divelab/Sys2Bench huggingface dataset:
Question: The age of mother one decade age was three times the age of her daughter. 10 years hence, mother’s age will be two times that of her daughter. The proposition of their current ages is:
Options:
A)7:3
B)6:3
C)8:3
D)2:3
E)6:3
Rationale: A
7:3
Let, Ages of mother and daughter 1 decade ago was 3A and A years correspondingly
Then, (3A + 10) + 10 = 2 [(A + 10) + 10]
3A + 20 = 2A + 40
X = 20
Needed Ratio = (3A + 10) : (A + 10)
= 70 : 30
= 7 : 3
Answer: A
Question: can you find the missing number in the sequence below
11 15 19 12 16 ? 13 17 21 14 18 22
Options:
A)14
B)23
C)25
D)20
E)None
Rationale: Correct Answer : D
break the given series
11 15 19
12 16 ?
13 17 21
14 18 22
now read the number from top to bottom
Answer: D
Question: The speed at which a woman can row a boat in still water is 300 kmph. If he rows downstream, where the speed of current is 42 kmph, what time will he take to cover 190 metres?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Speed of the boat downstream = 300 + 42 = 342 kmph
= 342 * 5/18 = 95 m/s
Hence time taken to cover 190 m = 190/95 = 2 seconds. Answer: B
Answer: B
Question: A prize of $600 is to be distributed among 15 winners, each of whom must be awarded at least $15. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
Options:
A)$200
B)$220
C)$285
D)$300
E)$360
Rationale: Total value of the prize =$600
Number of people = 15
2/5 of 600 (=$240) should be distributed among 3/5 of 15 (=9 people ) with each getting $15 each. Remaining money = 600-240 = $360. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $15. Thus, minimising the remaining 5 people (=15-9-1. '-1' to exclude 1 that needs to be maximised) = 5*15=75.
Thus the maximum award can be = 360-75 = $285, hence C is the correct answer.
Answer: C
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
Options:
A)Rs. 920
B)Rs. 960
C)Rs. 1060
D)Rs. 1200
E)Rs. 1300
Rationale: Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
ANSWER:B
Answer: B
Question: what is rate of interest if principal.amount be 400,simple interest 160 and time 2year.
Options:
A)10
B)12.5
C)20
D)12
E)14.5
Rationale: s.i=(p*r*t)/100
160=800r/100
r=160/8=20%
answer C
Answer: C
Question: A trade analyst announced 20% reduction in the unit price of car. As a result, the sales volume went up by 5%. What was the net effect on the sales revenue?
Options:
A)no change
B)decreases by 19.2%
C)increases by 19%
D)increases by 19.0%
E)None of these
Rationale: Explanation :
Reduction of price = (100 -20)% = 80% = 0.8
Increase of sale = (100+5)% = 105% = 1.05
Total effect = 0.8 X 1.01 = 80.8%, Decreases by 19.2%
Answer : B
Answer: B
Question: What is the sum of the different positive prime factors of 250?
Options:
A)10
B)11
C)15
D)7
E)18
Rationale: 250
25*10 --> 5*5*2*5 --> 5+2=7. Remember its asking for the DIFFERENT positive prime factors of 250.
D
Answer: D
Question: If a*b=2a-3b+ab,then3*5+5*3 is equal to
Options:
A)22
B)25
C)26
D)28
E)23
Rationale: 3*5+5*3= (2x3-3x5+3x5)+(2x5-3x3+5x3)
=22
ANSWER A 22
Answer: A
Question: If logx y = 10 and log2 x = 1000, what is the value of y?
Options:
A)2100
B)21000
C)210000
D)210
E)21100
Rationale: log2 x = 1000
=> x = 21000
logx y = 10
=> y = x10
= (21000)10
= 2(1000 × 10)
= 210000
Answer: Option C
Answer: C
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 59.
Options:
A)1000
B)800
C)900
D)700
E)1100
Rationale: Number of odd numbers between 1 and 59 is (59+1)/2=30
Therefore Sum of odd numbers 30*30= 900
ANSWER: C
Answer: C
Question: Mark is playing poker at a casino. Mark starts playing with 160 chips, 20% of which are $100 chips and 80% of which are $20 chips. For his first bet, Mark places chips, 10% of which are $100 chips, in the center of the table. If 70% of Mark's remaining chips are $20 chips, how much money did Mark bet?
Options:
A)$1,960
B)$1,740
C)$1,540
D)$3,080
E)$2,240
Rationale: Total chips 160
20% of $100 chips = 32 chips * $100 = $3,200
80% of $20 chips = 128 chips * $20 = $2,560
If x is the number of chips bet and y is the amount of chips remaining:
x + y = 160
y = 160 - x ~ (1)
[First round bet] + [Second round bet] = $3,200 + $2,560
[0.1x * $100 + 0.9x * $20] + [0.3y * $100 + 0.7y * $20] = $5,760
10x + 18x + 30y + 14y = 5760
28x + 44y = 5760 ~ (2)
Substitute (1) into (2) to solve for x:
28x + 44(160 - x) = 5760
28x + 7040 - 44x = 5760
16x = 1280
x = 80
Substituting x:
[First round bet] = [0.1x * $100 + 0.9x * $20] = 0.1(80)($100)+0.9(80)($20) = $800 + $1,440 = $2,240
Answer is E
Answer: E
Question: If a:b = 3:1, then find (a - 3b)/(2a - b)?
Options:
A)0
B)1
C)2
D)1/7
E)2/7
Rationale: a/b = 3/1 => a = 3b
(a - 3b)/(2a - b) = (3b - 3b)/(6b - b)
= 0/7b => 0
ANSWER:A
Answer: A
Question: How many times will the digit 8 be written when listing the integers from 1 to 1000?
Options:
A)164
B)297
C)300
D)345
E)482
Rationale: Many approaches are possible. For example:
Consider numbers from 0 to 999 written as follows:
1. 000
2. 001
3. 002
4. 003
...
...
...
1000. 999
We have 1000 numbers. We used 3 digits per number, hence used total of 3*1000=3000 digits. Now, why should ANY digit have preferences over another? We used each of 10 digits equal # of times, thus we used each digit (including 8) 3000/10=300 times.
Answer: C.
Answer: C
Question: My name is AJEET. But my son accidentally types the name by interchanging a pair of letters in my name. What is the probability that despite this interchange, the name remains unchanged?
A.
B.
C.
D.
Options:
A)5%
B)10%
C)20%
D)25%
E)35%
Rationale: This is a very crude method but i guess it's effective for such small problems.
Possible pairs of letters that could be interchanged are:
AJ
AE
AE
AT
JE
JE
JT
EE
ET
ET
Out of the the ten possibilities, only 1 would lead to an unchanged name.
Therefore, the probability is 1/10 = 10 %.
A more general approach goes as follows:
Each letter can be interchanged in the following ways.
'A' can be interchanged with 4 letters,' 'J' with 3, 'E' with 2 and 'E' with 1.
Therefore total possibilities equal 4+3+2+1=10.
Again only 1 would lead to an unchanged name.
Therefore the answer is 1/10 =10% ANS:B
Answer: B
Question: Six years ago, the ratio of the ages of Vimal and Saroj was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Saroj's age at present?
Options:
A)12
B)14
C)16
D)18
E)15
Rationale: Given that, six years ago, the ratio of the ages of Vimal and Saroj =6:5
Hence we can assume that
age of Vimal six years ago =6x
age of Saroj six years ago =5x
After 4 years, the ratio of their ages =11:10
⇒(6x+10):(5x+10)=11:10⇒10(6x+10)=11(5x+10)⇒5x=10⇒x=105=2
Saroj's present age
=(5x+6)=5×2+6=16
Answer is C.
Answer: C
Question: The remainder when positive integer nn (n>1n>1) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1. What is the least value of nn?
Options:
A)76
B)101
C)126
D)151
E)176
Rationale: We're asked to find the LEAST number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7. You might notice, rather quickly, that ALL of the answers gives us a remainder when divided by 25...
76 = 75 + 1
101 = 100 + 1
126 = 125 + 1
151 = 150 + 1
176 = 175 + 1
So the REAL question is "which of these 5 is the least number that has a remainder of 1 when divided by 7?" From here, you can just do the "brute force" math:
A: 76/7 = 10r6 NOT a match
B: 101/7 = 14r3 NOT a match
C: 126/7 = 18r0 NOT a match
D: 151/7 = 21r4 NOT a match
NONE of these numbers "fits" the description, so the answer MUST be E.
E: 176/7 = 25r1;
ANSWER:E
Answer: E
Question: What is the thousandths digit in the decimal equivalent of 62/5000?
Options:
A)0
B)1
C)2
D)5
E)6
Rationale: 62/5000 = 62 /(5*10^3)
= (62/5) *10^-3
=12.4 * 10^-3
=.0124
Thousandths digit = 2
Answer C
Answer: C
Question: What is the 4 digit number in which the 1st digit is 1/3 of the second, the 3rd is the sum of the 1st and 2nd, and the last is three times the second?
Options:
A)1100
B)1349
C)1160
D)1450
E)1500
Rationale: First digit is 1/3 second digit => The numbers can be 1 & 3, 2& 6, 3 & 9.
First + second = third => we can eliminate 3 & 9 since 3 + 9 = 12.
Last is 3 times the second => we can eliminate option 2 & 6 since 3 * 6 = 18.
Hence the number is 1349
B
Answer: B
Question: If f(x) = k(x - k) and k is a constant, what is the value of f(3) - f(2), in terms of k?
Options:
A) 1
B) k
C) 7k - 1
D) k^2 + k
E) k^2 - k
Rationale: First, distribute f(x). k(x - k) = kx - k^2. Now evaluate f(3) and f(2):
f(3) = k(3) - k^2 = 3k - k^2
f(2) = 2k - k^2
f(3)-f(2)=k .. Answer B
Answer: B
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
Options:
A)15.5 days
B)4.3 days
C)17.5 days
D)16.5 days
E)18.5 days
Rationale: C = 1/3 – 1/10 = 7/30 => 4.3 days
ANSWER:B
Answer: B
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the seven socks?
Options:
A)12
B)15
C)21
D)36
E)42
Rationale: Since given condition that if one sock is on left leg (L) and other colour is on right(R)...and we need to find how many such combinations are possible.
If L has one colour sock and R will have any 6C1 colour sock..
for one combination it is 6 and for seven colour combination it 7*6 = 42.
ANS option E is correct..
Answer: E
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3 . Find his average after 17th inning.
Options:
A)39
B)88
C)26
D)87
E)11
Rationale: Explanation:
Consider the avg for first 16 innings is x.
Then total runs scored till 16 innings is 16x.
Total runs after 17 innings = 16x + 87.
Thus, 16x+8717=x+316x+8717=x+3 ⇒ x = 36
So his average after 17 innings = 39.
Answer: A
Answer: A
Question: Sripad has scored average of 62 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
Options:
A)79
B)70
C)38
D)27
E)21
Rationale: Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 62.
i.e (58+58+x)/3 = 62
116 + x = 186
x = 70 marks.
Therefore, the maximum marks he can score in maths is 70.
Answer: B
Answer: B
Question: If 3 men or 4 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
Options:
A)8/3
B)6
C)5
D)4
E)3
Rationale: 3 men can finish a work in 16 days, so in 1 day 3 men finish 1/16th of work and in 1 day 1 men can finish, 1/48th of work.
similarly, in 1 day 1 women can finish 1/64th of work.
12 men in 1 day can finish, 12/48 = 1/4,
8 women in 1 day can finish = 8/64 = 1/8
1/4 + 1/8 = 3/8.
hence number of days to complete is 8/3 days.
ANSWER:A
Answer: A
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 31 years, then find the age of the person sitting in the middle of the row?
Options:
A)9 years
B)29 years
C)28 years
D)19 years
E)17 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (31 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 31 * 3 = 196 - 75 - 93 = 28 years.
ANSWER:C
Answer: C
Question: The prices of a scooter and a television set are in the ratio 3 : 2. If a scooter costs Rs. 6000 more than the television set, the price of the television set is ?
Options:
A)Rs. 6000
B)Rs. 10000
C)Rs. 12000
D)Rs 16000
E)Rs. 18000
Rationale: Let the price of a scooter be Rs. 3x and that of a television set Rs. 2x.
Then, 3x - 2x = 6000
x = 6000
∴ Cost of a television set = 2x
= Rs. 12000
Answer : C
Answer: C
Question: An emergency vehicle travels 10 miles at a speed of 50 miles per hour. How fast must the vehicle travel on return trip if the round trip travel time is to be 20 minutes?
Options:
A)75
B)26
C)20
D)12
E)91
Rationale: Explanation:
Going trip time = t = dsds = 1050×601050×60 = 12 minutes.
Given total time = 20 minutes
Return trip time = Total time – Going trip time = 20 – 12 = 8 minutes = 860860 hours.
As the distance is 10 miles during even return trip,
The return speed = dtdt = 1086010860 = 10×60810×608 = 75 mph
Answer: A
Answer: A
Question: What is the difference between the place value and face value of 3 in the numeral 1375?
Options:
A)296
B)297
C)298
D)29
E)31
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
B
Answer: B
Question: P can do a piece of work in 18 days and Q can do in 22 days, with the help of C, they finish the work in 6 days. How long will it take R to finish the work?
Options:
A)17days
B)18days
C)16 ½ days
D)17 ½ days
E)19 days
Rationale: Explanation:
(P+Q) 1 day work = 1/18 + 1/22 = 7/66
(P+Q+R) 1 day work = 1/6
R 1 day work =1/6 – 7/66 = 2/33
R can do piece of work in 16 ½ days
Answer: Option C
Answer: C
Question: A man can swim in still water at 12 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)2.67
C)1.2
D)1.5
E)4
Rationale: M = 12
S = x
DS = 12 + x
US = 12 + x
12 + x = (12 - x)2
12 + x = 24 -2x
3x = 12
x = 4
Answer: E
Answer: E
Question: The negative number c is divisible by 2. What is the remainder when dividing 5(7-c)(9+c) by 2?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: When we multiply any of these options: 5*11*5 (c=-4) or 5*17*-1 (c=-10) we end up with numbers ending in 5; so any number ending in 5 divided by 2 will always leave a remainder of 1. Hence the correct answer is B.
Answer: B
Question: Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days.
Options:
A)11
B)12
C)13
D)15
E)16
Rationale: Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
Answer is E.
Answer: E
Question: In a 1000 m race, A beats B by 70 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
Options:
A)145 m
B)176 m
C)168 m
D)163 m
E)218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 70) = 930 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/930 * 1000/900 = 1000/837 So, by the time A covers 1000 m, C covers 837 m.
So in 1000 m race A beats C by 1000 - 837 = 163 m.
Answer:D
Answer: D
Question: A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Options:
A)27 (1/3)kmph
B)21 (1/3)kmph
C)21 (1/7)kmph
D)26 (1/3)kmph
E)31 (1/3)kmph
Rationale: Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph = 21 (1/3)kmph.
Answer:B
Answer: B
Question: The average age of a class of 25 students is 19 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?
Options:
A)40 years
B)41 years
C)47 years
D)43 years
E)44 years
Rationale: If age of the teacher was 19, average would not have changed.
Since average increased by 2,
Age of the teacher=25+22×1=47
ANSWER:C
Answer: C
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 132 = 4 x 3 x 11
So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
B)
Answer: B
Question: A car takes 4 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)92Kmph
B)98Kmph
C)90Kmph
D)80Kmph
E)82Kmph
Rationale: Time = 4
Distence = 540
3/2 of 4 hours = 4 * 3/2 = 6 Hours
Required speed = 540/6 = 90 Kmph
C)
Answer: C
Question: A test has 160 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?
Options:
A)23
B)25
C)27
D)29
E)31
Rationale: A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points.
Let C be the number of correct answers and let I be the number of incorrect answers.
To get 40 points, a test taker must have at least 40 correct answers. Then C=> 40.
For every correct question above 40, the test taker has 4 incorrect answers.
Then, the I = 4*(C - 40).
Also, I + C <= 160. Thus 5C <= 320 and so C <= 64.
Then 40 <= C <= 64 and C can have 25 possible values.
The answer is B.
Answer: B
Question: Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8. If a total of 80 sandwiches were made, how many bologna sandwiches
were made?
Options:
A)15
B)30
C)35
D)42
E)48
Rationale: For deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts
and we should calculate how many sandwiches holds 1 part:
80 / 16 = 5 sandwiches in one part
For bologna we have 7 parts so:
7 * 5 = 35
Answer is C
Answer: C
Question: In a class,12 students like to play Basketball and 8 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
Options:
A)12
B)15
C)17
D)18
E)22
Rationale: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
12 +8 - 3 = 17
C)
Answer: C
Question: A patient was given three pills which he is required to take one after every thirty-five minutes.
How long can the pills run for him?
Options:
A)1 hour and 10 minutes.
B)1 hour and 15 minutes.
C)1 hour and 20 minutes.
D)1 hour and 50 minutes.
E)1 hour and 25 minutes.
Rationale: He took the first pill at the zero minute.
He took the second pill after 20 minutes = 0+35=35
He took the third pill after 20 minutes = 35+35=70
Then it will last for 70 minutes or an hour and 10 minutes.
Answer A
Answer: A
Question: A family pays $800 per year for an insurance plan that pays 65 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total.
Options:
A)$1,000
B)$1,200
C)$1,400
D)$1,500
E)$2,200
Rationale: Upfront payment for insurance plan = 800$
Family needs to pay 35 % of first 1000 $ in expense = 350$
Total amount paid by family when medical expenses are equal to or greater than 1000 $ = 800 + 350 = 1150 $
Total amount paid by insurance plan for first 1000 $ = 800 $
Total amount paid by family will equal amount paid by plan when medical expense = 1500 $
(Since insurance plan will pay 100% of amount that exceeds 1150$ )
Answer D
Answer: D
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
Options:
A)900 km
B)800 km
C)600 km
D)690 km
E)609 km
Rationale: Explanation:
D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Answer: Option C
Answer: C
Question: A car moves at 92 km/hr. What is the speed of the car in meters per second ?
Options:
A)20 2/9m sec
B)22 2/9m sec
C)25 5/9m sec
D)26 2/9m sec
E)28 2/9m sec
Rationale: Explanation:
Speed=(92∗5/18)m/sec
=230/9 m/sec
=25 5/9msec
Option C
Answer: C
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company or both. If 62 percent of these who attended the meeting were stockholders and 46 percent were employees. What percent were stockholders, who were not employees?
Options:
A)52
B)54
C)59
D)55
E)56
Rationale: I came up with the same answer choice B, but my approach was slightly different!
46% were employees which shall cover those who were only employees and those who were both shareholders and employees.
Thus, the number of attendants who were only shareholders is 100% - 46% = 54%.
Answer: B
Question: The C.P of 14 books is equal to the S.P of 18 books. Find his gain% or loss%?
Options:
A)16 2/3% loss
B)16 2/8% loss
C)16 3/3% loss
D)22 2/9% loss
E)56 2/3% loss
Rationale: 14 CP = 18 SP
18 --- 4 CP loss
100 --- ? => 22 2/9% loss
Answer:D
Answer: D
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 8480, what is the length of the plot in metres?
Options:
A)20
B)200
C)300
D)90
E)140
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 8480
[4L - 40] = 8480 / 26.50 = 320
4L = 360
L = 360/4= 90 meters. Answer: D
Answer: D
Question: If 10^(x-1)< 0.000125 <10^x, what is the value of an integer x?
Options:
A)-4
B)-3
C)-2
D)3
E)4
Rationale: -> Multiply 10^6- > (10^6){10^(x-1)}<125<(10^6)(10^x) -> 125 is bigger than 100
-> (10^6)(10^(x-1))=100 -> 10^(6+x-1)=10^2, x+5=2 -> x=-3
Thus, the answer is B
Answer: B
Question: Of 90 applicants for a job, 42 had at least 4 years' experience, 54 had degrees, and 8 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
Options:
A)10
B)8
C)14
D)16
E)12
Rationale: 90 - 8 = 82
82 - 42 - 54 = -14
Then 14 are in the intersection between 4 years experience and degree.
Answer : C
Answer: C
Question: What number is obtained by adding the units digits of 734^99 and 347^83?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The units digit of 734^99 is 4 because 4 raised to the power of an odd integer ends in 4.
The units digit of 347^83 is 3 because powers of 7 end in 7, 9, 3, or 1 cyclically. Since 83 is in the form 4n+3, the units digit is 3.
Then 4+3 = 7.
The answer is A.
Answer: A
Question: A man has Rs. 512 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)80
B)90
C)96
D)98
E)100
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 512
16x = 512
x = 32.
Hence, total number of notes = 3x = 96.
C
Answer: C
Question: A study group consists of 4 English majors, 6 biological sciences majors, and 5 engineers. In how many ways can 3 English majors, 3 biological science majors and 3 engineers selected from the given group?
Options:
A)987 ways
B)346 ways
C)600 ways
D)200 ways
E)134 ways
Rationale: The number of ways of selecting three English majors, two biological science majors and three engineers is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(3 * 2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 5 * 10
= 200 ways.
Answer: D
Answer: D