B. Together they can finish a job in 12 days. In how many days can A complete the job alone?
Options:
A)14
B)16
C)18
D)20
E)22
Rationale: B's rate is x and A's rate is 3x.
x + 3x = 1/12
x = 1/48
A's rate is 3x = 1/16
A can complete the job in 16 days.
The answer is B.
Answer: B
Question: A trader sells 66 meters of cloth for Rs. 660 at the profit of Rs. 5 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)26
B)88
C)90
D)42
E)5
Rationale: SP of 1m of cloth = 660/66 = Rs. 10
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 10 - Rs. 5 = Rs. 5
Answer:E
Answer: E
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
Options:
A)270
B)235
C)279
D)387
E)317
Rationale: A
270
Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
Answer: A
Question: Rs.385 were divided among X,Y,Z in such a way that X had Rs.20 more than Y and Z had Rs 15 more than X . How much was Y’s share?
Options:
A)Rs.130
B)Rs.145
C)Rs.150
D)Rs.152
E)Rs.155
Rationale: Let Y gets Rs x. Then We can say X gets Rs (x + 20 ) and Y gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs.145
B
Answer: B
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 3 years?
Options:
A)17300
B)17350
C)17280
D)17500
E)17600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 120/100 Ã— 120/100 Ã— 120/100= 17,280
C
Answer: C
Question: How many words can be formed by using all letters of the word 'FOUR' ?
Options:
A)50
B)24
C)36
D)44
E)21
Rationale: The word FOUR contains 4 different letters
Required number of words = 4P4 = 4! = 4*3*2*1 = 24
Answer is B
Answer: B
Question: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
Options:
A)25 years
B)37
C)36
D)29
E)21
Rationale: Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A) 25years
Answer: A
Question: If A can do 1/4 of a work in 3 days and B can do 1/6 of the same work in 4 days, how much will A get if both work together and are paid Rs. 180 in all?
Options:
A)Rs. 36
B)Rs. 60
C)Rs. 108
D)Rs. 120
E)None of these
Rationale: Whole work is done by A in (3*4) = 12days.
Whole work is done by B in (4*6)=24days.
A's wages: B's wages = A's 1 day's work:
B's 1 day's work =1/12:1/24=2:1
A's share = Rs. (2/3*180)=Rs. 120.
Correct Option: D
Answer: D
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is ?
Options:
A)285
B)227
C)271
D)187
E)199
Rationale: Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285.
Answer: A
Answer: A
Question: In how many ways Chief Minister and Minister be elected from a team of 15 members?
Options:
A)124
B)131
C)132
D)210
E)220
Rationale: To do this, if captain is elected first, then we have 15 ways of doing this.
For election of vice-captain, we have only 14 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 14*15 = 210 ways.
D
Answer: D
Question: what is 66.67% of 804 ?
Options:
A)587.69
B)536
C)627
D)300.87
E)567.67
Rationale: 66.67 % = 2/3
2/3 of 804 = 2/3 * 804 = 536 .... Ans - B
Answer: B
Question: An electric motor makes 1,400 revolutions per minutes. How many degrees does it rotate in one second?
Options:
A)8.400 d/sec
B)28.000 d/sec
C)38.000 d/sec
D)26.000 d/sec
E)35.000 d/sec
Rationale: 1400 revolutions / minute
= 1400*360 degrees / 60 seconds
= 8400 degrees / second
A
Answer: A
Question: 10 students are to be seated in two rows equally for the Mock test in a room. There are two sets of papers, Code A and Code B. each of two rows can have only one set of paper but different that from other row. In how many ways these students can be arranged ?
Options:
A)2775600
B)125600
C)7257600
D)1200560
E)None of these
Rationale: Solution: 5 students can be seated out of 10 students in 10C5 ways .
Remaining 5 will be seated in,
= 5C5 ways .
Students of each row can be arranged as,
= 5! *5! ways.
Two sets of paper can be arranged themselves in,
= 2! ways.
Thus, Total arrangement,
= 10C5 * 5! *5! *2
= 7257600.
Answer: Option C
Answer: C
Question: At a supermarket, John spent 1/5 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $11 on candy, how much did John spend at the supermarket?
Options:
A) $20
B) $30
C) $50
D) $90
E) $110
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/5 of his money on fresh fruits and vegetables, or (1/5)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $11 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/5)T + (1/3)T + (1/10)T + 11 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
6T + 10T + 3T + 330= 30T
19T + 330 = 30T
330 = 11T
T = 30
John spent $90 at the supermarket.
Answer: B
Answer: B
Question: A student scored an average of 65 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)86
B)165
C)76
D)125
E)26
Rationale: Given M + P + C = 65 * 3 = 195 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 195
= 125
Answer:D
Answer: D
Question: A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be:
Options:
A)10 m
B)12.5 m
C)17.5 m
D)21.25 m
E)None
Rationale: let height of the building be x meters
40.25 : 28.75 :: 17.5 <=> 40.25 x X = 28.75 x17.5
x= 28.75 x 17.5 / 40.25
x = 12.5
Answer: Option B
Answer: B
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3600, what will be the difference between Q and R's share?
Options:
A)2788
B)4500
C)7282
D)2782
E)2729
Rationale: 4 --- 3600
5 --- ? => 4500
Answer:B
Answer: B
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
Options:
A)127.6
B)127.5
C)127.9
D)127.3
E)127.1
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000
= 127.5 m.
Answer: B
Answer: B
Question: Write 850,000,000,000 in scientific notation.
Options:
A)8.5 * 10^11
B)800.900 * 10^11
C)8.900 * 10^11
D)80.9000* 10^11
E)08.900 * 10^11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
850,000,000,000 = 8.5* 100,000,000,000 = 8.% * 10 11**
correct answer A
Answer: A
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3
B)1/9
C)1/6
D)1/8
E)1/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: A
Question: If m and n are positive integers and m^2 + n^2 = 10, what is the value of m^3 + n^3?
Options:
A)28
B)224
C)320
D)512
E)1,600
Rationale: You need to integers which squared are equal 10.
Which could it be ? Let's start with the first integer:
1^2 = 1
2^2 = 4
3^2 = 9
Stop. The integers can't be greater than 3 or we will score above 10.
The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
The only pair that matches is 3^2 + 1^2 = 10.
So 3^3 + 1^3 = 28.
Answer A.)
Answer: A
Question: If the mode of Set Z is equal to the median of Set Z, Set Z could be
Options:
A)[0, 1, 2, 2, 3, 4, 5, 6]
B)[2, 2, 5, 7, 9]
C)[x, x+1, x+2, x+2, x+3, x+3]
D)[10, 102, 105, 105]
E)[4, 7, 10, 11, 25/2, 13, 13, 17, 29, 51, 51, 51]
Rationale: Correct Answer: (C)
Set Z could be The mode is the most common number; the median is the middle number when the numbers are arranged from least to greatest. Any number plus an integer value is greater than the original number, so x + 1 is greater than x, x + 2 is greater than x + 1, etc., so set (C) is arranged from least to greatest. Its median is the average of (x+2) and (x+2), which must be (x+2). (x+2) is also the most common number, so the mode of set C is equal to the median of set C.
Answer: C
Question: Mary needs some meat from the butchers shop a meter away from her house.
Each step Mary takes is 20 centimeters.
How many minutes will it take if each step lasts a minute ?
Options:
A)50
B)20
C)30
D)1
E)2
Rationale: The answer is A. mary will take 50 steps at one minute a step
Answer: A
Question: An express traveled at an average speed of 100 km/hr, stopping for 3 min after every 75 kn. How long did it take to reach its destination 600 km from the starting point?
Options:
A)6 hrs 71 min
B)6 hrs 21 min
C)6 hrs 81 min
D)6 hrs 41 min
E)3 hrs 21 min
Rationale: Time taken to cover 600 km = 600/100 = 6 hrs.
Number of stoppages = 600/75 - 1 = 7
Total time of stoppages = 3 * 7 = 21 min
Hence, total time taken = 6 hrs 21 min.
Answer: B
Answer: B
Question: If A is thrice as fast as B and together can do a work in 30 days. In how many days A alone can do the work?
Options:
A)36
B)42
C)28
D)54
E)40
Rationale: A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/30
= 3+1/3x = 4/3x = 1/30
x = 30*4/3 = 40
ANSWER:E
Answer: E
Question: Pastry Chef Pierre takes x hours to decorate a wedding cake. Pastry chef Franco takes y hours to decorate a wedding cake. If Pierre works alone for z hours and is then joined by Franco until 20 cakes are decorated, for how long did the two pastry chef's work together.
Options:
A)20xz-y/(x+y)
B)y+z/(20xz)
C)20x(y-z)/(x+y)
D)20xy-z/(x+y)
E)y(20x-z)/(x+y)
Rationale: time by pierre to complete 1 cake=x
time by franco to complete 1 cake=y
in z hours pierre completes= z/x work
then the both chef guy works together; let the time taken together be t
then we have
(work done by Pierre guy in z hours)+(work done by both guy in t hours)=20
=> (z/x)+(1/x+1/y)*t=20
=> t= (20-(z/x))/(1/x+1/y)=(20x-z)*y/(x+y)
y(20x-z)/(x+y)
ANSWER:A
Answer: A
Question: A number when divided by 342 gives a remainder 47.When the same
number is divided by 19 what would be the remainder?
Options:
A)0
B)9
C)19
D)29
E)18
Rationale: Number=342 K + 47 = 19 * 18 K + 19 * 2 + 9=19 ( 18K + 2) + 9.
The given number when divided by 19 gives 18 K + 2 as quotient
and 9 as remainder.
ANSWER B 9
Answer: B
Question: Of the three- digit integers greater than 700, how many have two digits R that are equal to each other and the remaining digit different from the other two?
Options:
A)90
B)82
C)80
D)45
E)36
Rationale: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
R=27+27+26 = 80
Answer: C
Answer: C
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
Options:
A)26
B)24
C)25
D)27
E)30
Rationale: Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
ANSWER B
Answer: B
Question: In a question on division with zero remainder, a candidate took 12 as divisor instead of 20. The quotient obtained by him was 25. The correct quotient is?
Options:
A)A)15
B)B)24
C)C)28
D)D)29
E)E)30
Rationale: Number = (25 * 12) = 300
Correct quotient = 300/20 = 15
A)
Answer: A
Question: If A and B are in the ratio 3:4, and B and C in the ratio 12:13, then A and C will be in the ratio
Options:
A)3:13
B)9:13
C)36:13
D)13:9
E)none
Rationale: Solution: (A/B)*(B/C) = (3/4)*(12/13);
Or, A/B = 36/39 = 9:13.
Answer: Option B
Answer: B
Question: A man rows his boat 80 km downstream and 38 km upstream, taking 3 hours each time. Find the speed of the stream?
Options:
A)6
B)9
C)7
D)8
E)2
Rationale: Speed downstream = d/t = 80/(3) = 27 kmph
Speed upstream = d/t = 38/(3) = 9 kmph
The speed of the stream = (27 - 9)/2 = 9 kmph
Answer:B
Answer: B
Question: What is the absolute value of twice the difference of the roots of the equation F=5y^2 − 20y + 15 = 0 ?
Options:
A) 0
B) 1
C) 2
D) 3
E) 4
Rationale: F=5y^2 − 20y + 15 = 0 --> y^2 − 4y + 3 = 0 --> y=1 or y=3. The difference is 2, twice the difference is 4.
Answer: E.
Answer: E
Question: Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 7, and 8 seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 2:00 pm (i.e. two hours later)?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: The least common multiple is 2*2*2*3*5*7=840.
7200 seconds / 840 = 8 + remainder.
The answer is C.
Answer: C
Question: Before a salary increase, the weekly salary of a worker for 45 hours in a week was as much as the worker is paid now for 40 hours of work in a week. What is the percent increase in the worker's salary per hour?
Options:
A)5
B)7.5
C)8
D)10
E)12.5
Rationale: Let x be the original salary per hour.
Let y be the salary per hour after the increase.
40y=45x
y=(45/40)x=1.125x
The salary increased 12.5%.
The answer is E.
Answer: E