divelab/Sys2Bench huggingface dataset:
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
Options:
A)17/26
B)17/25
C)17/29
D)17/24
E)17/21
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:B
Answer: B
Question: A group of 10 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
Options:
A) E/(12 - n)
B) (12 - n)/E
C) nE / [10(10-n)]
D) E/[12(12-n)]
E) (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =10
initial cost for each =E/10
when n people decided not to participate
Cost for each =E/10-n
C
Answer: C
Question: In a division, divident is 729, divisior is 38 and quotient is 19. Find the remainder.
Options:
A)A)4
B)B)3
C)C)2
D)D)5
E)E)7
Rationale: Explanation:
729 = 38 x 19 + r
729 = 722 + r
r = 729 - 722 = 7
Answer: Option E
Answer: E
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 20 percent of the cards for himself and split the remaining cards evenly among his 4 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 4 younger brothers to get an equal number of cards?
Options:
A)110
B)112
C)116
D)118
E)120
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/4)*(x/5) is an integer
Or x/20 is an integer.
Hence we need the lowest multiple of 20 from the given options.
Let us start from the lowest value:
Option A: 110. This is not a multiple of 20
Option E: 120 = 20*6. This is a multiple of 20. Hence the correct answer.
Correct Option: E
Answer: E
Question: A number is doubled and 13 is added. If resultant is trebled, it becomes 93. What is that number
Options:
A)8
B)9
C)12
D)14
E)16
Rationale: Explanation:
=> 3(2x+13) = 93
=> 2x+13 = 31
=> x = 9
Option B
Answer: B
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Options:
A)165 ways
B)178 ways
C)916 ways
D)156 ways
E)145 ways
Rationale: Total number of persons in the committee
= 5 + 6 = 11
Number of ways of selecting group of eight persons
= ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2) = 165 ways.
Answer:A
Answer: A
Question: Jake bought oranges at the supermarket for Y dollars an orange and sugar for M dollars per kilogram.
Then, he made lemonade using P oranges and Q kgs of sugar per liter and he sold Z liters of lemonade for X dollars per liter.
How much money has he made after selling all the lemonade?
Options:
A)ZX(PY+QM)
B)ZPM-ZQY
C)XZ-PYZ-QMZ
D)XZ-(MQ-YP)
E)XQ-PY+ZM
Rationale: First, the cost of the lemonade per liter= PY+QM dollars
Since Jake sold Z liters of lemonade, the cost price= Z(PY+QM) dollars
The selling price=ZX dollars
Profit=ZX-Z(PY+QM)
=(X-PY-QM)Z
The answer is C!!
Answer: C
Question: Joe works d days a month at 20 dollars per day for n months out of the year. Which of the following represents his monthly pay?
Options:
A)n/(d20)
B)d20
C)10nd/6
D)d20/n
E)20dn
Rationale: Total income of Joe in a year = d*20*n dollars. Now Monthly income = Total/12 = d*20*n / 12 = 10nd/6 Answer is C
Answer: C
Question: This year, MBB Consulting fired 7% of its employees and left remaining employee salaries unchanged. Sally, a first-year post-MBA consultant, noticed that that the average (arithmetic mean) of employee salaries at MBB was 10% more after the employee headcount reduction than before. The total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction?
Options:
A)98.5%
B)100.0%
C)102.3%
D)104.5%
E)105.0%
Rationale: 100 employees getting 1000$ avg, so total salary for 100 ppl = 100000
7% reduction in employees lead to 93 employees and a salary increase of 10% of previous avg salary
Thus the new avg salary is = 10%(1000)+1000 = 1100
so total salary of 93 employees is 93*1100 = 102300
Now the new salary is more than previous salary by x%. x = (102300/100000)*100 = 102.3%
So the Answer is C
Answer: C
Question: Find the surface area of a cuboid 16 m long, 14 m broad and 12 m high
Options:
A)868 sq.cm
B)1168 sq.cm
C)1152 sq.cm
D)900 sq.cm
E)None of these
Rationale: Explanation:
Surface area = [2 (16 x 14 + 14 x 12 + 16 x 12)] cm2 = (2 x 584)cm2 = 1168 cm2.
Answer: B
Answer: B
Question: 40 × ? + (12 + 8) × 3/5 = 1212
Options:
A)A)7
B)B)5
C)C)4
D)D)18
E)E)30
Rationale: Explanation:
=> 40 × ? + (12 + 8) × 3/5 = 1212
=> 40 × ? = 1212 - (12 + 8) × 3/5
=> 40 × ? = 1212 - 20 × 3/5
=> 40 × ? = 1212 - 20 × 3/5 = 1200
=> ? = 1200/40 = 30
Answer: Option E
Answer: E
Question: A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
Options:
A)100 m
B)276 m
C)186 m
D)187 m
E)124 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 200 - 100 = 100 m.
Answer: A
Answer: A
Question: 5359 x 51 = ?
Options:
A)273232
B)273243
C)273247
D)273250
E)273309
Rationale: 5359 x 51	= 5359 x (50 + 1)
= 5359 x 50 + 5359 x 1
= 267950 + 5359
= 273309
E)
Answer: E
Question: A focus group of three people is to be chosen from four pairs of boss-subordinate for a study. What is the number of different focus groups that can be chosen if two people who are boss-subordinate cannot both get in the group ?
Options:
A)16
B)24
C)26
D)30
E)32
Rationale: Each pair can send only one representative to the focus group. Let's see in how many ways we can choose 3 individuals (as there should be 3 members) out of 4 to send only one representatives to the group : 4C3=4.
But each of these 3 pairs can send two persons (boss or subordinate): 2*2*2=2^3=8.
Total # of ways: 4C3*2^3=32.
Answer: E.
Answer: E
Question: Combine terms: 10a + 26b -4b – 16a.
Options:
A)4a + 22b
B)-28a + 30b
C)-6a + 22b
D)28a + 30b
E)5a + 30b
Rationale: Solution:
10a + 26b -4b – 16a.
= 10a – 16a + 26b – 4b.
= -6a + 22b.
Answer: (C)
Answer: C
Question: Find the resultant profit if A sells a cupboard at a profit of 6% to B and B sells the same to C at a profit of 9%.
Options:
A)15%
B)16%
C)14.5%
D)15.54%
E)None of these
Rationale: Explanation:
The resultant profit = 1.06 * 1.09 = 1.1554 = 15.54%
Alternatively, the resultant profit = [x + y + xy/100]
= 6 + 9 + (6*9)/100
= 15 + 0.54
= 15.54%
ANSWER D
Answer: D
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 300. What is their H.C.F.?
Options:
A)20
B)25
C)30
D)60
E)75
Rationale: Let the numbers be 2x, 3x, and 4x.
LCM of 2x, 3x and 4x is 12x.
12x = 300
x = 25
HCF of 2x, 3x and 4x = x = 25
The answer is B.
Answer: B
Question: In a group of 25 factory workers, 18 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.
Options:
A)10
B)9
C)8
D)7
E)4
Rationale: Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 18
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 10 are men. (B - 8= 18 - 8= 10)
So 10 out of 11 men have brown eyes.
A
Answer: A
Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is
Options:
A)greater than 1
B)equal to 1 / 2
C)equal to 1
D)equal to 1 / 4
E)None
Rationale: Solution
A square and a rhombus on the same base are equal in area.
Answer C
Answer: C
Question: Three numbers are in the ratio 3:5:7. The largest number is 28. What is the difference between smallest and largest number?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: The three numbers are 3x, 5x, and 7x.
The largest number is 28 = 7*4, so x = 4.
The smallest number is 3*4 = 12.
28 - 12 = 16
The answer is C.
Answer: C
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)20/9 sec
B)23/9 sec
C)20/7 sec
D)29/7 sec
E)21/9 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (54 + 72)*5/18 = 7*5 = 35 mps.
The time required = d/s = 100/35 = 20/7 sec.
Answer:C
Answer: C
Question: What is the least number should be added to 1056, so the sum of the number is completely divisible by 27?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: (1056 / 27) gives remainder 3
24 + 3 = 27, So we need to add 24
D
Answer: D
Question: Of the votes cast on a certain proposal, 66 more were in favor of the proposal than were against it. If the number of votes against the proposal was 40 percent of the total vote, what was the total number of votes cast? (Each vote cast was either in favor of the proposal or against it.)
Options:
A)290
B)310
C)330
D)350
E)370
Rationale: Let x be the total number of votes cast.
0.6x = 0.4x + 66
0.2x = 66
x = 330
The answer is C.
Answer: C
Question: A two digit number is 18 less than the sum of the squares of its digits. How many such numbers are there?
Options:
A)22
B)67
C)200
D)288
E)111
Rationale: Option 2
Only 47 and 67 satisfy the condition
Answer:B
Answer: B
Question: A train 100m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Options:
A)46
B)50
C)40
D)36
E)41
Rationale: Speed of the train relative to man =100/10 m/sec
=10m/sec.
=10x18/5km/hr
= 36 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 36 =41km/hr.
Answer:E
Answer: E
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
A)12
B)15
C)16
D)18
E)19
Rationale: one day work done by A=1/20
work done by A in 2 days=1/10
work done by A,B,C on 3rd day=1/10+1/10=1/5
1/5th of the work will be completed at the end of 3 days
the remaining work =1-1/5=4/5
1/5 of work is completed in 3 days
total work wiil be done in 3*5=15 days
ANSWER:B
Answer: B
Question: HOW MANY KGS OF TEA WORTH RS.25/KG MUST BE BLENDED WITH 30 KGS OF TEA WORTH RS.30/KG SO THAT BY SELLING THE BLENDED VARIETY AT RS.30/KG THERE SHOULD BE A GAIN OF 3%
Options:
A)36
B)8
C)7
D)6
E)6.3
Rationale: (x+30)*30=(103/100)(25x+30*30)
Solving we get 6.3.
Answer is E.
Answer: E
Question: If 5 ministers are to be seated at a round table conference, then how many different ways can they be seated?
Options:
A)240
B)60
C)24
D)720
E)180
Rationale: Simple formula:
There are (n - 1)! ways to arrange n distinct objects in a circle.
so its (5-1)! =4! = 24=C
Answer: C
Question: Last week Vartan spent 15 percent of his wages on recreation. This week, his wages are 10 percent less than last weekʼs wages and he spent 30 percent of his wages on recreation. The amount he spends on recreation this week is what percent of the amount he spent on recreation last week?
Options:
A)100%
B)160%
C)180%
D)200%
E)220%
Rationale: Say Vartan's wages last week were $100, so he spent 0.15*100=$15 on recreation;
This week's wages is 0.9*100=$90, so he spends 0.3*90=$27 on recreation;
27/15=1.8, hence the amount he spends on recreation this week is 180% of the amount he spent on recreation last week: 15*1.8=27.
Answer: C.
Answer: C
Question: Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Maria live from the mountains?
Options:
A)787 miles
B)772 miles
C)287 miles
D)979 miles
E)288 miles
Rationale: Explanation:
Time taken for trip from home to mountains = 9 h
Time taken for trip from mountains to home = 4 h
Let distance from home to mountains = x miles
let avg speed from home to mountains = y miles/h
Given avg speed on the trip home is 40 m/h faster than speed from home to mountains = y + 40 m/h
⇒ (x/9) = y and (x/4) = y + 40
by solving this, we get y = 32 m/h and the distance x=32 × 9 = 288 miles.
Answer:E
Answer: E
Question: A man rows his boat 85 km downstream and 25 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)6
B)12
C)5
D)8
E)9
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 25/(2 1/2) = 10 kmph
The speed of the stream = (34 - 10)/2
= 12 kmph
Answer: B
Answer: B
Question: In a business, A and C invested amounts in the ratio 5 : 3 , whereas the ratio between amounts invested by A and B was 3 : 2 . If Rs 1863200 was their profit, and they invest half of profit in business again, then how much amount did B receive?
Options:
A)245000
B)480200
C)274000
D)248600
E)None of these
Rationale: Explanation :
Assume that investment of C = 3x
Then, investment of A =5x
Investment of B = 10x/3
A:B:C = 5x : 10x/3 : 3x = 5 : 10/3 : 3 =15 : 10 : 9
Amount divided between them = 1863200/2 = 931600
B's share = 931600 * 10/(15+10+9) = 931600*10/34
= 27400*10 = 274000.
Answer : Option C
Answer: C
Question: On Wednesday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up B percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of B?
Options:
A)20%
B)30%
C)33 1⁄3%
D)40%
E)50%
Rationale: Let the original price be 100
discounted Price = 80
New Price = 20 +100 =120
B=(40/80)*100
Ans:E
Answer: E
Question: Subtracting 3% of A from A is equivalent to multiplying A by how much ?
Options:
A)0.97
B)9.4
C)0.094
D)94
E)None
Rationale: Answer
Let A - 3% of A = AB.
⇒ (97 x A) / 100 = AB
∴ B = 0.97
Correct Option: A
Answer: A
Question: A is twice as good a work man as B and together they finish the work in 12 days. In how many days A alone can finish the work?
Options:
A)12 days
B)14 days
C)28 days
D)18 days
E)16 days
Rationale: WC = 2:1
2x + x = 1/12 => x = 1/36
2x = 1/18
A can do the work in 18 days.
ANSWER:D
Answer: D
Question: A group consists of 4 men, 6 women and 3 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
Options:
A)400
B)360
C)287
D)278
E)281
Rationale: Explanation:
Two men, three women and one child can be selected in â´Câ‚‚ * â¶Câ‚ƒ * âµCâ‚ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 3
= 360 ways.
Answer:B
Answer: B
Question: A boat can move upstream at 50 kmph and downstream at 20 kmph, then the speed of the current is?
Options:
A)5
B)9
C)5
D)15
E)12
Rationale: US = 50
DS = 20
M = (50- 20)/2 = 15
Answer: D
Answer: D
Question: In how many ways can 4 different resistors be arranged in series?
Options:
A)6
B)24
C)120
D)360
E)720
Rationale: 4! = 4 * 3 * 2 * 1 = 24
Ans - B
Answer: B
Question: How many two-element subsets of <1, 2,3,4,5> are there that do not contain the pair of elements 2 and 4?
Options:
A)1
B)2
C)4
D)5
E)9
Rationale: 5C2 - 1 = 9 Answer is E
Answer: E
Question: Ramesh spends 20% of his monthly salary on food, 10% of the remaining on conveyance and clothes and saves 75% of the remaining amount. If his monthly salary is Rs.20,000, how much money does he save every month ?
Options:
A)Rs.2645
B)Rs.7945
C)Rs.3694
D)Rs. 10080
E)Rs.1589
Rationale: Explanation:
Ramesh's monthly income = Rs.20,000
He spends 20% on food.
The total money spent on food = 20/100 * 20000 = Rs. 4000
Now, his monthly remaining income = Rs.20000 – Rs.4000 = Rs. 16000
Out of Rs. 16000, he spends 10% on conveyance and clothes.
The total money spent on conveyance and clothes = 10/100 * 16000 = Rs. 1600
Now, his monthly remaining income = Rs.16000 – Rs.1600 = Rs. 14400
Out of Rs. 14400, he saves 70%.
Amount saved = 70/100 * 14400 = Rs. 10080
ANSWER:D
Answer: D
Question: Find the next no.
82, 51, 28, 20, ?
Options:
A)14
B)24
C)34
D)44
E)54
Rationale: 82=9^2+1
51=7^2+2
28=5^2+3
20=4^2+4
then next no is
3^2+5=14
ANSWER:A
Answer: A
Question: n people were sitting on a circular manner , if each of two present in the party except the pairs were adjacent sang a song , if a song lasted for 2 mins and 28 minutes was taken for singing song , find n
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: each of 2 present in the party =>no. of pairs possible=nc2
possible adjacent pairs=n
total required combinations=nc2-n
time taken by each combination to sing a song=2 min
total time taken=2(nc2-n)=28
on solving the above equation, we get n=14
ANSWER:D
Answer: D
Question: At a conference table, 4 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these 4 employees?
Options:
A)12
B)10
C)14
D)8
E)6
Rationale: Head's sit is fixed. Now 3 people is left with 3 seats.
3 people can sit on 3 seats in 3! ways or 6 ways.
Ans is E
Answer: E
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is e, what is the difference between the probability that e is even and the probability that e is odd?
Options:
A) 1/9
B) 1/6
C) 2/9
D) 1/4
E) 1/2
Rationale: Age of Boys e:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Answer: A
Question: Set A is {1, 3, 5, 7, 9}
Set B is {10, 12, 14, 16, 18}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
Options:
A)I only
B)I and II only
C)I and III only
D)II and III only
E)I, II, and III
Rationale: The mean and median of Set A is 5.
The mean and median of Set B is 14.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Answer: B
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 1% p.a. in 9 years. What is the sum?
Options:
A)42315
B)42877
C)44625
D)38925
E)22887
Rationale: Principal = (100 * 4016.25) / (1 * 9)
= Rs.44625.
Answer:C
Answer: C
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 14-meter platform and caught it after it had traveled 41.7 meters. How many times did the ball bounce?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Ans: 6
Division of total diatance travelled will be 14+14+7+3.5+1.75+0.9+0.5 ANS B
Answer: B
Question: When n is divided by 24, the remainder is 6. What is the remainder when 3n is divided by 8?
Options:
A)3
B)4
C)5
D)6
E)2
Rationale: Let n=6 (leaves a remainder of 6 when divided by 24)
3n = 3(6) =18, which leaves a remainder of 2 when divided by 8.
Answer E
Answer: E
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Options:
A)197
B)240
C)279
D)268
E)269
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer:B
Answer: B
Question: What amount does Kiran get if he invests Rs.8000 at 10% p.a. compound interest for two years, compounding done annually?
Options:
A)42 6/8%
B)42 4/7%
C)43 6/7%
D)42 6/7%
E)42 6/9%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: D
Answer: D
Question: How many distinct integer values of n satisfy the inequality||n-3| + 4| ≤ 14?
Options:
A)15
B)12
C)17
D)18
E)19
Rationale: so i can write this as In-3I+4<=14
or In-3I<=10
so n can have -7 to 13 = 12 true values....
B
Answer: B
Question: Edward walks along Sunrise Boulevard daily. He starts walking at 07:00 from block 10 and walks to block 90 where he turns around and walks back to block 70, where he stops at 07:10. The blocks along the boulevard are numbered sequentially (1,2,3), and each block measures 16 meters. What is Edward's speed in meters per minute?
Options:
A)108
B)160
C)198
D)216
E)252
Rationale: Total distance from 10 to 90 =80 + from 90 to 70 =20
So the dist is 100×16(per block dist)
Speed = 1600mts/10min =160m/min
B is the answer
Answer: B
Question: Of the 600 employees of Company X, 70 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 30 percent ?
Options:
A)200
B)160
C)112
D)257
E)56
Rationale: Original (Long-Term is 70%)
Total = 600
Long-Term = .7(600) =420
New (Long-Term is 30%)
New Total = 800 - y
New Long-Term = 420 - y
420 - y = .3 (800 - y)
y = 257
Answer: D
Answer: D
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
A)5678
B)7654
C)9944
D)9950
E)10000
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: If m is an integer such that (-2)^2m=2^(12-m) then m=?
Options:
A)1
B)2
C)4
D)5
E)6
Rationale: (-2)^(2m) = 4^m
and
2^(12-m) = 4^((12-m)/2)
Therefore,
m = (12-m)/2
2m = 12 - m
m = 4
Answer C
Answer: C
Question: The value of 99^(92/99) x 99 is:
Options:
A)9989
B)9893
C)9890
D)9809
E)9810
Rationale: (100 â€“ 7/99) x 99 = 9900 â€“ 7
= 9893.
ANSWER:B
Answer: B
Question: 3660÷12÷5=?
Options:
A)61
B)67
C)89
D)54
E)32
Rationale: 3660 ÷ 12 = 305
305 ÷ 5 = 61
Answer is A
Answer: A
Question: In a certificate by mistake a candidate gave his height as 25% more than actual height. In the interview panel, he clarified that his height was 5feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
Options:
A)10
B)20
C)30
D)35
E)43
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.25-1)* 100 = 20
B
Answer: B
Question: Jackson invested $700,000, dividing it all unequally between Account P and Account Q. At the end of the year, it turned out that Account P had earned 12% interest and Account Q had earned 25% interest. If Jackson earned a total of $60,000 in interest between the two accounts, which of the following is approximately the amount he put in account P?
Options:
A)$115,384
B)$120,000
C)$121,072
D)$124,129
E)$130,000
Rationale: x be the amount invested in account P
0.12*x +(300000-x)*0.25=60,000
15000/.13=x
x=1500000/13=11...=$130,000
hence answer is E
Answer: E
Question: 14 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
Options:
A)144
B)131
C)115
D)189
E)45
Rationale: there are 14 business exec and in each handshake 2 business execs are involved.
hence 14C2=91
Also, each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake.
total=91+98=189
ANS: D
Answer: D
Question: Sunil invested $ 2200 fir 2 years and $ 2100 for 3 years at the same rate of Simple Interest. If the total interest from these investments is $ 1400, what is the rate of interest?
Options:
A)12 3/4%
B)12 %
C)13 %
D)16%
E)13 2/4%
Rationale: (2200x2xR)/100+(2100x3xR)/100=1400
107R=1400
R= 13 %
Answer is C
Answer: C
Question: If two dice are thrown together, the probability of getting an even number on both dice is
Options:
A)1/4
B)1/5
C)1/6
D)1/3
E)1/2
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on both dies is 9/36 = 1/4
P(E) = 1/4.
A)
Answer: A