divelab/Sys2Bench huggingface dataset:
Question: Which of the following is divisible by the first six positive integer multiples of 19?
(i) 52440
(ii) 114600
(iii) 19038
Options:
A)None
B)i only
C)iii only
D)ii and iii only
E)i and ii only
Rationale: A positive integer x is divisible by 19, 2*19,...,6*19 if and only if it is divisible by their least common multiple, which in this case is 3*4*5*19. In particular, x is divisible by 10, so iii is not divisible by the first six positive integer multiples of 19.
3*4*5*19=60*(20-1)=1140. 1140*100=114000, so clearly (ii) is not divisible by the first six positive integer multiples of 19.
It remains to verify (i). 52440-40*1140=52440-45600=6840=6*1140, so (i) is divisible by 1140.
Answer B.
Answer: B
Question: Machine A and machine W are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine W. Machine W produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: [Reveal]Spoiler:
TimeW: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6=A
Answer: A
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
Options:
A)160 km
B)180 km
C)200 km
D)220 km
E)240 km
Rationale: Down Stream Speed :(14+4)km/hr =18 km/hr
Up Stream Speed:(14-4)km/hr=10km/hr
(x/18)+(x/2/20)=19
x=180km
ANSWER:B
Answer: B
Question: A cube has a volume of 27 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Options:
A)216
B)48
C)64
D)80
E)100
Rationale: Volume = 27 = side^3
i.e. Side of Cube = 3
New Cube has dimensions 6, 6, and 6 as all sides are twice of teh side of first cube
Volume = 6*6*6 = 216 square feet
Answer: option A
Answer: A
Question: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion. In 16 years from now, Lyn the circus Lion will be exactly half as old as Ele, the circus Elephant. How old is Ele today?
Options:
A)47
B)48
C)43
D)42
E)41
Rationale: Ele, the circus Elephant, is currently three times older than Lyn, the circus Lion.
Ele = 3*Lyn
Usually, ages are integers so there is a good possibility that the age of Ele is 48 (the only option that is a multiple of 3).
Then age of Lyn would be 16. In 16 yrs, Ele would be 64 and Lyn would be 32 - so Lyn would be half as old as Ele.
Answer (B)
Answer: B
Question: What is the smallest number which when increased by 3 is divisible by 18, 70, 100 and 21?
Options:
A)5037
B)5447
C)5867
D)6297
E)6617
Rationale: When increased by 3, the number must include at least 2^2*3^2*5^2*7 = 6300
The answer is D.
Answer: D
Question: What is the probability of flipping a fair coin four times and the coin landing on heads on exactly three flips?
Options:
A)1/3
B)1/4
C)2/3
D)2/5
E)1/8
Rationale: Probability = (Favorable combination)/(Total combination)
Favorable combination = (HHHT, HHTH, HTHH,THHH) ==> 4
Total combination = 8 (2^4)
Probability = (4)/(16) = 1/4
(B)
Answer: B
Question: Rectangular Floors X and Y have equal area. If Floor X is 14 feet by 18 feet and Floor Y is 9 feet wide, what is the length of Floor Y, in feet?
Options:
A) 13 1/2
B) 18
C) 18 3/4
D) 21
E) 28
Rationale: The area of a rectangle is: Area = length x width
We are given that floor X is 14 feet by 18 feet and that floor Y is 9 feet wide. So we can say:
length of X = 14
width of X = 18
width of Y = 9
length of Y = n
We also can say:
Area of Floor X = Area of Floor Y
(length of X)(width of X) = (length of Y)(width of Y)
(14)(18) = 9n
(14)(2) = n
28 = n
Answer E.
Answer: E
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability W that the number of men is equal to that of women?
Options:
A)W=18/35
B)W=16/35
C)14/35
D)13/35
E)12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: A
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many Z such committees are possible?
Options:
A)20
B)40
C)50
D)Z=80
E)Z=120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: D
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
Options:
A)09:30 p.m
B)11:23 p.m
C)10:30 p.m
D)07:30 p.m
E)05:93 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: C
Answer: C
Question: 4, 5, 7, 11, 19, (...)
Options:
A)32
B)22
C)35
D)27
E)28
Rationale: 4
4 × 2 - 3 = 5
5 × 2 - 3 = 7
7 × 2 - 3 = 11
11 × 2 - 3 = 19
19 × 2 - 3 = 35
Answer is C
Answer: C
Question: Two pyramids are thrown with faces 1,2,4,6. Find the probability to get a sum of even number on an their faces?
Options:
A)5/8
B)3/4
C)1/4
D)7/4
E)3/5
Rationale: 1 pyramid can show 4 different kind of arrangements
1,2,4=7
1,2,6=9
1,4,6=11
2,4,6=12
So, out of 4 outcomes
3 are odd and 1 is even.
In question given two pyramids are thrown.
So, to make some of their faces as even
Condition 1: some of both individual faces of each pyramid is odd
3/4 * 3/4
=9/16
Condition 2: some of both individual faces of pyramid is even
1/4 + 1/4
=1/16
Total such conditions = 9/16 + 1/16
= 10/16
= 5/8
ANSWER:A
Answer: A
Question: A certain number when divided by 39 leaves a remainder 17, what is the remainder when the same number is divided by 13?
Options:
A)7
B)8
C)9
D)6
E)4
Rationale: Explanation:
39 + 17 = 56/13 = 4 (Remainder)
Answer: E
Answer: E
Question: Average of all prime numbers between 30 to 50
Options:
A)37
B)37.8
C)39
D)39.8
E)40
Rationale: Explanation:
Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47
Average of prime numbers between 30 to 50 will be
(31+37+41+43+47 / 5)=199 / 5=39.8
Option D
Answer: D
Question: A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
Options:
A)20
B)26
C)32
D)39
E)51
Rationale: total transaction in two days = 4-2 = 2 feet
in 38 days it will climb 38 feet
on the 39th day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =39
D
Answer: D
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > CD
B)XB < YD
C)AX > XB
D)AX < CD
E)AX > AB
Rationale: A--X------B
C-----Y---D
AX < CD.
Answer: D.
Answer: D
Question: The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter strings can be formed in which the two occurrences of the letter I are separated by at least one other letter?
Options:
A)12
B)18
C)24
D)36
E)48
Rationale: Total no of ways arranging 5 letter with one letter redundant is 5!/2!=60
No of ways two I's can be together 4!=24
no of ways at least one alpha is between two I's =60-24=36
ANS:D
Answer: D
Question: A 8% stock yields 20%. The market value of the stock is:
Options:
A)Rs 48
B)Rs 45
C)Rs 40
D)Rs 50
E)Rs 55
Rationale: Explanation:
For an income of Rs. 20, investment = Rs. 100.
For an income of Rs 8, investment =Rs.100/20 X8 =Rs 40
Market value of Rs. 100 stock = Rs 40
Answer is C
Answer: C
Question: At what rate percent on simple interest will Rs.750 amount to Rs.825 in 5 years?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 75 = (750*5*R)/100
R = 2%.Answer: A
Answer: A
Question: In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?
Options:
A)16
B)8
C)1
D)1/8
E)1/64
Rationale: Say r=1 => V1 = 1/8
when r=1/2; V2 = 1
V2 = 1*V1.
Answer : B
Answer: B
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
Options:
A)0
B)1
C)2
D)3
E)None of these
Rationale: Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
ANSWER IS C
Answer: C
Question: A vending machine randomly dispenses four different types of fruit candy. There are twice as many apple candies as orange candies, twice as many strawberry candies as grape candies, and twice as many apple candies as strawberry candies. If each candy cost $0.4, and there are exactly 90 candies, what is the minimum amount of money required to guarantee that you would buy at least three of each type of candy?
Options:
A)$3.00
B)$20.75
C)$33.20
D)$42.75
E)$45.00
Rationale: Let number of Apple , Orange , strawberry and grape candies be A, O ,S and G respectively .
A= 2O
S= 2G
A= 2S
A= 4G
A+O+S+G = 90
=>A + A/2 + A/2 +A/4 = 90
=> 9A/4 = 90
=> A = 40
O = 20
S = 20
G = 10
Cost of each candy = .25 $
Mininum amount of money required to guarantee that you would buy at least three of each type of candy
We can buy 40 Apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies .
Total = 83 candies
Amount required = 83 * .4 = 33.20 $
Answer C
Answer: C
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $5 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)$28
B)$82
C)$110
D)$138
E)$195
Rationale: by the question, the equation would be 150 p - 85*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 195. Answer E for me.
Answer: E
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)277 m
B)240 m
C)627 m
D)892 m
E)288 m
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x
= 240 m.
Answer: B
Answer: B
Question: If two positive numbers are in the ratio 1/9 : 1/5, then by what percent is the second number more than the first?
Options:
A)80%
B)90%
C)60%
D)50%
E)65%
Rationale: Given ratio = 1/9 : 1/5 = 5 : 10
Let first number be 5x and the second number be 9x.
The second number is more than first number by 4x.
Required percentage = 4x/5x * 100 = 80%.
Answer:A
Answer: A
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 8:00 a.m., at what time was it one-eighth full?
Options:
A)9:00 a.m.
B)7:00 a.m.
C)6:00 a.m.
D)4:00 a.m.
E)2:00 a.m.
Rationale: To go from one-eighth (1/8) full to half (1/2) full culture of bacteria should quadruple: 1/8*4=1/2, as it quadruples every hour then container was one-eighth full at 8:00 a.m -1 hour = 7:00 a.m.
Answer: B.
Answer: B
Question: C and D enter into partnership with capital as 7:9. At the end of 8 months, C withdraws. If they receive the profits in the ratio of 8:9 find how long D's capital was used?
Options:
A)months
B)months
C)months
D)months
E)months
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
ANSWER:D
Answer: D
Question: A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 1,600 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A)5.55%
B)5.65%
C)5.75%
D)5.85%
E)5.95%
Rationale: The amount of sodium chloride is 0.05*10,000 = 500 gallons
500/8400 = 5/84 which is about 5.95%
The answer is E.
Answer: E
Question: The product of two successive numbers is 4160. Which is the smaller of the two numbers?
Options:
A)78
B)64
C)88
D)67
E)37
Rationale: B
4160
From the given alternatives,
64 × 65 = 4160
∴ Smaller number = 64
Answer: B
Question: A basket has 6 apples and 4 oranges. FOUR fruits are picked at random. The probability that at least 3 apples are picked is
Options:
A)25/42
B)25/48
C)19/42
D)25/47
E)25/43
Rationale: Total fruits = 10Since there must be at least two apples,(6C3 * 4C1)/10C4 + 6C4/10C4 = 19/42.Answer:C
Answer: C
Question: A man complete a journey in 10 hrs. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
Options:
A)271 km
B)224 km
C)243 km
D)222 km
E)215 km
Rationale: B
224 km
Let the total distance be x km.
Then, [(1/2 x) / 21 + (1/2 x) / 24] = 10
15x = 168 * 20 => x = 224 km.
Answer: B
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)16 8/3% loss
C)19 2/3% loss
D)13 2/3% loss
E)26 2/3% loss
Rationale: 15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Answer: A
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Options:
A)288
B)286
C)298
D)2776
E)8811
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer:D
Answer: D
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday?
Options:
A)0.096
B)0.125
C)0.128
D)0.512
E)0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.6
Therefore, probability of no rain = 0.4
0.6*0.6*0.4 = 0.096
Hence A
Answer: A
Question: How many combinations of three letters taken from letters (a, b, b, c, c, d) are possible?
Options:
A)10
B)13
C)35
D)36
E)56
Rationale: So 4C3 for abcd - 4 choices
3 more for bb(a,c or d)
3 more for cc(a,b or d)
total 10
Ans :A
Answer: A
Question: If x#y is defined to equal x^3/y for all x and y, then (-1#2)#3 =
Options:
A)4/3
B)1/3
C)1/12
D)-1/12
E)1/24
Rationale: (-1)^3 / 2 = 1/2
(1/2)^3 / 3 = 1/24
so E is my answer
Answer: E
Question: A part-time employee’s hourly wage was increased by 25%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
Options:
A)9%
B)15%
C)20%
D)50%
E)100%
Rationale: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 25% wage increase, the employee makes $1.25/hour
We want the employee's income to remain at $100/week.
So, we want ($1.25/hour)(new # of hours) = $100
Divide both sides by 1.25 to get:
new # of hours = 100/1.25
≈ 80 hours
So, the number of hours decreases from 100 hours to (approximately) 80 hours.
This represents a 20% decrease (approximately) .
Answer : C
Answer: C
Question: Find the median of the data 25, 37, 47, 18, 19, 26, 36.
Options:
A)22
B)23
C)24
D)25
E)26
Rationale: Arranging the data in ascending order, we get 18, 19, 25, 26, 36, 37, 47
Here, the number of observations is odd, i.e., 7.
Therefore, median = (n + 1/2)th observation.
= (7 + 1/2)th observation.
= (8/2)th observation
= 4th observation.
4th observation is 26.
Therefore, median of the data is 26. ANSWER :E
Answer: E
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother three years younger to her was born. What is the difference between the ages of her parents?
Options:
A)2 years
B)4 years
C)5 years
D)7 years
E)8 years
Rationale: Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 3) years = 41 years.
Required difference = (41 - 36) years = 5 years.
Answer: Option C
Answer: C
Question: A batch of cookies was divided among three tins: 2/3 of all the cookies were placed in either the blue tin or the green tin, and the rest were placed in the red tin. If 1/4 of all the cookies were placed in the blue tin, what fraction E of the cookies that were placed in the other tins were placed in the green tin?
Options:
A)15/2
B)9/4
C)5/9
D)7/5
E)9/7
Rationale: Blue tin or red tin: 2/3 (N)
Red tin: (1/3)N
Blue tin: (1/4)N
What the last statment meant, is it wants this fraction: (# of cookies in green tin)/(# of cookies in red and green tin)
# of cookies in green tin = 2N/3 - N/4 = 8N- 3N/12 = 5N/12
# of cookies in red and green tin = N/3 + 5N/12 = 9N/12
Fraction E= 5N/12 * 12/9N = 5/9 (C)
Answer: C
Question: If the cost price is 96% of the selling price, then what is the profit percent?
Options:
A)4.17%
B)5%
C)6.12%
D)3.25%
E)5.75%
Rationale: Let S.P. = $100
C.P. = $96
Profit = $4
Profit% = 4/96 * 100 = 25/6 = 4.17%
Answer is A
Answer: A
Question: It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is?
Options:
A)2:9
B)3:1
C)3:4
D)3:9
E)3:6
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120/x + 480/y = 8 or 1/x + 4/y
= 1/15 --- (i)
And, 200/x + 400/y = 25/3 or 1/x + 2/y
= 1/24 --- (ii)
Solving (i) and (ii), we get x = 60 and y
= 80
Ratio of speeds = 60:80 = 3:4
Answer:C
Answer: C
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
A)120 meter
B)299 meter
C)666 meter
D)155 meter
E)144 meter
Rationale: Speed = 48*(5/18) m/sec = 40/3 m/sec
Length of Train (Distance) = Speed * Time
(40/3) * 9
= 120 meter
Answer: A
Answer: A
Question: John distributes his pencil among his 4friends Rose, Mary, Ranjan, and Rohit in the ratio 1/2 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
Options:
A)45
B)65
C)70
D)77
E)98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.
D)
Answer: D
Question: If the tens digit of positive integer x is 3 and the tens digit of positive integer y is 3, how many possible values of the tens digit of 2(x+y) can there be?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 30 + p and 30 + q respectively.
2(30+p+30+q)= 120 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 20 up to 56.
There can be 4 possibilities for the tens digit.
The answer is C.
Answer: C
Question: The editor of an anthology of short stories will select authors from a pool of 10 authors, of which 4 are female. If the anthology is to include the work of 6 authors of which at least 2 are female, in how many ways can the editor select the authors?
Options:
A)155
B)165
C)175
D)185
E)195
Rationale: 10C6 = 210
The number of ways to select 6 males is 6C6 = 1
The number of ways to select 5 males and 1 female is 6C5*4C1 = 24
210 - 1 - 24 = 185
The answer is D.
Answer: D
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.15000 at the end of the year, B's share is
Options:
A)Rs.4000
B)Rs.5400
C)Rs.7500
D)Rs.6600
E)None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(15000 x 4 / 11)
= Rs.5400.
Answer B
Answer: B
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)228
B)280
C)287
D)115
E)191
Rationale: Explanation:
x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: B
Question: 82
a7
+ 6b
____
190
If a and b represent positive single digits in the correctly worked computation above, what is the value of a + 2b ?
Options:
A)2
B)6
C)9
D)11
E)12
Rationale: Adding the digits in unit's place , 2+ 7 + b = 10 (Since a and b are positive single digits )
=> b = 1
Now adding the digits in ten's place , 8+a + 6 + 1= 19 (1 has been carried over from unit's place addition)
=> a= 4
a+2b = 4+2*1
=6
Answer B
Answer: B
Question: Two persons Raj and Ramu started working for a company in similar jobs on January 1, 1991. Raj's initial monthly salary was Rs 400, which increases by Rs 40 after every year. Ramu's initial monthly salary was Rs 500 which increases by Rs 20 after every six months. If these arrangements continue till December 31, 200. Find the total salary they received during that period.
Options:
A)Rs 108000
B)Rs 144000
C)Rs 132000
D)Rs 152400
E)None of these
Rationale: Explanation :
Raj's salary as on 1 jan 1991 is Rs 400 per month.
His increment in his month salary is Rs 40 per annum
His total salary from 1 jan 1991 to 31st dec 2000
i.e. in ten years
=>12[2(400)+(10−1)40]×10/2.
=>Rs 69,600.
Ramu's salary as on Jan 1st 1991 is Rs 550 and his half yearly increment in his month salary is Rs 20.
His total salary from 1 jan 1991 to dec 31, 2000
=>6[2(500)+(20−1)20]×20/2.
=>Rs 82,000.
Total salary of Raj and Ramu in the ten year period:
=> Rs. 69600+ Rs. 82800.
=>Rs 1,52,400.
Answer : D
Answer: D
Question: A completes a work in 15 days and B complete the same work in 30 days. If both of them work together, then the number of days required to complete the work will be
Options:
A)8 days
B)9 days
C)10 days
D)12 days
E)13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 15 ×30/ 45 = 10 days.
Answer : C
Answer: C
Question: Which of the following numbers is between 1⁄2 and 1⁄4?
Options:
A).65
B).55
C).29
D).22
E).20
Rationale: Isn't it C?
1/2 = .50
1/4 = .25
The only answer between that is C, .29.
Answer: C