divelab/Sys2Bench huggingface dataset:
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
Options:
A)2 : 1
B)1 : 2
C)4 : 3
D)1 : 1
E)3 : 2
Rationale: Explanation:
5% of A + 4% of B = 2/3(6% of A + 8% of B)
5A/100 + 4B/100 = 2/3(6A/100+8B/100)
⇒5A + 4B = 2/3(6A + 8B)
⇒15A + 12B = 12A + 16B
⇒ 3A = 4B
⇒ AB = 4/3
⇒ A:B=4:3
Answer: Option C
Answer: C
Question: the twonumbers (23__)^32 and (12__)^ 33 has 6 in the last digit what is the missing digit ?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: it should be 6
as last digit in all powers of nos with unit digit 6 is 6.
ANSWER:C
Answer: C
Question: √184,513 is between
Options:
A)100 and 200
B)200 and 300
C)300 and 400
D)400 and 500
E)500 and 600
Rationale: Look at (A). 200^2 = 40,000 which is much lower than 184,513
Going down the options, you will see that 500^2 = 250,000 which is the first one greater than 184,513.
Hence, answer will be between 400 and 500.
Answer (D)
Answer: D
Question: Kamal obtained 76, 60, 72, 65 and 82 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)71
B)69
C)72
D)75
E)NOne
Rationale: Sol.
Average
= 76 + 60 + 72 + 65 + 82 / 5)
= (355 / 5)
= 71.
Answer A
Answer: A
Question: A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid.
The value of the 8th installment is:
Options:
A)50
B)54
C)65
D)47
E)37
Rationale: Let the first installment be 'a' and the common difference between any two consecutive installments be 'd'
Using the formula for the sum of an A.P :-
S=n/2[2a+(n−1)d].
We have,
3600=40/2[2a+(40-1)d].
3600=20[2a+39d].
180 =2a+39d. ----(i)
Similarly,
2400=30/2[2a+(30-1)d].
160=2a+29d. ----(ii)
On solving both the equations we get:
d=2 and a=51
Hence, the Value of 8th installment is :-
=51+(8−1)2.
=65. Answer : C
Answer: C
Question: A set of numbers has the property that for any number x in the set, x+6 is also in the set. If -6 is in the set, which of the following must also be in the set
1. 0
2. -12
3. 12
Options:
A)1 only
B)2 only
C)1 and 2 only
D)1 and 3 only
E)1,2 and 3
Rationale: If X is in the set than X+ 6 is also in the set
If -6 in the set than
-6+6= 0 is also in the set
Since + 6 is Present, 6 + 6= 12 Is also present in the set .
Therefore Ans D
Answer: D
Question: The arithmetic mean of the scores of a group of students in a test was 70. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
Options:
A)A)71.4.
B)B)91.7
C)C)84.09
D)D)81.1
E)E)71.2
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 70 * 100
= 1600 + 775 + 55x = 7000
= 55x = 4625
= x = 84.09
Answer:C
Answer: C
Question: Two fifth of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
Options:
A)1/6
B)11/20
C)2/3
D)3/4
E)11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-3/5*3/4=11/20.
Answer: B.
Answer: B
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
Options:
A)18.9 sec
B)88.9 sec
C)22.9 sec
D)16.8 sec
E)72.0 sec
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer: D
Answer: D
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/6%
B)16 5/3%
C)26 2/3%
D)16 2/3%
E)16 3/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: D
Question: To be considered grade AC, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AC eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AC eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
Options:
A)800
B)840
C)864
D)900
E)1,080
Rationale: We're asked for the smallest possible mass, so what could the lowest mass be per egg AC? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Answer: B
Question: A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds?
Options:
A)2 : 15
B)1 : 5
C)2 : 3
D)3 : 2
E)None of these
Rationale: First cart speed will be 24/3=8
Second cart speed is 120/2=60
So, ratio is 8/60=2/15
ANSWER:A
Answer: A
Question: we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Total no. of cubes=n^3
here n^3 =125 which makes n=5,
also minimum no. of cuts required =3(n-1)
hence, 3(5-1)=12 cuts.
ANSWER:E
Answer: E
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?
Options:
A)9 a.m
B)10 a.m
C)10-30 a.m
D)11 a.m
E)None
Rationale: Solution
Distance covered by A in x hours	= 20 x km
Distance covered by B in (x - 1) hours	= 25 (x - 1) km
= 20x + 25 (x - I)
= 110
= 45x = 135
x = 3. So, they meet at 10 a.m
Answer B
Answer: B
Question: If x is a positive integer, then the least value of x for which x! is divisible by 10 is?
Can someone please explain intuitively what the question is asking?
Options:
A)5
B)9
C)12
D)15
E)30
Rationale: In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 1.
5! = 120 has 1 trailing zeros.
Answer: A
Answer: A
Question: Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
Options:
A) 8
B) 2
C) 6
D) 0
E) 12
Rationale: If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : D
Answer: D
Question: Simplify: 839478 x 625
Options:
A)527346750
B)524673750
C)526473750
D)526475730
E)None of them
Rationale: 839478 x 625 = 839478 x 5^4 = 8394780000/16
= 524673750.
Answer is C.
Answer: C
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line after each of Frederick, Gale, and Harold?
Options:
A)1,008
B)1,296
C)1,512
D)2,018
E)2,016
Rationale: Place D and E first: 8 options for D, 7 options for E.
We are left with 6 empty places. A, B and C must take first 3 places and F, G, H must take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: E.
Answer: E
Question: The remainder of the division of a number by 63 is 27. What will be the remainder when that number is divided by 6?
Please explain
Options:
A)4
B)5
C)6
D)7
E)0
Rationale: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:
1) Choose a number X that when divided by 63 gives you 27 as a remainder. So I did x = 63 + 27 = 90. (90/63 = 1R27)
2) Divide that number by 6. 90/5 = 15R0
Since the remainder is 0, the correct answer is choice E.
Answer: E
Question: Calculate the circumference of a circular field whose radius is 10 centimeters.
Options:
A)20 π cm
B)19 π cm
C)28 π cm
D)25 π cm
E)30 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*10 = 20 π cm
Answer: A
Answer: A
Question: I. a2 - 13a + 42 = 0,
II. b2 - 15b + 56 = 0 to solve both the equations to find the values of a and b?
Options:
A)If a > b
B)If a ≥ b
C)If a < b
D)If a ≤ b
E)If a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
I. a2 - 13a + 42 = 0
=>(a - 6)(a - 7) = 0 => a = 6, 7
II. b2 - 15b + 56 = 0
=>(b - 7)(b - 8) = 0 => b = 7, 8
=>a ≤ b
Option D
Answer: D
Question: What distance will be covered by a bus moving at 90 kmph in 20 seconds?
Options:
A)500
B)600
C)289
D)276
E)207
Rationale: 90 kmph = 90 * 5/18
= 25 mps
D = Speed * time = 25 * 20
= 500 m.
Answer:A
Answer: A
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 4 minutes more to walk to work than to ride his bike to work, then x equals?
Options:
A)4
B)6
C)10
D)15
E)20
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 240 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=240----> 40x=240--> x = 6
Option B
Answer: B
Question: Sum of the squares of 3 no.'s is 179 and the sum of their products taken two at a time is 131. Find the sum?
Options:
A)20
B)21
C)26
D)28
E)30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 179 + 2* 131
a + b + c = √441 = 21
B
Answer: B
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
Options:
A)s.4528
B)s.3624
C)s.4527
D)s.4530
E)s.4521
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 4
= Rs.3624
Answer:B
Answer: B
Question: a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
Options:
A)13 km/hr.
B)12 km/hr.
C)9 km/hr.
D)15 km/hr.
E)11 km/hr.
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B.
Answer: B
Question: Of the 7 distinguishable wires that lead into an apartment, 4 are for cable television service, and 3 are for telephone service. Using these wires, how many distinct combinations of 3 wires are there such that at least 1 of the wires is for cable television?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Given:
Total number of wires = 5
Number of cable wires = 2
Number of telephone wires = 3
To find:
Number of combination which has at least one cable wires
Solution:
No of ways of selecting'at least'1 cable wire means, we can select more than one as well. The minimum we can select is one and the maximum we can select, given the constraints that 3 wires need to be selected in total and there are 2 cable wires, is 2
Since it is a combination of wires, the arrangement is not important
Approach 1:
Number of ways of selecting at least one cable wire in a selection of 3 wires from 5 wires =Selection 1(Number of ways of selecting one cable wire and two telephone wires )+Selection 2(Number of ways of selecting two cable wires and 1 telephone wire)
Selection 1
Number of ways of selecting one cable wire = 2C1 = 2
Number of ways of selecting 2 telephone wires = 3C2 = 3
Total = 2C1 * 3C2 = 6 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 2
Number of ways of selecting one cable wire = 2C2 = 1
Number of ways of selecting 2 telephone wires = 3C1 = 3
Total = 2C2 * 3C1 = 3 ( m ways of doing something and n ways of doing something else together give m*n ways of doing - the holy grail rule in Combinatorics)
Selection 1 + Selection 2 = 9 ways of selecting 3 wires out of 5 such that at least one is a cable wire
Approach 2
Number of ways of selecting 3 wires out of 5 such that at least one is a cable wire =Selection X(Total number of ways of selecting 3 wires from the 5) -Selection Y(total ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires)
Total number of ways of selecting 3 wires out of 5 = 5C2 = 10
Number ways of selecting 3 wires such that none is a cable i.e all the three are telephone wires = 3C3 ( 3 telephone wires and we are selecting all the three at once) = 1
Selection X - Selection Y =10
Answer is Option E
Answer: E
Question: 80 370 ? 1550 2440 3530
Options:
A)900
B)840
C)750
D)860
E)960
Rationale: 10^2 - 20 = 80
20^2 - 30 = 370
30^2 - 40 = 860
40^2 - 50 = 1550
50^2 - 60 = 2440
60^2 - 70 = 3530.
ANSWER:D
Answer: D
Question: If a clock takes seven seconds to strike seven, how long will it take to strike ten ?
Options:
A)7 seconds
B)9 seconds
C)10 seconds
D)10.5 seconds
E)None of these
Rationale: for 7 strikes it have 6 interval so for 1 interval it takes 7/6sec
therefor for 10 strike it require 9 interval so time required=(7/6)*9=10.5sec
ANSWER:D
Answer: D
Question: The measurements obtained for the interior dimensions of a rectangular box are 120 cm by 120 cm by 180 cm. If each of the three measurements has an error of at most 1 centimeter, which of the following is the closes maximum possible difference, in cubic centimeters, between the actual capacity of the box and the capacity computed using these measurements?
Options:
A)55,600
B)53,600
C)54,600
D)58,600
E)57,600
Rationale: The options are well spread so we can approximate.
Changing the length by 1 cm results in change of the volume by 1*120*180 = 21600 cubic centimeters;
Changing the width by 1 cm results in change of the volume by 120*1*180 = 21600 cubic centimeters;
Changing the height by 1 cm results in change of the volume by 120*120*1 = 14400 cubic centimeters.
So, approximate maximum possible difference is 21600 + 21600 + 14400 = 57600 cubic centimeters.
Answer: E
Answer: E
Question: 3^14 + 3^14 + 3^14 =
Options:
A)9^12
B)3^16
C)9^14
D)3^15
E)3^17
Rationale: Since we have 3^14 added together 3 times, we can factor out a 3 and we get 3(3^14) which is equal to 3^15.
The answer is D.
Answer: D
Question: A certain manufacturer sells its products	to stores in 112 different	regions worldwide, with an average (arithmetic mean) of 181 stores per region. If last year these stores sold an	average of 51,752 units of the manufacturer’s product per store, which of the following is closest to the total number of units of manufacturer’s product	sold	worldwide last	year?
Options:
A)10^4
B)10^5
C)10^6
D)10^8
E)10^9
Rationale: 51752*181*112 or
51000*180*112 or
50000*200*100
=10^9
E
Answer: E
Question: A ship sails 4 degrees north, then 13 S. then 17 N. then 22 S. and has finally 11 degrees of south latitude. What was her latitude at starting ?
Options:
A)0
B)1
C)2
D)3
E)None of these
Rationale: Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 22 = -11
And x = 3.
Answer D
Answer: D
Question: Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, B’s share is:?
Options:
A)Rs.310/-
B)Rs.305/-
C)Rs.205/-
D)Rs.210/-
E)Rs.215/-
Rationale: A:B:C = 3:4:5
Total parts = 12
B's share is = 4 parts
12 -----> Rs.600/-
4 -----> Rs.200/-
B's total = 200 + 5 = Rs.205/-
C)
Answer: C
Question: A can do a work in 21 days and B alone can do it 28 days, they begin the work together, but A left after some days. B completed the remaining work in 21 days. After how many days did A leave ?
Options:
A)10
B)8
C)3
D)15
E)16
Rationale: Explanation:
(A+B) 1 day work = {1/21+1/28}=1/12 = 12days is required for A&B
B’S 1 day work = 1/28
B’s 21 days work = 21/28
1 - 21/28 = 7/28 - 1/4
1/4 *12=3 days
Answer: Option C
Answer: C
Question: A train travels from city C to city D. The average speed of the train is 60 miles/hr and it travels the first quarter of the trip at a speed of 90 mi/hr. What is the speed of the train in the remaining trip?
Options:
A)30
B)45
C)54
D)72
E)90
Rationale: Using the RTD chart, with A being the first quarter, B the rest of the trip and All the combinedtrip.
_______R_____T______D
C.........90........3..........270
D.........54.......15.........810
All........60.......18........1080
Let me explain how we fill in the chart:
1) Starting with what we know, we add 90 and 60
2) Picking an easy number for the total distance (6*9=54), so I chose 540. Multiply by 2 to get the whole trip, and we get 1080. Add 1080 for all-distance.
3) 1/4 of the whole distance happened at a Rate of 90. So, 1080/4=270, add 270 under A-D.
4) 2080 - 270 = 810, for the rest of the trip. Add 810 under B-D.
5) Claculate the individual Times for A and All, using T=D/R. Add the results, 3 and 18, under A-T and All-T.
6) 18-3=15, this is the remaining Time for B. Add 15 under B-T.
7) Finally, 15R=810 -->R=810/15 --> R= 54ANS C
Answer: C
Question: A man spends Rs. 1600 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 . 2800 a year. What is his average monthly income?
Options:
A)1900
B)2010
C)2100
D)2200
E)2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 2800 = Rs. 22800
So, Average monthly income = 22800/12 = Rs. 1900
A
Answer: A
Question: A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?
Options:
A)49
B)37
C)59
D)72
E)60
Rationale: C
59
The first 56 balls could be of all colours except red. This would leave 8 balls, all of which are red. so any three chosen would be red.
Answer: C
Question: A student chose a number, multiplied it by 6, then subtracted 138 from the result and got 102. What was the number he chose?
Options:
A)40
B)120
C)130
D)140
E)150
Rationale: Solution:
Let xx be the number he chose, then
6⋅x−138=102
6x=240
x=40
Answer A
Answer: A
Question: In a lottery there are 20 prizes and 35 blanks. A lottery is drawn at random. What is the probability of getting a prize
Options:
A)2/13
B)4/11
C)5/11
D)6/11
E)3/13
Rationale: total draws = prizes+blanks= 20+35=55
probability of getting a prize = 20/55 = 4/11
correct option is B
Answer: B
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face.
Options:
A)2/113
B)2/141
C)1/216
D)2/115
E)3/140
Rationale: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Answer: C
Question: Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 160 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from
Options:
A)50 to 70
B)70 to 100
C)110 to 130
D)130 to 150
E)150 to 170
Rationale: if there are 1630 students majoring in electrical then there must be 70 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 10.
if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 10, hence the number of students both majoring mechanical and electrical will be at least 50
so there must be at least 50 students who major in both
see the answers option the only possible answer is A !
Answer: A
Question: The average of 11 results is 60. If the average of first 6 results is 58 and that of the last six is 63, find the sixth result?
Options:
A)50
B)52
C)65
D)42
E)66
Rationale: Sixth result = 58*6 + 63*6 - 60*11 = 66
Answer is E
Answer: E
Question: n∑n=1 1/log2n(a) =?
Options:
A)n(n + 1)/2 loga2
B)n(n - 1)/2 log2a
C)n(n + 1)2n2/4 loga2
D)n(n + 1)2n2/4 loga3
E)None of these
Rationale: n∑n=11/log2n(a) = n∑n=1loga(2n)
=n∑n=1nloga2
=n(n + 1)/2 loga2
ANSWER:A
Answer: A
Question: A sum of money deposited at compound interest (compounded yearly) amounts to $3200 in 2 years and to $3296 in 3 years. What is the interest rate?
Options:
A)2%
B)3%
C)4%
D)5%
E)6%
Rationale: 3296 - 3200 = 96
96 / 3200 = 0.03 = 3%
The answer is B.
Answer: B
Question: Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of X/Y ?
Options:
A)3.
B)2.
C)1/2.
D)1/3.
E)There isn't enough data to answer the question.
Rationale: Answer is A : 3
X - Y = (X + Y)/2
Solving for X/Y =3
Answer: A
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 15m/h. what is the speedof the person while he was going to his office?
Options:
A)8km/h
B)10km/h
C)12km/h
D)13km/h
E)14km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=15
\inline \Rightarrow 1.5k = 15
\inline \Rightarrow k=10km/h
B
Answer: B
Question: What is the maximum value of x, in the equation 2x+y=42,if y>x
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: x will have max value when y will have least possible value which can be a little greater than x as y>x.
when x=y , then
2x+y=3x = 42
x=14.
ANSWER:E
Answer: E
Question: A man walks at a speed of 5 km/hr and runs at a speed of 10 km/hr. How much time will the man require to cover a distance of 10 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
Options:
A)2.5
B)3.5
C)4
D)2
E)1.5
Rationale: Required time = (5)/5 + (5)/10 = 1.5 hours.
Answer:E
Answer: E
Question: The “connection” between any two positive integers a and b is the ratio of the smallest common multiple of a and b to the product of a and b. For instance, the smallest common multiple of 8 and 12 is 24, and the product of 8 and 12 is 96, so the connection between 8 and 12 is 24/96 = 1/4
The positive integer y is less than 20 and the connection between y and 6 is equal to 1/1. How many possible values of y are there?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: Since “connection” between y and 6 is 1/1 then LCM(6, y)=6y, which means that 6 and y are co-prime (they do not share any common factor but 1), because if the had any common factor but 1 then LCM(6, y) would be less than 6y.
So, we should check how many integers less than 20 are co-prime with 6, which can be rephrased as how many integers less than 20 are not divisible by 2 or 3 (6=2*3).
There are (18-2)/2+1=9 multiples of 2 in the range from 0 to 20, not inclusive;
There are (18-3)/3+1=6 multiples of 3 in the range from 0 to 20, not inclusive;
There are 3 multiples of 6 in the range from 0 to 20, not inclusive (6, 12, 18) - overlap of the above two sets;
Total multiples of 2 or 6 in the range from 0 to 20, not inclusive is 9+6-3=12;
Total integers in the range from 0 to 20, not inclusive is 19;
Hence, there are total of 19-12=7 numbers which have no common factor with 6 other than 1: 1, 5, 7, 11, 13, 17 and 19.
Answer: A.
Answer: A