divelab/Sys2Bench huggingface dataset:
Question: If x is the product of three consecutive positive integers, which of the following must be true?
I. x is an integer multiple of 3.
II. x is an integer multiple of 6
III. x is an integer multiple of 4
Options:
A)a) I only
B)b) II only
C)c) I and II only
D)d) I and III only
E)e) I,II and III
Rationale: The answer should be D i.e. X will be an integer and multiple of 3 and 6.
Let us take example n, n+1, n+2 as 3 three consecutive positive integers.
In a sequence of consecutive integers a number is multiple of 3 after every interval of 2 numbers i.e 3,4,5,6 Or 8,9,10,11,12
Hence in a product of 3 consecutive integers, the product is always divisible by 3.
Now, in a consecutive sequence every alternate is an even number, and when an even number is multiplied by 3 we will have 6 as one of the multiple also.
Now for a number to be a multiple of 4 we need at least 2 2's. this is only possible if the first number of three consecutive positive integers is an even number so that 3 is also even and we have 2 2's. But incase the sequence starts with odd we will have one 2 hence, the divisibility by 4 depends on the first number to be even
AnswerC
Answer: C
Question: IN Common Wealth Games an athlete runs 200 meters in 32 seconds. Hisspeed is ?
Options:
A)25 km/hr
B)27 km/hr
C)30 km/hr
D)32 km/hr
E)None of these
Rationale: Explanation :
(200/1000)/(32/3600)=22.72 km/hr
Answer : E
Answer: E
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
Options:
A)0.075 days
B)0.45 days
C)0.55 days
D)0.25 days
E)0.15 days
Rationale: B = 1/8 – 1/22 =0.075 days
ANSWER:A
Answer: A
Question: At a certain college, 50 percent of the total number of students are freshmen. If 40 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 20 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
Options:
A)14%
B)4%
C)15%
D)5%
E)25%
Rationale: Let's say there is a TOTAL of100students at this college.
50 percent of the total number of students are freshmen.
# of freshmen = 50% of 100 =50
40 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 40% of 50=20
...and, of these, 20 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 20% of 20=4
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
4/100= 4%
Answer: B
Answer: B
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 30% on the cost price?
Options:
A)65
B)69.5
C)67.5
D)62.5
E)22.5
Rationale: CP = 47.50
SP = 47.50*(130/100) = 61.75
MP*(95/100) = 61.75
MP = 65
Answer:A
Answer: A
Question: Among the answers given below, which is nearly equal to √7?
Options:
A)2.3
B)1.9
C)2.6
D)2.5
E)3.0
Rationale: 2.6 is nearly equal to the square root of 7
2.6*2.6=6.76
2.5*2.5=6.25
difference
7 - 6.76=0.24
7 - 6.25=0.75
Since 0.24 is lesser of both, 2.6 is closer.
Answer is C
Answer: C
Question: If each day a tree loses half its remaining leaves, what fraction of its leaves will it have lost after 7 days ?
Options:
A)X-1/8
B)X-1/32
C)X-1/64
D)X-1/128
E)X-1/164
Rationale: LET NO OF LEAVES IX X ..IST DAY X/2 ..2ND DAY X/4 ..3RD DAY X/8 , FOURTH DAY X/16 , 5TH DAY X/32 , 6TH DAY X/64 SO ON SO FOURTH.
FINALLY ON LEAVE WILL BE LEFT ..SO ON 3RD DAY LEAVE LOST IS X-1/128 ANSWER D
Answer: D
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.32 per ounce, what is the share of Arabica in this blend?
Options:
A)20%
B)24%
C)30%
D)33%
E)40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .3(1-a) = .32
.4a + .3 - .3a = .32
a= .2
therefore: .2/1 ounce = 20%. Therefore, the answer should be A
Answer: A
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/9 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?
Options:
A)18
B)144
C)104
D)216
E)250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/9)*360 = 40 gallons.
Remaning paint = 320 gallons
Paint used in the second week = (1/5)*320 = 64 gallons
Total paint used = 104 gallons.
Option C
Answer: C
Question: Jim and Reneesh will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Reneesh have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win?
Options:
A)5/6
B)2/3
C)1/2
D)5/12
E)1/3
Rationale: 1/3
probability of jim winning is basically the sum of three probabilities:
probability of jim picking rock and reneesh picking scissors = 1/3*1/3 = 1/9
probability of jim picking scissors and reneesh picking paper = 1/3*1/3=1/9
probability of jim picking paper and reneesh picking rock = 1/3*1/3=1/9
1/9 + 1/9 + 1/9 = 3/9 = 1/3=E
Answer: E
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 290 m in length?
Options:
A)18.9 sec
B)88.9 sec
C)22.9 sec
D)24.00 sec
E)72.0 sec
Rationale: D = 110 + 290 = 400 m
S = 60 * 5/18 = 50/3
T = 400 * 3/50 = 24.00 sec
Answer: D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 21 seconds. Find the length of the train.
Options:
A)350 m
B)145 m
C)240 m
D)135 m
E)255 m
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 15 = 350 meter
ANSWER: A
Answer: A
Question: A number is doubled and 4 is added. If the resultant is divided by 5, it becomes 25. What is that number?
Options:
A)73.5
B)68
C)60.5
D)None of these
E)Cannot be determined
Rationale: Solution
Let the number be x.
Then, (2x + 4)/5 ‹=› 25
‹=› 2x+4 = 125
‹=› 2x= 121
x= 60.5
Answer C
Answer: C
Question: A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water?
Options:
A)7h
B)3h
C)4h
D)2h
E)9h
Rationale: Explanation:
Upstream speed = B-S
Downstream speed = B+s
B-S = 15/5 = 3 km/h
Again B= 4S
Therefore B-S = 3= 3S
=> S = 1 and B= 4 km/h
Therefore B+S = 5km/h
Therefore, Time during downstream = 15/5 = 3h
Answer: B
Answer: B
Question: Out of 40 applicants to a law school, 15 majored in political science, 20 had a grade point average higher than 3.0, and 10 did not major in political science and had a GPA equal to or lower than 3.0. How many of Q applicants majored in political science and had a GPA higher than 3.0?
Options:
A)5
B)10
C)15
D)25
E)35
Rationale: Total applicants = 40
Political science = 15 and Non political science = 40 - 15 = 25
GPA > 3.0 = 20 and GPA <= 3.0 = 20
10 Non political science students had GPA <= 3.0 --> 15 Non political science students had GPA > 3.0
GPA > 3.0 in political science = Total - (GPA > 3.0 in non political science) Q= 20 - 15 = 5
Answer: A
Answer: A
Question: A person buys an article at Rs.340. At what price should he sell the article so as to make a profit of 10%?
Options:
A)600
B)882
C)374
D)356
E)521
Rationale: Cost price = Rs.340
profit = 10% of 340 = Rs.34
Selling price = Cost price + Profit
= 340 + 34 = 374
Answer: C
Answer: C
Question: At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?
Options:
A)4%
B)7%
C)9%
D)3%
E)1%
Rationale: Let sum = x. Then, S.I. = 2x/5, Time
= 10 years.
Rate = (100 * 2x) / (x * 5 * 10)
= 4%
Answer: A
Answer: A
Question: A and B are two circles. The radius of A is twice as large as the diameter of B. What is the ratio between the areas of the circles?
Options:
A)1:8.
B)1:2.
C)1:4.
D)1:16
E)1:6.
Rationale: Given :
The radius of A is twice as large as the diameter of B. => R(a) = 2*D(b) = 2*2*R(b) = 4R(b).
The radius are in ratio of 1:4 thus the area will be in the ratio of square of radius. 1:16.
Hence D.
Answer: D
Question: Nathan is 3.4 miles from home and is traveling at 60 mph. How long until he is home?
Options:
A)About 9 minutes
B)About 5 and a half minutes
C)About 12 minutes and a half
D)About 16 minutes
E)About 2 minutes
Rationale: 60/3.4=5.5 m correct answer B
Answer: B
Question: Two persons starting from the same place walk at a rate of 9kmph and 12.5kmph respectively. What time will they take to be 24.5km apart, if they walk in the same direction?
Options:
A)7 hrs
B)22 hrs
C)5 hrs
D)12 hrs
E)16 hrs
Rationale: The relative speed of the boys = 12.5kmph – 9kmph
= 3.5 kmph
Distance between them is 24.5 km
Time= 24.5km / 3.5 kmph = 7 hrs
Answer : A
Answer: A
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,925, what was the total number of pairs of contact lenses that she sold?
Options:
A) 11
B) 13
C) 15
D) 17
E) 19
Rationale: (x+5)*150 +x*85=1925
=>x=5
total lens=5+(5+5)= 15
Answer C
Answer: C
Question: X can finish a work in 20 days. Y can finish the same work in 16 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
Options:
A)2
B)3
C)9
D)5
E)8
Rationale: Work done by X in 1 day = 1/20
Work done by Y in 1 day = 1/16
Work done by Y in 12 days = 12/16 = 3/4
Remaining work = 1 – 3/4 = 1/4
Number of days in which X can finish the remaining work = (1/4) / (1/20) = 5
D
Answer: D
Question: In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find x.
Options:
A)3
B)4
C)5
D)6
E)None of the above
Rationale: (x+2)×60+x×120+(x−2)×180/(x+2)+x+(x−2)=100
⇒ 360x−240/3x = 100
⇒ 60x = 240 ⇒ x = 4
Answer E
Answer: E
Question: In how many different ways can the letters of the word ATRIUMS be arranged in such a way that the vowels occupy only the even positions?
Options:
A)72
B)96
C)120
D)144
E)180
Rationale: The 3 vowels can be arranged in 3 even places in 3! ways.
The 4 consonants can be arranged in 4 odd places in 4! ways.
The number of arrangements with vowels in even positions = 3! Ã— 4! = 6 Ã— 24 = 144
The answer is D.
Answer: D
Question: In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Options:
A)187 ways
B)500 ways
C)168 ways
D)659 ways
E)175 ways
Rationale: We can select one boy from 20 boys in 20 ways.
We select one girl from 25 girls in 25 ways
We select a boy and girl in 20 * 25 ways i.e.,
= 500 ways.
Answer:B
Answer: B
Question: Recently, I decided to walk down an escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty " six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty " four stairs, I would only require eighteen seconds to get to the bottom. If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom?
Options:
A)43
B)44
C)45
D)40
E)46
Rationale: 26 steps 30 seconds and for 34 steps only 18 seconds left to reach botto.
Means he covered 8 steps (i.e.34-26) in 12 (i.e 30-18)seconds
The spped of the boy is 8 steps in 12 seconds
after further simplyfy..2 steps in 3 seconds
After 34 steps only 18 seconds, means 12 more steps are left
Total Steps are 34+12 = 46
ANSWER:E
Answer: E
Question: A person bought 114 glass bowls at a rate of Rs. 13 per bowl. He sold 108 of them at Rs. 17 and the remaining broke. What is the percentage gain for A?
Options:
A)40
B)3000/11
C)5900/247
D)2790/11
E)2709/8
Rationale: CP=114*13=1482 and SP=108*17=1836
Gain %= 100*(1836-1482)/1482= 5900/247
ANSWER:C
Answer: C
Question: A man can hit the target once in four shots. If he fires four shots in succession, what is the probability that he will hit the target?
Options:
A)1
B)1/256
C)81/256
D)175/256
E)185/256
Rationale: In four shots he can hit once,twice,thrice,all hit
the probability of hitting the target isp(1hit out of 4)+P(2hit out of 4)+p(3hit out of 4)+p(All hit)
it is total probability-probability of not hitting yhr target
=>1-(3/4*3/4*3/4*3/4)
=>175/256
ANSWER:D
Answer: D
Question: When x is multiplied by 3, the result is 18 more than the result of subtracting x from 26. What is the value of x?
Options:
A)-4
B)-2
C)11
D)13
E)22
Rationale: The equation that can be formed is:
3x-18=26-x
or, 4x=44
or, x=11.
C answer.
Answer: C
Question: Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks. If 1 person is to be randomly selected from the 2,500 people, what is the probability that the person selected will be one who invests in municipal bonds but NOT in oil stocks?
Options:
A)9/50
B)7/25
C)7/20
D)21/50
E)27/50
Rationale: Among a group of 2,500 people, 35 percent invest in municipal bonds, 18 percent invest in oil stocks, and 7 percent invest in both municipal bonds and oil stocks.
As per the attached venn diagram, we have to find the number of people in shaded portion.
=35%-7%=28%
Thus, probability = 0.28 = 7/25
(2,500 people, 18 percent invest in oil stocks is not required.)
Answer is (B)
Answer: B
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 2
II. y = 0
III. x = 0
Options:
A)I only
B)II only
C)III only
D)I and III only
E)I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer C
Answer: C
Question: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. if he sells the scooter for Rs. 5800, his gain percent is :
Options:
A)4 4/7&
B)5 5/11%
C)10%
D)12%
E)15%
Rationale: Cost price (C.P)= 4700+800=5500
selling price (S.P)= 5800
Gain = (S.P) - (C.P)=5800-5500= Rs. 300, Gain %= (300/5500*100)%= 5 5/100%
Correct Answer : (B)
Answer: B
Question: If Friday occurred on 21th January 2005. What was the day of the week on 21th January 2004?
Options:
A)Sunday
B)Wednesday
C)Friday
D)Monday
E)Tuesday
Rationale: There are 2 odd days in the year 2004
So, the day on 21th January 2005 will be two days beyond the day on 21th January 2004
On 21th January 2004, it was Wednesday
Answer: B
Answer: B
Question: The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is?
Options:
A)35yr
B)25yr
C)20yr
D)30yr
E)40yr
Rationale: Let their ages be x years and (x+10) years
Then, (x+10) - 15 = 2(x-15)
x - 5 = 2x-30
x = 25
Present age of the elder person = 25+10 = 35 years
Answer is A
Answer: A
Question: How many triangles can be formed by joining the vertices of an octagon?
Options:
A)50
B)56
C)23
D)12
E)89
Rationale: Here n = 8
Hence, the number of triangles that can be formed by joining the vertices of an octagon
=n(n−1)(n−2)/6=8(8−1)(8−2)/6=8.7.6/6=56
Anwer is B
Answer: B
Question: In the equation m = 36.12n, n and m are integers. If m/n leaves a remainder of r, which of the following must divide into r?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: 1) It says it is a equation, so m=36.12n should be 36.12 * n..
2) It says n is an integer, again it means 36.12 * n..
Otherwise n would be just a digit and it would be mentioned..
Although not clearly mentioned that 36.12n is actually 36.12 * n, BUT entire info points towards that..
and that is why I have taken m/n = 36.12
Answer: B
Question: Hector runs a one-product widget shop. Each month, his fixed costs, whether he produces anything or not, amount to x dollars. The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces. He generally can sell widgets for p dollars each. What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month?
Options:
A)x/(y - p)
B)x/(p - y)
C)x
D)x/p
E)x/y
Rationale: Two ways...
1) let t be the total number, so cost = t*y+x and selling price=t*zp..
No profit no loss....t*y+x=t*p.....T=x/(p-y)...
B
Answer: B
Question: In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
Options:
A)33
B)25
C)88
D)29
E)10
Rationale: A : B = 200 : 169.
A : C = 200 : 182.
\inline \fn_jvn {\color{Black} \frac{C}{B}=\left ( \frac{C}{A}\times \frac{A}{B} \right )=\left ( \frac{182}{200}\times \frac{200}{169} \right )=182:169}
When C covers 182 m, B covers 169 m.
When C covers 350 m, B covers \inline \fn_jvn {\color{Black}\left ( \frac{169}{182}\times 350 \right )m} = 325 m
Therefore, C beats B by (350 - 325) m = 25 m.
Answer: B) 25 m
Answer: B
Question: Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Options:
A)Rs. 169.50
B)Rs. 170
C)Rs. 175.50
D)Rs. 180
E)Rs. 190
Rationale: Explanation:
Since first and second varieties are mixed in equal proportions.
So, their average price = Rs. 126 + 135 = Rs. 130.50
2
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x - 153/22.50=1
x - 153 = 22.50
x = 175.50
ANSWER IS C
Answer: C
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
A)4567
B)3588
C)9944
D)5465
E)6784
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: C
Question: Angelina walked 180 meters from her home to the grocery at a constant speed. She then walked 240 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Options:
A)2
B)3
C)4
D)6
E)12
Rationale: let the speed be X...
so time taken from home to grocery= 180/x..
the speed to gym = 2x..
so time taken = 240/2x=120/x..
its given 180/x-120/x=40..
60/x=40 => 40x = 60 => x =60/40
x=1.5m/secs..
so grocery to gym=2*1.5=3m/s...
Answer : B
Answer: B
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the total share of A & B in profit of Rs.12100 after a year?
Options:
A)Rs.6030
B)Rs.4050
C)Rs.6050
D)Rs.7050
E)Rs.6080
Rationale: 6300:4200:10500
3:2:5
A'share =3/10 * 12100 = 3630
B's share =2/10*12100 = 2420
Required total share = 3630 + 2420 = 6050
Answer : C
Answer: C
Question: One fourth of a solution that was 12% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
Options:
A)34%
B)28%
C)22%
D)18%
E)8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 12% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-36% = 28%
ans B it is.
Answer: B
Question: Nathan took out a student loan for 1200$ at 10 percent annual interest, compounded annually. If he did not repay any of the loan or interest during the first 3 years, which of the following is the closest to the amount of interest he owed for the 3 years.
Options:
A)360
B)390
C)400 dollars
D)410
E)420
Rationale: A straight Q requiring direct formulae..
when compounded annually the final amount= P(1+ r/100)^n..
here P=1200, r=10 and n=3..
1200(1+ 10/100)^3..
1200*1.1^3=1597.2
interest =1597-1200=397, which is nearly 400 in the choices given
ANSWER:C
Answer: C
Question: In a race with 30 runners where 5 trophies will be given to the top 9 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
Options:
A)9^5 ways
B)8^9 ways
C)7^8 ways
D)8^7 ways
E)8^6 ways
Rationale: 9 people can be prized with 5 distinct prizes in 9^5 ways
ANSWER:A
Answer: A
Question: Look at this series: 65, 77, 84, __, 91, 98, 65, 105, ... What number should fill the blank?
Options:
A)60
B)70
C)82
D)77
E)65
Rationale: E
65
In this series, 7 is added to the previous number; the number 65 is inserted as every third number.
Answer: E
Question: What will come in place of the x in the following Number series? 1, 2, 4, 7, 12, 19, X
Options:
A)23
B)30
C)31
D)41
E)29
Rationale: There is one series here
(the numbers are being increased by prime numbers 1, 2, 3, 5, 7, 11....)
1 + 1 = 2
2 + 2= 4
4 + 3= 7
7 + 5 = 12
12 + 7 = 19
Hence 19 + 11 = 30
The correct choice is B
Answer: B
Question: If soundharya rows 49 km upstream and 77 km down steam taking 7 hours each, then the speed of the stream
Options:
A)6 kmph
B)5 kmph
C)2 kmph
D)3 kmph
E)4 kmph
Rationale: Speed upstream = 49/7 = 7 kmph
Speed down stream = 77/7 = 11kmph
Speed of stream = ½ (11-7) = 2 kmph
ANSWER:C
Answer: C
Question: In a certain apartment building, there are one-bedroom and two-bedroom apartments. The rental prices of the apartment depend on a number of factors, but on average, two-bedroom apartments have higher rental prices than do one-bedroom apartments. Let M be the average rental price for all apartments in the building. If M is $1,500 higher than the average rental price for all one-bedroom apartments, and if the average rental price for all two-bedroom apartments is $6,000 higher that M, then what percentage of apartments in the building are two-bedroom apartments?
Options:
A)40%
B)35%
C)30%
D)20%
E)28%
Rationale: Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 1500 : 6000 -----> 1 : 4
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 5) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/5) * 100 ---> 20%
Answer : D
Answer: D
Question: 3 6 7 12 13 18 19 24 . ?
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 3 3x2 (3x2)+1 3x4 (3x4)+1 3x6 (3x6)+1 3x8 (3x8)+1
ans 25
ANSWER:B
Answer: B
Question: The sum W of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Wn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted.
Options:
A)4345
B)4302
C)4258
D)4214
E)4170
Rationale: a method to do it under one minutes is to take advantage of the choices given...
lets work on the last digit as we have different units digit in each choice...
total sum of 1 to 100 inclusive will have 0 as the last digit..
this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...
now for single digit in sum W of even number from 25 to 63..
25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..
here too the units digit is 0, but 64 has to be excluded from the total..
two ways from here on..
1) we are subtracting 0 from 0
so units digit should be 0, but we have to add 64..
so last/units digit =4..
2)we subtract 64 from sum of even int..
so units digit=80-4=76..
or units digit =6...
so our answer should have units digit as 10-6=4..
only D has 4 as units digit..
ans D
Answer: D
Question: o mow a grass field a team of mowers planned to cover 15 hectares a day. After 4 working days they increased the daily productivity by 33×13%33×13%, and finished the work 1 day earlier than it was planned.
A) What is the area of the grass field?
B) How many days did it take to mow the whole field?
C) How many days were scheduled initially for this job?
Options:
A)387
B)39
C)37
D)20
E)28
Rationale: Hint: See problem 20 and solve by yourself.
Answer: A) 120 hectares; B) 7 days; C) 8 days.
Answer:D
Answer: D