divelab/Sys2Bench huggingface dataset:
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
Options:
A)Rs.10,840
B)Rs.10,720
C)Rs.10,560
D)Rs.10,280
E)None of these.
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
ANSWER:C
Answer: C
Question: How many perfect squares are divisors of the product (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)?
Options:
A)504
B)672
C)864
D)936
E)1008
Rationale: N=(1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)
1!=1
2!=1*2
3!=1*2*3
4!=1*2*3*4
5!=1*2*3*4*5
6!=1*2*3*4*5*6
7!=1*2*3*4*5*6*7
8!=1*2*3*4*5*6*7*8
9!=1*2*3*4*5*6*7*8*9
N=(2^8)(3^7)(4^6)(5^5)(6^4)(7^3)(8^2)(9^1)
=(2^30)(3^13)(5^5)(7^3)
To find the number of perfect squares each exponent in the prime factorization must be even .
Comparing to the form (2^p)(3^q)(5^r)(7^s).
In this case,
p can take values from 0 to 30
q can take values from 0 to 13
r can take values from 0 to 5
s can take values from 0 to 3
Number of even exponents
p=16
q=7
r=3
s=2
Number of perfect squares= 16*7*3*2 = 672
Answer B
Answer: B
Question: In a dance competition the points in each round for the first,second,third and fourth position were 100,50,20,10 . No other points were given. Ashita participated in several rounds in the competition and the product of her score was 50000. In How many rounds did she participate?
Options:
A)3
B)2
C)1
D)5
E)Cannot be determined
Rationale: Correct answer is E because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that she played 15 rounds out of only 5 rounds were there in which she was awarded some points.
Answer: E
Question: A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
Options:
A)5
B)6
C)10
D)13
E)28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 48
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 48
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=48
(2r-4)*r = 48
2r^2 - 4r - 48=0
r cannot be negative so r = 6
and c = 8
So, Answer will be B
Answer: B
Question: 7 people, A, B, C, D, E, F and H, go to a movie and sit next to each other in 8 adjacent seats in the front row of the theatre. In how many different arrangements will there be at least one person between A and F?
Options:
A)8! - 7!2
B)5! - 7!2
C)6! - 7!2
D)8! - 6!2
E)8! - 9!2
Rationale: We need to find at least one person between A and F which is equal to Total ways - No one between A and F
Eight people can be arranged in 8! ways.
No one between A and F is equal to 7!*2! (consider A and F as one. 7 people can be arranged in 7! and A and F in 2!)
So, total ways = 8! - 7!2
ANS:A
Answer: A
Question: A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?
Options:
A)72 days
B)20 days
C)24 days
D)36 days
E)34 days
Rationale: Explanation:
(man + boy)’s 1 day’s work = 1/24
Their 20 day’s work = 1/24 × 20 = 5/6
The remaining 1/6 work is done by the man in 6days
Therefore, the man alone will finish the work in 6 × 6 days = 36 days
Man’s 1 day’s work = 1/36
Therefore, boy’s 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72
Therefore, the Boy alone will finish the work in 72 days.
Answer: Option A
Answer: A
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 22 years younger than Albert. How old is Betty?
Options:
A)8
B)9
C)11
D)15
E)18
Rationale: A = 2M = M+22
M = 22
A = 44
A = 4B, and so B = 11
The answer is C.
Answer: C
Question: The average (arithmetic mean) of four numbers is 4x + 1. If one of the numbers is x, what is the average of the other three numbers?
Options:
A)x + 1
B)3x + 3
C)5x + 4/3
D)5x + 4
E)15x + 12
Rationale: If the average of four numbers is 4x + 1, then the sum of all four numbers if 4 * (4x + 1) = 16x + 12. If one of the numbers is x, then the average of the remaining three numbers would be: (16x + 4 - x)/3 = (15x + 4)/3 = 5x + 4/3.
Answer is C.
Answer: C
Question: In a college, 70% of total 100 Arts students are Locals. 50% of students from 200 Science students are locals and 85% of total 120 Commerce students are locals. What is the total percentage of locals from Arts, Science and Commerce.
Options:
A)56
B)86.7
C)25.7
D)66
E)64.7
Rationale: locals from Arts = 70% of 100 = 70
locals from Science = 50% of 200 = 100
locals from Commerce = 85% of 120 = 102
total local percentage = (70+100+102)/(100+200+120) = 272/420 = 0.647
E
Answer: E
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1300 votes. What is the total number of votes polled?
Options:
A)A)4500
B)B)5200
C)C)6900
D)D)7520
E)E)6500
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1300
20x/100 = 1300
x = 1300*100/20 = 6500
Answer is E
Answer: E
Question: At a certain amateur bands rock show the ratio of freaks to nerds (N) to geeks is 1:2:3. If these are the only types of people in the crowd, and each person in the crowd has the same chance of yelling rock on!, what are the chances that the next person who yells rock on!will be a geek?
Options:
A)1
B)1/2
C)1/3
D)1/4
E)1/6
Rationale: Another approach is toassign some nice valuesfor the number of freaks, nerds and geeks.
Given: the ratio of freaks to nerds to geeks is 1:2:3
So, let's say there is: 1 freak, 2 nerds and3geeks for a TOTAL of6people.
P(next person who yellsrock on!is a geek) = (# of geeks in the crowd)/(TOTAL # of people in the crowd)
=3/6
= 1/2
Answer:
B
Answer: B
Question: What is the product of all the possible values of x if x^2 - 9x + 20?
Options:
A)–29
B)–12
C)12
D)20
E)168
Rationale: Explanation:
=> y= x^2 - 9x + 20
=> y= (x-4) (x-5)
=> x= 4, y= 5
Product y = (4)(5) = 20
answer option 20
ANSWER:D
Answer: D
Question: Which of the following number is divisible by 24 ?
Options:
A)18
B)19
C)20
D)24
E)26
Rationale: 24 = 3 x8, where 3 and 8 co-prime.
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8.
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8.
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3.
Also, 736 is divisible by 8.
3125736 is divisible by (3 x 8), i.e., 24.
D)
Answer: D
Question: An arithemetic sequence of numbers begins p, 2p + 2, 4p + 3... What is the 10th member of this sequence?
Options:
A)A)37
B)B)28
C)+ 13
D)D)53
E)+ 13
Rationale: Common difference of an arithmetic series is constant.
2p+2-p=4p+3-2p-2
p=1
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37
Ans:B
Answer: B
Question: A one-foot stick is marked in 1/4 and 1/6 portion. How many total markings will there be, including the end points?
Options:
A)8
B)10
C)12
D)14
E)16
Rationale: LCM of 24 = 12
1/4 marking are (Table of 3) 0...... 3 ........... 6.......... 9 .......... 12
(Total = 5)
1/6 marking are (Table of 2) 0 ....... 2 ...... 4...... 6........ 8......... 12 ((Total = 6)
Overlapping markings are 0 ........ 6 ......... 12 (Total = 3)
Total markings = 5+6-3 = 8
Answer = A
Answer: A
Question: Find the odd one out:
125, 106, 87, 76, 65, 58, 53
Options:
A)33
B)87
C)26
D)18
E)222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 87 is the answer.
ANSWER: B
Answer: B
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 30 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 2/7 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
Options:
A)5 minutes, 17.6 seconds
B)5 minutes, 21.8 seconds
C)5 minutes, 23.6 seconds
D)5 minutes, 44.44 seconds
E)6 minutes, 10.4 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 30 seconds. The only number is 5 minutes, 44.44 seconds.
Another approach:
2/7 close to 20 second when added to the 5 minutes, 30 seconds, it means it passes 5 minute 44.44 seconds
Answer: D
Answer: D
Question: In a group of 400 readers who read science fiction or literacy works or both, 250 read science fiction and 230 read literacy works. How many read both science fiction and literacy works?
Options:
A)70
B)80
C)90
D)100
E)110
Rationale: Consider total number of reader n(S U L) = 400
People who read science fiction n(S) = 250
People who read literacy works n(L) = 230
both science fiction and literacy n(S ∩ L) = ?
n(S U L) = n(S)+ n(L) - n(S ∩ L)
400 = 250 + 230 - n(S ∩ L)
n(S ∩ L) = 480 - 400
n(S ∩ L) = 80
SO People read both science fiction and literacy works are 80
ANSWER:B
Answer: B
Question: Lindsay can paint 1/x of a certain room in 25 minutes. What fraction of the same room can Joseph paint in 25 minutes if the two of them can paint the room in an hour, working together at their respective rates?
Options:
A)1/7x
B)3x/(x – 3)
C)(3x – 7) / 7x
D)1/ (x – 3)
E)(x – 3) / x
Rationale: Lindsey and Joseph together can paint the room in 1 hour
in 25 mins they can paint 3/7 part of the room.
Lindsay alone paints 1/x part of the room in 25 mins
Take Joseph paints 1/y parts in 25 mins
1/x + 1/y = 3/7
1/y = 3/7 - 1/x = (3x-7)/7x ANs C
Answer: C
Question: 5 girls and 3 boys are arranged randomly in a row. Find the probability that:
1) there is one boy on each end.
2) There is one girl on each end.
Options:
A)3/28 & 5/14
B)5/28 & 3/14
C)5/14 & 3/28
D)3/28 & 1/14
E)1/28 & 5/14
Rationale: Total # of arrangements is 8!;
1. The # of arrangements where there is one boy on each end is C^2/3∗2∗6! where C^2/3C32 is # of ways to select which 2 boys will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;
P=C^2/3∗2∗6!/8!=3/28
2. The # of arrangements where there is one girl on each end is C^2/5∗2∗7!, where C^2/5 is # of ways to select which 2 girls will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;
P=C^2/5∗2∗6!/8!=5/14
Answer: A.
Answer: A
Question: A Paul's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
Options:
A) 1:2
B) 4:5
C) 1:1
D) 3:2
E) 5:3
Rationale: A Paul's company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996.1996- x----- y------- x+y
1997- x1---- y1-- x1+y1
x1= a*x .....(P)
y1= 1.07*y...(Q)
x1+y1/x+y = 1.01
solve using P and Q and find x/y
Answer: A
Question: How many numbers from 29 to 79 are exactly divisible by 11?
Options:
A)1
B)2
C)6
D)4
E)5
Rationale: Numbers=(79/11)-(29/11)
=7-2
=5 numbers
Answer is option E
Answer: E
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)2787
B)288
C)277
D)400
E)122
Rationale: Explanation:
2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: D
Question: On dividing 73 by a number, the quotient is 9 and the remainder is 1. Find the divisor?
Options:
A)A)8
B)B)15
C)C)16
D)D)17
E)E)18
Rationale: d = (D-R)/Q
= (73 - 1)/9
= 72/9 = 8
A)
Answer: A
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Options:
A)30%
B)70%
C)100%
D)120%
E)None
Rationale: Solution
Let C.P. = Rs. 100.	Then, Profit = Rs.320,
S.P. = 420.
Let C.P. = Rs. 125% of Rs. 100	= Rs.125.
New S.P. = Rs.420.
Profit = Rs. (420 - 125)	= Rs.295.
∴ Required percentage	= (295 / 420 x 100)%
= 1475 / 21%
= 70%.
Answer B
Answer: B
Question: A batsman makes a score of 92 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.
Options:
A)36
B)39
C)42
D)44
E)None of the above
Rationale: Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
∴ 16(x – 3) + 92 = 17x or x = (92 – 48) = 44.
Answer D
Answer: D
Question: Using all the letters of the word "PROBLEMS", how many words can be formed, which begin with P and end with S?
Options:
A)680
B)560
C)720
D)120
E)650
Rationale: There are eight letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with P and S all the remaining six blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
ANSWER:C
Answer: C
Question: A bag contains 2 yellow, 5 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options:
A)7/12
B)5/12
C)3/7
D)2/7
E)5/7
Rationale: Total number of balls = 2 + 5 + 2 = 9
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 9 = 9C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 7 (=9-2) balls = 7C2
(∵ There are two blue balls in the total 9 balls. Total number of non-blue balls = 9 - 2 = 7)
P(E) = n(E)/n(S)
=7C2 / 9C2
=7/12
Ans- A
Answer: A
Question: 896.7 – 573.07 – 95.007 = ?
Options:
A)228.623
B)224.777
C)233.523
D)414.637
E)None of these
Rationale: Solution
Given expression = 896.7 - (573.07 + 95.007) = 896.7 - 668.077 = 228.623. Answer A
Answer: A
Question: Two cars are traveling in the same direction along the same route. The red car travels at a constant speed of 10 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. If the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Options:
A)0.1
B)0.5
C)1
D)1.2
E)2
Rationale: Option B
20+10t=50t
t=0.5
Answer: B
Question: 20 workers can finish a work in 30 days. After how many days should 5 workers leave the job so the work is completed in 35 days?
Options:
A)7
B)6
C)15
D)4
E)3
Rationale: Work done by 15 workers in 35 days = 15*35=525 men days.
Now, work remaining= 600–525=75 men days and we have 5 workers .
So 5 workers will work for 75/5=15 days.
ANSWER:C
Answer: C
Question: A triangle has a perimeter 21. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: The SHORTER sides have integral lengths equal to x and x + 1
Let the longest side be 'a'
So, a + x + (x +1) = 21
a + 2x = 20.......eqn (1)
We know that the sum of the lengths of the shorter sides has to be more than the length of the longer one. i.e 2x+1> a
a =8
E
Answer: E
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options:
A)24
B)89
C)67
D)56
E)45
Rationale: Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then,	(5x + 3/4x + 3)=11/9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
Answer:A
Answer: A
Question: A man has Rs. 80 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)7
B)2
C)13
D)15
E)10
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 80 16x = 80 x = 5.
Hence, total number of notes = 3x = 15.
Answer:D
Answer: D
Question: Solve for the given equation 121 x 54 =?
Options:
A)68225
B)75625
C)76569
D)45854
E)45858
Rationale: Explanation:
This question can be solved by 2 approaches:
=> Direct Multiplication
=> Numerical Operations
Direct multiplication is quite time consuming and involves a lot of calculations. An easier approach is based on numerical operations.
=> 121 x (10/2)4 = 121 x 10000/16 = 75625
ANSWER: B
Answer: B
Question: Find the simple interest on Rs.235 for 3 months at 8 paisa per month?
Options:
A)s.57.8
B)s.56.4
C)s.29.3
D)s.33
E)s.74
Rationale: Explanation:
I = (235*3*8)/100 = 56.4
Answer: Option B
Answer: B
Question: If 15% of 30% of 50% of a number is 117, then what is the number?
Options:
A)5200
B)3050
C)4400
D)4500
E)None of these
Rationale: Let the number be a
Given, 15/100 * 30/100 * 50/100 * a = 117
=> 3/20 * 3/10 * 1/2 * a = 117
=> a = 10 * 20 * 10 * 2 = 5200.
ANSWER:A
Answer: A
Question: Bradley owns x video game cartridges. If Bradley’s total is one-third the total owned by James and four times the total owned by Charles, how many video game cartridges do the three of them own altogether, in terms of x?
Options:
A)(16/3)x
B)(17/14)x
C)(13/4)x
D)(19/12)x
E)(17/4)x
Rationale: x = Bradley’s total
3x = James’s total
(1/4)x = Charles’s total
Add each total
x + 3x+ (1/4)x = 4x + (1/4)x = = (17/4)x
Answer : E
Answer: E
Question: If 9 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
Options:
A) 10•9•8•7•6•5•4•3•2•1
B) 10•10
C) 10•9
D) 45
E) 36
Rationale: We got #9 people who shake each other's hands once ==> a pair of 2
9!/7!2! = 9*8/ 2*1 = 36.
Hence answer E.
Answer: E
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 50 revolutions. How many revolutions does the second wheel make in covering d feet?
Options:
A)50xy
B)50y - x
C)50x - y
D)50y/x
E)50x/y
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
50 = d/(x*pi)
d = 50 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (50 * x * pi) / (y*pi) = 50x/y
Answer (E)
Answer: E
Question: How many 4-letter word with or without meaning can be formed out
of the letters of the word 'LOGARITHMS' if repetition of letters is
not allowed
Options:
A)2000
B)1000
C)5040
D)5000
E)500
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
ANSWER C
Answer: C
Question: Rs. 6000 is lent out in two parts. One part is lent at 7% p.a simple interest and the other is lent at 9% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
Options:
A)9:3
B)9:5
C)5:8
D)5:4
E)9:2
Rationale: Let the amount lent at 7% be Rs. x
Amount lent at 9% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 7/100 x + 9/100 (6000 - x)
= 540 - 2x/100
=> 540 - 1/50 x = 450
=> x = 4500
Amount lent at 10% = 1500
Required ratio = 4500 : 1500 = 9:3
Answer:A
Answer: A
Question: 200 is what percent of 50?
.
Options:
A)0.2%
B)2%
C)5%
D)400%
E)500%
Rationale: 200= x*50/100
x = 400%
Ans; D
Answer: D
Question: If 50 honey bees make 50 grams of honey in 50 days, then 1 honey bee will make 1 gram of honey in how many days?
Options:
A)1
B)3.5
C)20
D)49
E)50
Rationale: Explanation :
Let the required number days be x.
Less honey bees, More days (Indirect Proportion)
Less honey, Less days (Direct Proportion)
Honey bees 1 : 50 :: 50 : x
Honey 50 : 1
=> 1 x 50 x x = 50 x 1 x 50
=> x = 50.
Answer : E
Answer: E
Question: A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is
Options:
A)6
B)12
C)22
D)52
E)None
Rationale: Sol.
Let the required number be x.
Then, (11x + 11) = 11(x + 1) is divisible by 13. So, x = 12.
Answer B
Answer: B
Question: The average of first five multiples of 5 is:
Options:
A)9
B)15
C)17
D)8
E)10
Rationale: Explanation :
(5(1+2+3+4+5)/5
= 5x15/5
= 15
Answer : B
Answer: B
Question: The sum of the first 92 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?
Options:
A) 5,050
B) 7,500
C) 10,500
D) 11,700
E) 19,600
Rationale: 101+103+.......199
If we remove 100 from each of these it will be sum of 1st 100 odd numbers.
so 101+103+.......199 = 92 * 100 + (1+3+5+7+......)
sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050
Sum of 1st 92 positive even integers = 2550
sum of 1st 100 odd numbers = 5050 - 2550 = 2500
so 101+103+.......199 = 92 * 100 + (1+3+5+7+......) = 9200 + 2500 = 11700
D is the answer.
Answer: D
Question: The third proportional to 1 and 3 is?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: (3*3)/1 = 9
ANSWER:A
Answer: A
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $9,500, what is the bonds face value?
Options:
A) $6,000
B) $6,750
C) $7,425
D) $7,600
E) $9,375
Rationale: Interest = 0.05*face value = 0.04*9,500 --> face value = 0.04*9,500/0.05 = 7,600.
Answer: D.
Answer: D
Question: One computer can upload 100 megabytes worth of data in 4 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 20 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
Options:
A) 6
B) 2.5
C) 9
D) 11
E) 13
Rationale: Since the first computer can upload 100 megabytes worth of data in 4 seconds then in 4*5=20 seconds it can upload 5*100=500 megabytes worth of data, hence the second computer in 20 seconds uploads 1300-500=800 megabytes worth of data. The second computer can upload 100 megabytes of data in 2.5 seconds.
Answer: B.
Answer: B
Question: Suresh age after 15 years will be 5 times his age 5 years back, What is the present age of Suresh
Options:
A)15
B)10
C)14
D)8
E)7
Rationale: x+15 = 5(x-5)
<=> 4x = 40 => x = 10
ANSWER B
Answer: B
Question: The difference between the length and breadth of a rectangle is 60 m. If its perimeter is 300 m, then its area is:
Options:
A)1520 m2
B)2420 m2
C)4258 m2
D)4725 m2
E)None
Rationale: EXPLANATION
We have: (l â€“ b) = 60 and 2(l + b) = 300 or (l + b) = 150.
Solving the two equations, we get: l = 105 and b = 45.
Area = (l x b) = (105x 45) m2 = 4725 m2.
Answer D
Answer: D
Question: Which of the following are roots of an equation (x^-2)+(4x^-1)-5=0
Options:
A)1/5 and -1
B)-1/5 and 1
C)1/5 and 1
D)-1/5 and -1
E)-5/2 and -1
Rationale: Given: (x^-2) + (4x^-1) - 5 = 0
Rewrite as: 1/(x²) + 4/x - 5 = 0
Remove fractions by multiplying both sides by x² to get: 1 + 4x - 5x² = 0
Rearrange to get: 5x² - 4x - 1 = 0
Factor to get: (5x + 1)(x - 1) = 0
So, EITHER 5x + 1 OR x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If x - 1 = 0, then x = 1
So, the roots (solutions) are -1/5 and 1
The answer is B.
Answer: B