divelab/Sys2Bench huggingface dataset:
Question: On children's day 405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?
Options:
A)15
B)18
C)9
D)45
E)78
Rationale: Explanation :
Solution: Let the total number of children be x. then, x*(20% of x) = 405
1/5 * x^2 =405 <==> x^2 = 2025 <==> x =45.
.'. Number of sweets received by each child = 20% of 45 = 9
Answer : C
Answer: C
Question: The value of a scooter depreciates in such a way that its value of the end of each year is 3/4 of its value of the beginning of the same year. If the initial value of the scooter is Rs.40,000, what is the value at the end of 3 years ?
Options:
A)3277
B)2977
C)16875
D)6077
E)17112
Rationale: Explanation: 40,000(34)3=1687540,000(34)3=16875
Answer:C
Answer: C
Question: If a·b·c·d=510, where a, b, c and d are positive integers, and a<b<c<d, which of the following could be the value of d−a?
Options:
A)9
B)10
C)11
D)13
E)15
Rationale: prime factorize : 510 = 2*3*5*17
Hence a = 2 and d = 17 .
Hence answer is 17 - 2 = 15
Answer E
Answer: E
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 10 Gallons of water and 20 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
Options:
A)37.5
B)75
C)100
D)150
E)175
Rationale: Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 20 gallons salt is added and 10 gallons of water is added.
So salt now becomes -> (0.2x + 20) and water --> (0.6x+10)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+20) = (0.6x+10)/2,
Solving, x = 150.
ANSWER:D
Answer: D
Question: In Town X, 60 percent of the population are employed, and 15 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)75%
C)32%
D)40%
E)52%
Rationale: Total employed people 60%, out of which 15 are employed males, hence 45% are employed females.
(employed females)/(total employed people)=45/60=3/4=75%
Answer: B.
Answer: B
Question: You have recently learned to knit, and all you know how to make is rectangles. You are going to knit a rectangle and have enough yarn for 1,000 stitches. The rectangle will have C stitches in a row and D stitches in a column. If the number of stitches in a row is no less than 8 and no more than 125, how many different combinations of rectangular shapes are possible?
Options:
A)4
B)5
C)6
D)8
E)10
Rationale: firstly factors of 1,000 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1,000
the question says each row will have stitches no less than 4 and no more than 35,
therefore, we should be interested in the factors between 8 and 125 (inclusive)
8(in each row) * 125(number of columns) =1,000, similarly
10 * 100
20 * 50
25 * 40
40 * 25
50 * 20
100 * 10
125 * 8
total possibilities = 8
option D
Answer: D
Question: How many positive integers w less than 30 have no common prime factor with 30?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: w=30=2*3*5. So, the number must be less than 30 and not have primes 2, 3, or 5.
This means that the number could be: 1, 7, 11, 13, 17, 19, 23, or 29. Total of 8 numbers.
Answer: D.
Answer: D
Question: A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 40 grams of protein daily, how many grams of food X are in the mixture.
Options:
A)100
B)140
C)150
D)160
E)200
Rationale: Let x be the amount of food X.
0.1x + 0.15(300-x) = 40
0.05x = 5
x = 100
The answer is A.
Answer: A
Question: A football team lost 5 yards and then gained 8. What is the team's progress?
Options:
A)2
B)3
C)5
D)6
E)8
Rationale: For lost, use negative. For gain, use positive.
Progress = -5 + 8 = 3 yards
B
Answer: B
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 32 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)12%
E)None of these
Rationale: Explanation :
C.P. of 56 kg rice = (26 * 20 + 30 * 36) Rs. = (520 + 1080) Rs. = 1600 Rs.
S.P. of 56 kg rice = (56 * 32) Rs. = 1792 Rs.
Profit % = (1792−1600/1600∗100)% = 12%
Answer : D
Answer: D
Question: a man can row 18 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
Options:
A)13 km/hr.
B)6 km/hr.
C)9 km/hr.
D)15 km/hr.
E)11 km/hr.
Rationale: Let man’s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate downstream=27 km/hr.
Hence,rate of stream=1/2(27-9)km/hr=9 km/hr.
Answer is C.
Answer: C
Question: The calendar of the year 2040 can be used again in the year?
Options:
A)2063
B)2061
C)2111
D)2191
E)2068
Rationale: Explanation:
Given year 2040 when divided by 4, leaves a remainder 0.
NOTE: When remainder is 0, 28 is added to the given year to get the result.
So, 2040 + 28 = 2068
Answer: E
Answer: E
Question: There are five leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
Options:
A)7 leopard and 3 sheep
B)4 leopard and 7 sheep
C)6 leopard and 4 sheep
D)4 leopard and 1 sheep
E)2 leopard and 5 sheep
Rationale: D
4 leopard and 1 sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer: D
Question: If Y = X+Z, 10 < Z < 0 and -1 < X < 0, which of the following is correct?
Options:
A)Y = 9
B)0 < y < 9.
C)-9 < y < 0
D)y < -9.
E)y < -30
Rationale: X is -ve & Z is +ve
For min. value max. numerator and minimize denominator
take X=-0.9 & Z=9.9
Y=(-0.9)+9.9
Y = 9
Ans A
Answer: A
Question: Four friends A, B,C and D decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share 3 time, no apples were left.How many apples were there?
Options:
A)4096
B)4055
C)4092
D)4085
E)4095
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 12 times. So answer is (2^12)-1=4095
Answer E
Answer: E
Question: Which of the following can be a perimeter t of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
Options:
A)I only
B)III only
C)II and III only
D)I, II, and III
E)Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: t>0.
Answer is D.
Answer: D
Question: 6, 11, 21, 36, 56, 81, 111, 146, ?
Options:
A)51
B)71
C)186
D)61
E)91
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : C.
Answer: C
Question: The volume of a cube is 729 cc. Find its surface.
Options:
A)486
B)556
C)255
D)287
E)267
Rationale: a3 = 729 => a = 9
6a2 = 6 * 9 * 9 = 486
Answer:A
Answer: A
Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:
Options:
A)Rs. 3500
B)Rs. 3750
C)Rs. 3840
D)Rs. 3900
E)Rs. 4900
Rationale: Let the cost of chairs be 'x' and tables be 'y'.
10x=4y i.e., x=(2/5)y
and given that 15x+2y=4000
15((2/5)y)+2y=4000
8y=4000 i.e., y=500 and x=200
The total price of 12 chairs and 3 tables is: 12*(200)+3*500=2400+1500=3900
ANSWER:D
Answer: D
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Options:
A)50
B)99
C)88
D)77
E)44
Rationale: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
Answer: A
Question: What is the possible ways to make 3 digit numbers from 1 to 5 number(repetition is allowed)?
Options:
A)220
B)130
C)127
D)125
E)225
Rationale: Repetition is allowed to make 3 digit number.So it is easy to calculate.
5*5*5=125 ways.
Answer:option D
Answer: D
Question: What is the ratio of y to x if (x + 3y) / ( x - y) = 5/3?
Options:
A)-15/4
B)-5/3
C)-1/15
D)1/7
E)15/1
Rationale: Solving for y/x gives, 1/7 (D)
Answer: D
Question: A 40-liter solution of alcohol and water is 5 percent alcohol. If 6.5 liters of alcohol and 3.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Options:
A)13%
B)14%
C)15%
D)16%
E)17%
Rationale: The percent of alcohol in the solution is (0.05(40) + 6.5) / 50 = 8.5/50 = 17%
The answer is E.
Answer: E
Question: If the function m& is defined as m&=1/(m+1) for all m≠-1, then (1&)&=
Options:
A)3
B)5/2
C)2/3
D)1/2
E)1/3
Rationale: 1&= 1/(1+1)= 1/2
(1&)&= 1/{(1/2)+1}= 1/(3/2)==> 2/3
Hence C
Answer: C
Question: An investor invests in a new fund. The fund averages 20% growth annually for the first three years, but it loses 40% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
Options:
A)91.23%
B)95.56%
C)97.86%
D)101.45%
E)103.68%
Rationale: 0.6*1.2^3 = 1.0368
The answer is E.
Answer: E
Question: A is thrice as good a workman as B and therefore is able to finish a job in 30 days less than B. working together, they can do it in
Options:
A)days
B)½ days
C)1/4 days
D)days
E)days
Rationale: Explanation:
B = 3A
3A – A =30 days
A = 15days
Then, B = 90 days
(A + B) = 15 × 90/ 120 =11 1/4 days .
Answer: Option C
Answer: C
Question: The average salary/head of allthe workers in a workshop is Rs.1200, if the average salary/head of 10 technician is Rs.1400 and the average salary/head of the rest is Rs.900, the total no. of workers in the work-shop is ?
Options:
A)18
B)17
C)15
D)19
E)21
Rationale: Let the total number of workers be y.So sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y -10 workers.10 x 1400 + 900(y -10) = 1200 y⇒ 14000 + 900y - 9000 = 1200y⇒ 300y = 5000∴ y = 17 So total number of workers = 17 B
Answer: B
Question: Find a two digit number, given that the sum of the digits is 11 and the difference of the digits is 5.?
Options:
A)78
B)53
C)89
D)83
E)99
Rationale: Using elimination method find which of the options fit the description of the number
... from the option only 83 meets this description
sum of digits---8+3 = 11
difference of digits ---8-3 = 5
Answer D.
Answer: D
Question: The ratio of incomes of two person P1 and P2 is 5 : 4 and the ratio of their expenditures is 3 : 2. If at the end of the year, each saves Rs.1800, then what is the income of P1?
Options:
A)s.800
B)s.2400
C)s.4000
D)s.3200
E)s.4500
Rationale: Let the income of P1 and P2 be Rs. 5x and Rs.4x respectively and let their
expenditures be Rs.3y and 2y respectively.
Then, 5x – 3y = 1800 …(i) and 4x – 2y = 1800 ……..(ii)
On multiplying (i) by 2, (ii) by 3 and subtracting, we get : 2x = 1800 -> x = 900
P1’s income = Rs 5*900 = Rs.4500
ANSWER:E
Answer: E
Question: A certain hobby shop sold model cars for $5.00 each and model trains for $8.00 each. If a customer purchased both cars and trains from the store for a total of $31.00, what total number of cars and trains did the customer purchase?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: we can take numbers, as price of car 5, 8 for train and 31 total for ease.
Now we can determine quickly that total number should range between 31/8 <= N <=31/5 , so ans should be between 3 and 7.
Now solving the expression 5A+8B =31
decreasing 31 in multiple of 5 and checking divisibility of that number by 8. this way we get
3 cars, 2 trains we get $31.00 total 3*5 + 2*8= 31
Hence total number is 3 + 2 = 5
Ans C
Answer: C
Question: A pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer’s suggested retail price. If during a sale, the store discounts an additional 20 percent from the discount price, what would be the lowest possible price of a container of pet food that had a manufacturer’s suggested retail price o f $ 25.00?
Options:
A)$ 14.00
B)$ 11.20
C)$ 14.40
D)$ 16.00
E)$ 18.00
Rationale: For retail price = $25
First maximum discounted price = 25 - 30% of 25 = 25-7.5 = 17.5
Price after additional discount of 20% = 17.5 - 20% of 17.5 = 17.5 - 3.5 = 14
Answer: Option A
Answer: A
Question: The average age of a husband and his wife was 23 years at the time of their marriage.After 5 years they have a one year old child.The average of the family is now?
Options:
A)18 years
B)23 years
C)29 years
D)26 years
E)19 years
Rationale: sum of the present age of husband, wife and child =(23*2+5*2)+1 = 57 years
required average = 57/3 = 19 years. Answer :E
Answer: E
Question: What would be the compound interest on Rs.7700/- at 15 ¼% per annum for 2 years compounded annually
Options:
A)2520.57/-
B)2522.50/-
C)2527.57/-
D)2532.57/-
E)2533.45/-
Rationale: Principal = Rs. 7700/-
time = 2 years
rate = 15 ¼%
Amount = P(1+R/100)n
= 7700 × (1 + 61/(4 × 100)2)
= 7700 × [(1 + 61/400)2]
= 7700 × [(461/400)2)]
= 7700 × 461/400 × 461/400
= 7700 × 1.1525 × 1.1525
= 7700 × 1.32825625
= 10227.573125
C.I = 10227.573125 - 7700 = 2527.57/-
C
Answer: C
Question: Sixty percent of the rats included in an experiment were female rats. If some of the rats died during an experiment and 70 percent of the rats that died were male rats, what was the ratio of the death rate among the male rats to the death rate among the female rats?
Options:
A)7 : 2
B)7 : 3
C)2 : 7
D)3 : 7
E)Cannot be determined from the information give
Rationale: Let x be the total number of rats in the experiment.
Male = 0.4x
Female = 0.6x
Let a be the total number of rats that died during experiment.
Male = 0.7a
Female =0.3a
Death rates
Male = 0.7a/0.4x
Female = 0.3a/0.6x
Ratio of death rates among males and females = 0.7a/0.4x*0.6x/0.3a
=0.7/0.2
=7/2
Ans = A
Answer: A
Question: If x is divisible by 7, 89, and 45, which of the following must be the least multiple of x?
Options:
A)28035
B)28060
C)28040
D)28045
E)20835
Rationale: If x is divisible by 7,89 and 45,then x must be a multiple of 7, 89 and 45.
Hence,the least multiple of x will be 7*89*45=28035.
ANSWER:A
Answer: A
Question: If x is an integer, and 169 < x^2 <= 361, which of the following is the sum of all possible values of x?
Options:
A) 135
B) 124
C) None of the above
D) 105
E) 116
Rationale: The range of x is from 14 .. to 19 and -14 to -19 so the sum is 0 hence ans C, I guess, unless I am missing something!
Answer: C
Question: In how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together?
Options:
A)220.
B)240
C)260
D)280
E)300
Rationale: We have 11 English and 9 French books, no French books should be adjacent.
Imagine 11 English books in a row and empty slots like below:
*E*E*E*E*E*E*E*E*E*E*E*
Now if 9 French books would be placed in 12 empty slots, all French books will be separated by English books.
So we can "choose" 9 empty slots from 12 available for French books, which is 12C9=220.	ANS:A
_________________
Answer: A
Question: Dick and Jane each saved $5,000 in 1989. In 1990 Dick saved 10 percent more than in 1989, and together he and Jane saved a total of $10,000. Approximately what percent less did Jane save in 1990 than in 1989?
Options:
A)10%
B)15%
C)20%
D)25%
E)30%
Rationale: 1990
Dick saved = $ 5500
Jane saved = $ 4500 (jane saved $500 less than she did the prior year)
Jane saved approximately $500/5000$ (10%) less in 1990
Answer: A
Answer: A
Question: A leak in the bottom of a tank can empty the full tank in 9 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?
Options:
A)7580
B)12960
C)8290
D)8640
E)None
Rationale: Solution
Work done by the inlet in 1 hour	= (1/9 - 1/12)
= 1/36
Work done by the inlet in 1 min.	= (1/36 × 1/60)
= 0.000463
Volume of 0.000463 part = 6 litres.
Therefore, Volume of whole	= 1/0.000463 x6
‹=› 12960 litres.
Answer B
Answer: B
Question: 50% of a number is added to 120, the result is the same number. Find the number?
Options:
A)240
B)288
C)1687
D)997
E)121
Rationale: (50/100) * X + 120 = X
X = 240
Answer:A
Answer: A
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 90kmph, find the rate at which the train B runs.
Options:
A)40
B)60
C)135
D)80
E)100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 80 kmph, speed of B must be 80*(3/2) = 135 kmph
C
Answer: C
Question: A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 600 more than that by the previous schema, his sales were worth?
Options:
A)12028
B)12000
C)12019
D)12197
E)12012
Rationale: [1000 + (X-4000) * (2.5/100)] - X * (5/100)
= 600
X = 12000
Answer: B
Answer: B
Question: Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits can does Grace have available during her trip?
Options:
A)2,520
B)1,260
C)620
D)360
E)120
Rationale: the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination formula (don't know how to use math symbols here).
This gives you 5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
Answer: B
Question: Which of the following is equal to 3.14 x 10(power 6) ?
Options:
A)31400.0
B)3140000
C)3140.0
D)314.0
E)None of them
Rationale: = 3.14 x 10(power 6)
= 3.14 x 1000000
= 3140000.
Answer is B.
Answer: B
Question: A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Options:
A)10
B)20
C)21
D)25
E)24
Rationale: Explanation:
Suppose the can initially contains 7x and 5x of mixtures A and B respectively.
Quantity of A in mixture left =(7x-7/12 x9)litres =(7x -21/4)litres .
Quantity of B in mixture left =(5x-5/12 x9)litres =(5x -15/4)litres .
(7x -21/4) / (5x -15/4) +9 = 7/9
28x - 21 /20x + 21 = 7/9
252x - 189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21 litres of A.
ANSWER IS C
Answer: C
Question: The average age of father and his two sons is 22 Years. Five years ago, the average age of the two sons was 19 Years. If the difference between the ages of the two sons is four years, what is the present age of the father?
Options:
A)18
B)46
C)47
D)48
E)49
Rationale: The total present age of father and two sons is 3x22 = 66 yrs
The total present age of sons is (19+5) X 2 = 48Years
so, present age of father is 66 â€“ 48 = 18 yrs
Answer A
Answer: A
Question: If a boat goes 9km upstream in 108 minutes and the speed of the stream is 2 kmph, then the speed of the boat in still water is ?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Rate upsteram =(9/108*60)kmph=5kmph.
speed of the stream =2kmph let speed in still water be xkm/hr. then speed upstream=(x-2)km/hr. x-2=5==>x=7km/hr Answer(C)
Answer: C
Question: What is the difference between the place value of 2 in the numeral 7229?
Options:
A)160
B)165
C)180
D)190
E)200
Rationale: Answer: Option 'C'
200 - 20 = 180
Answer: C
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets ?
Options:
A)33
B)39
C)50
D)29
E)28
Rationale: Explanation:
Number of runs made by running = 120 - (3*4 + 8*6)
= 120 - (60)
= 60
Required percentage = \inline (\frac{60}{120}\times 100) % = 50%
Answer: C) 50%
Answer: C
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is?
Options:
A)688
B)798
C)698
D)699
E)998
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer:C
Answer: C
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations Q of classes are available?
Options:
A)3
B)6
C)Q=7
D)Q=9
E)Q=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: D
Question: If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:
Options:
A)50
B)51.47
C)51.49
D)53
E)54.68
Rationale: Required average
= (55 x 50 + 60 x 55 + 45 x 60)/(55 + 60 + 45)
= (2750 + 3300 + 2700)/160
= 8750/160
= 54.68
Answer is E
Answer: E
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
Options:
A)22
B)17
C)66
D)13
E)57
Rationale: d2 = 122 + 42 + 32 = 13
Answer: D
Answer: D
Question: A certain car averages 30 miles per gallon when driving in the city and 35 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Options:
A)34
B)30
C)33
D)36
E)38
Rationale: Answer A
No of Miles per Gallon = Total no of miles/Total no of Gallons
=10+50/(10/30+50/35) ~ 34.05
Answer: A
Question: What will come in place of the x in the following Number series? 18, 22, 30, x ,78, 142
Options:
A)34
B)33
C)46
D)56
E)75
Rationale: (C)
The pattern is +4, +8, +16, +32, +64
So the missing term is = 30 + 16 = 46 .
Answer: C
Question: Everyone in the class was supposed to bring at least pencil with them to the exam. There are 30 people in the class. If 5 people brought 1 pencil, 18 brought 2, and 6 brought 3 or more, how many people forgot to bring a pencil?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: As the categories do not overlap, you can simply subtract the different category counts from the class total to get the answer: 20-5-18-6=1. The answer is B: 1.
Answer: B
Question: The number of diagonals of a polygon of n sides is given by the formula v=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
Options:
A) 3
B) 5
C) 6
D) 7
E) 8
Rationale: v=n(n-3)
v=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: B
Question: 109 × 109 + 91 × 91 = ?
Options:
A)20162
B)18322
C)13032
D)18662
E)None of these
Rationale: Explanation :
(a + b)2 + (a − b)2 = 2(a2 + b2)
(Reference : Basic Algebraic Formulas)
1092 + 912 = (100 + 9)2 + (100 − 9)2 = 2(1002 + 92) = 2(10000 + 81) = 20162. Answer : Option A
Answer: A