divelab/Sys2Bench huggingface dataset:
Question: In an election between two candidates first candidate got 80% of votes polled and second Candidate got 2800 votes. The total number of votes polled was?
Options:
A)12000 votes
B)13000 votes
C)14000 votes
D)10980 votes
E)19900 votes
Rationale: Total = 100 %,
First person got 80%
second person got remaining 20 % of votes.
than 20 % = 2800
20% = 20Ã—140 = 2800
100% =100Ã—140 =1400 votes
C
Answer: C
Question: Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
Options:
A)50 sec
B)58 sec
C)24 sec
D)22 sec
E)21 sec
Rationale: Explanation:
Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s
We are calculating the time taken by the slower train to pass the driver of the faster one
.Hence the distance = length of the smaller train = 500 m
Time = distance/speed = 500/(125/6) = 24 sec
Answer: Option C
Answer: C
Question: The average of 10 numbers is calculated as 46. It is discovered later on that while calculating the average, the number 75 was incorrectly read as 25, and this incorrect number was used in the calculation. What is the correct average?
Options:
A)48
B)51
C)60
D)71
E)96
Rationale: The total sum of the numbers should be increased by 50.
Then the average will increase by 50/10 = 5.
The correct average is 51.
The answer is B.
Answer: B
Question: A man is 32 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)16
B)19
C)15
D)22
E)30
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 24) years.
(x + 32) + 2 = 2(x + 2)
x + 34 = 2x + 4
=> x =30 .
Answer: E
Answer: E
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 56 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
Options:
A)70
B)245
C)400
D)35
E)350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 56, so 0.14*{total} = 56 --> {total} = 400.
Answer: C.
Answer: C
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)8m.
B)6m.
C)4m.
D)2m.
E)5m.
Rationale: Explanation:
Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer: Option D
Answer: D
Question: If x^2=x+4, then x^3=?
Options:
A)3x+2
B)3x-2
C)2x+1
D)2x-3
E)5x+4
Rationale: Given X^2 = X+4
X^3 = X*X^2 = x*(X+4)-- Substituted from above.
= X^2 + 4X = X+4+4X = 5X+4.
Hence E.
Answer: E
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
Options:
A)81:122
B)81:121
C)81:122
D)81:197
E)81:112
Rationale: Ratio of the sides = ³√729 : ³√1331
= 9 : 11
Ratio of surface areas = 92:112
= 81:121
Answer: B
Answer: B
Question: If x^2 - 1 = 0 and x > 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 + 5x + 6
Rationale: x^2-1 = 0
x= +1 or x = -1
if we substitute x= 1 in the equation x^2 +2x-3 = 1+2-3 = 0
D is also the answer
Answer: D
Question: If 235477 × 455233 × K^2 is divisible by 3, which of the following could be the value of K?
Options:
A)6000209
B)6111209
C)3456576
D)6111309
E)6111109
Rationale: The first two terms are not divisible by 3, so we need the third term to be divisible by 3. The only way that (k^2) is going to be a multiple of 3 is if k is a multiple of 3. Therefore, we need the single answer that is a multiple of 3.
Answer =(E)
Answer: E
Question: Twin primes are defined as prime numbers that can be expressed as p and (p + 2), and any number p that is a member of such a pair is considered to have a twin. For example, 3 and 5 are twin primes, and 3 has a twin. Each of the following prime numbers has a twin EXCEPT
Options:
A)7
B)13
C)17
D)23
E)29
Rationale: A. 7 --> 5 is a twin prime of 7;
B. 13 --> 11 is a twin prime of 13;
C. 17 --> 19 is a twin prime of 17;
D. 23 --> neither 23-2=21 nor 23+2=25 is a prime, hence 23 has no twin prime;
E. 29 --> 31 is a twin prime of 29.
Answer: D.
Answer: D
Question: Tough and Tricky questions: Number Properties.
If (z + 3)/6 is an integer, what is remainder when z is divided by 6?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: 6/6=1
Ans B
Answer: B
Question: If the number 892,132,27x is divisible by 11, what must be the value of x?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11
Given number: 892,132,27x
Sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x (i)
Sum of digits at even places = 9 + 1 + 2 + 7 = 19 (ii)
(i) - (ii) = 15 + x - 19 = x - 4
Hence x should be = 4 to make this a multiple of 11 (0) Option D
Answer: D
Question: Express 35 mps in kmph?
Options:
A)122
B)188
C)126
D)140
E)124
Rationale: 35 * 18/5 = 126 kmph
Answer: C
Answer: C
Question: Abhijit started a business investing 4000. Anuja joined him after six months with an amount of 8000 and Sunil joined them with 12,000 after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, two years after Abhijit started the business?
Options:
A)2 : 4 : 3
B)2 : 4 : 4
C)2 : 5 : 5
D)2 : 3 : 3
E)2 : 5: 3
Rationale: Ratio of their investments
= 4× 24 : 8 × 18 : 12 × 12 = 2 : 3 : 3
Answer D
Answer: D
Question: What are the chances you would pull an Ace or Heart from a well-shuffled deck of cards?
Options:
A)1 of 4
B)4 of 12
C)1 of 13
D)4 of 13
E)1 of 52
Rationale: You must add the number of cards in each suit in the deck (13/52) to the number of aces of in the deck (4/52) and subtract the number of aces of hearts in the deck (1/52). This will give you the number of 16/52 which when the fraction is reduced will give you the answer of 4/13. Answer is D.
Answer: D
Question: A moving truck uses 28 gallons of diesel fuel in traveling 504 miles. In order for the truck to travel the same distance using 21 gallons of diesel fuel, by how many miles per gallon must the truck’s fuel mileage be increased?
Options:
A)6
B)10
C)8
D)12
E)21
Rationale: There are two sets 28G1 gallons and 21G2 gallons details given.
28 gallons covering 504 miles
Then 1 G1 is used to cover 18 miles.
Now for 21 G2 covering 504 miles.
then 1 G2 is used to cover 24 miles.
There must 24 - 18 = 6 miles per gallon increment is needed for 21 gallons to improve the mileage to cover 504 miles.
IMO A is correct answer.
Answer: A
Question: 25 bikes are running between two places A & B. In how many ways can a person go from A to B and return by a different bikes?
Options:
A)200
B)250
C)400
D)600
E)650
Rationale: He can go in any car out of the 25 cars.
Hence He can go in 25 ways.
Since he can not come back in the same car that he used for travelling,
He can return in 24 ways.
Total number of ways = 25 x 24 = 600
D
Answer: D
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $35 more. What was his original selling price?
Options:
A)$180
B)$280
C)$420
D)$550
E)$700
Rationale: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 35
0.07 = 35
P = 500
The original selling price was 500*1.1 = 550.
The correct answer is D.
Answer: D
Question: If 5 |x| /=1, which of the following must be true?
Options:
A)x>1/5
B)x<1/5
C)x=1/5
D)x=1
E)x=10
Rationale: if 5 |x| /=1
then |x|=1/5
ANSWER C x=1/5
Answer: C
Question: A pool which was 2/3 full to begin with, was filled at a constant rate for 5/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
Options:
A)8 hrs 45 mins.
B)9 hrs.
C)9 hrs 30 mins.
D)11 hrs 40 mins.
E)15 hrs 30 mins
Rationale: The pool was 2/3 full initially.
In 5/3 hrs, it was filled to 6/7 of its capacity.
Therefore, in 5/3 hrs, 6/7 - 2/3 was the amount of volume filled.
So, 5/3 hrs = 6/7 - 2/3 = 4/21
Therefore, for filling the vessel from empty to full, you would require 5/3 * 21/4 = 35/4 = 8 Hrs 45 Mins.
Hence A
Answer: A
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest W?
Options:
A) 60
B) 61
C) 62
D) 63
E) 64
Rationale: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=W
answer is A.
Answer: A
Question: A is twice as good a workman as B and together they finish a piece
in 18 days. In how many days will A alone finish the work?
Options:
A)27 days
B)32 days
C)54 days
D)16 days
E)29 days
Rationale: Sol. (A’s 1 day’s work):)(B’s 1 days work) = 2 : 1.
(A + B)'s 1 day's work = 1/18
Divide 1/18 in the ratio 2 : 1.
:. A’s 1 day's work =(1/18*2/3)=1/27
Hence, A alone can finish the work in 27 days.
Option: A
Answer: A
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 30% ?
Options:
A) 0
B) 1
C) 2.50
D) 1.73
E) 4
Rationale: Let x be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = x/10
Probability that the second contestant selected is also a male = x-1/9
Total probability = x(x-1)/ 90 < 1/30 (this probability is less than 30%)
Solving for x we get, x(x-1)< 3. This implies that the maximum value of x can be 1.73.
Answer D!
Answer: D
Question: The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 14 km/hr respectively. They will meet for the first time in?
Options:
A)50min
B)40min
C)34min
D)25min
E)20min
Rationale: Clearly, the two will meet when they are 1000 m apart
To be 20+14 = 34 km apart, they take 1 hour
To be 1000 m apart, they take 34 * 1000/1000 = 34 min.
Answer is C
Answer: C
Question: An article is bought for Rs.1000 and sold for Rs.700, find the loss percent?
Options:
A)18 2/3%
B)16 7/3%
C)16 2/8%
D)16 2/3%
E)30%
Rationale: 1000 ---- 300
100 ---- ? => 30%
Answer:E
Answer: E
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)250%
E)200%
Rationale: Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 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%(approximately).
ANSWER IS B
Answer: B
Question: Write 890,000,000,000 in scientific notation.
Options:
A)8.9 * 10 11
B)800.900 * 10 11
C)8.900 * 10 11
D)80.9000* 10 11
E)08.900 * 10 11
Rationale: a * 10 n , where a is a real number such that 1 * |a| < 10 and n is an integer.
890,000,000,000 = 8.9* 100,000,000,000 = 8.9 * 10 11**
correct answer A
Answer: A
Question: Uncle Bruce is baking chocolate chip cookies. He has 36 ounces of dough (with no chocolate) and 18 ounces of chocolate. How many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20% chocolate?
Options:
A) 3
B) 6
C) 7.2
D) 7.8
E) 9
Rationale: Answer is E.
x/x+36=1/5
x=9
18-9=9
Answer: E
Question: In how many ways to select 3 girls and 2 boys from a class? A class contains 5 boys and 5 girls.
Options:
A)10
B)30
C)22
D)20
E)25
Rationale: The way is 5C3+5C2
5C3=5!/2!*3!=5*4*3!/3!*2*1=10
5C2=5!/2!*3!=5*4*3!/3!*2*1=10
=10+10=20 ways to select 3 girls and 2 boys from a class
Answer is option D
Answer: D
Question: If a mixture is 3⁄7 alcohol by volume and 4⁄7 water by volume, what is the ratio of the volume of alcohol to the volume of water in this mixture?
Options:
A)3⁄7
B)4⁄7
C)3⁄4
D)4⁄3
E)7⁄4
Rationale: Should be a sub-600 level Q..
volume= {3/7}/{4/7}=3/4
ANSWER:C
Answer: C
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :
Options:
A)500
B)387
C)298
D)267
E)191
Rationale: Explanation:
Given that the student got 125 marks and still he failed by 40 marks
=> The minimum pass mark = 125 + 40 = 165
Given that minimum pass mark = 33% of the total mark
Answer: A) 500
Answer: A
Question: If 40! × 40!/40^n is an integer, what is the largest possible value of n?
Options:
A)24
B)10
C)7
D)3
E)1
Rationale: 40! × 40!/40^n is an integer.
Or 40! × 40!/(4^2n*5^n)
This means we need to find the power of 5 in the numerator. We can safely say that the number of powers of 5 will be lower than the number of powers of 4 in the numerator.
Largest power of 5 in 40! = [40/5] + [40/25] = 5
Since there are 2 20!'s, power of 5 in the numerator = 2*5 = 10
Hence the largest value of b for which 40! × 40!/40^n is integer = 10
Correct Option : B
Answer: B
Question: If the GCD of two distinct numbers (not equal, both integers, greater than 1) is 3, then which of the following can be true? A. They are prime.
B. They are odd.
C. They do not have a common prime factor.
D. They do not have a common factor other than 3.
Options:
A)Only A
B)Only B
C)Only C
D)Only D
E)Only A and D
Rationale: The GCD of two distinct numbers (not equal, both integers, greater than 1) is 3 means that they don't share factors greater than 3. Allowed factors are 1, 2, and 3. Defined factors are 1 and 3.
A. They are not prime. 3 is the only prime number that is divisible by 3, so one number can be prime but the other number cannot be.
B. They can be odd. For example: 9 has factors of 1 and 3 (1 x 3 x 3), and 15 has factors of 1, 3, and 5 (1 x 3 x 5). 9 and 15 are both odd and have a GCD of 3.
C. They do have a common prime factor. That prime factor is 3.
D. They have a common factor other than 3. Both numbers have common factors of 3 and 1.
Therefore only (B) is correct.
Answer: B
Question: 60 + 5 * 12 / (180/3) = ?
Options:
A)60
B)120
C)13
D)61
E)None of these
Rationale: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
ANSWER IS D
Answer: D
Question: Find the odd man out. 125, 127, 130, 135, 142, 153, 165
Options:
A)165
B)142
C)153
D)130
E)125
Rationale: Explanation :
Prime numbers 2, 3, 5, 7, 11, 13 are added successively. Hence, 165 is wrong
Answer : Option A
Answer: A
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB > CD
B)XB < YD
C)AX > XB
D)CY < XB
E)AX > AB
Rationale: A--X------B
C-----Y---D
CY < XB.
Answer: D.
Answer: D
Question: If p is the product of the integers from 1 to 32, inclusive, what is the greatest integer k for which 3^k is a factor of p?
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: 32! has 3, 6, 9,....30 as factors, which are 10 multiples of 3.
We need to add 4 more to 10 because of 9, 18, and 27.
The answer is C.
Answer: C
Question: A shopkeeper sells his goods at cost price but uses a weight of 800 gm instead of kilogram weight. What is his profit percentage?
Options:
A)25%
B)18%
C)20%
D)40%
E)45%
Rationale: 100(1000-800)/800 = 25%
Profit percentage = 25%
ANSWER A
Answer: A
Question: Jamboree and GMAT Club Contest Starts
QUESTION #10:
How many words (with or without meaning)P can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
Options:
A) 660
B) 600
C) 500
D) 300
E) 240
Rationale: In general, repetitions are taken care of by dividing the permutation by the factorial of the number of objects that are identical. in this case,P if you think logically, A,B,C,D options are not divisible by 6!. 6 is total number of letters in the word SELFIE. Only option E is divisible by 6!. So correct answer is E that is 240
Answer: E
Question: If a certain sample of data has a mean of 31.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?
Options:
A)(27.0; 36.5)
B)(24.5; 38.0)
C)(28.0; 32.5)
D)(26.5; 35.0)
E)(29.0; 32.5)
Rationale: The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5.
The values between 26 and 36 are within 2.5 standard deviations from the mean.
The answer is B.
Answer: B
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies L and Y . The ratio of p to V in smothie L is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie L?
Options:
A)5
B)10
C)15
D)20
E)25
Rationale: The ratio of p to V in smothie L is 4 is to 1 and that in Y is 1is to 5.p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Answer: D
Question: A taxi company charges $1.85 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90?
Options:
A)4 miles
B)4 1/4 miles
C)4 3/4 miles
D)5 1/3 miles
E)6 1/4 miles
Rationale: If we start out with $4.90 and have to spend $1.85 for the first quarter-mile, we will have $3.05 left to spend on quarter-mile intervals.
Since $3.05/$0.15 = 20.33, we can buy 20.33 more quarter-miles, and will travel 21.33 quarter miles in all:
21.33 × 1/4 = 5 1/3 miles.
The correct answer is choice (D).
Answer: D
Question: 25,168, ? , 8176
Options:
A)1168
B)1169
C)1167
D)1166
E)1165
Rationale: 25*7-7 is 168.
168*7-7is1169
1169*7-7 is 8176
So 1169
ANSWER:B
Answer: B
Question: An Olympic diver received the following scores: 7.0, 8.5, 8.0, 6.5, and 5.0. The standard deviation of her scores is in which of the following ranges?
Options:
A)1.01 to 1.99
B)2.01 to 2.99
C)3.01 to 3.99
D)4.01 to 4.99
E)5.01 to 5.99
Rationale: 7+8.5+8+6.5+5/5=35/5=7
∣7−7∣^2 =0^2 = 0
∣8.5−7∣^2 =1.5^2 = 2.25
∣8−7∣^2 =1^2 = 1
∣6.5−7∣^2 =0.5^2 = 0.25
∣5−7∣^2 =2^2 = 4
sqrt 2.25+1+.25+4/5 =1.22
Answer : A
Answer: A
Question: ?% of 360 = 144
Options:
A)277
B)36
C)64
D)40
E)None of these
Rationale: ?% of 360 = 144
or, ? = 144×100/360=40
Answer D
Answer: D
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 30% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
Options:
A)80
B)95
C)105
D)137
E)210
Rationale: Set up equation:
x = total number of workers
120 = 0,3 * 2/3 * x + 0,8 * 1/3 * x
120 = 14/30 x
x = 257
257 - 120 = 137
Answer D
Answer: D
Question: A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $30000 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
Options:
A)5
B)4
C)9
D)10
E)15
Rationale: Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x
Gievn: Total $1250 scholarships = $30000
6x*1250 = 30000
Solve for x = 4
Option B
Answer: B
Question: A rectangular garden has a 5-metre-wide road outside around all the four sides. The area of the road is 600 square metres. What is the ratio between the length and the breadth of that plot?
Options:
A)3 : 2
B)4 : 3
C)5 : 4
D)Data inadequate
E)None of these
Rationale: Area of shaded portion = 600 m.
∴ (l + 10)(b + 10) – lb = 600
or, lb + 10b + 10l + 100 – lb = 600
or, 10 (b + (l) = 500
∴ b + l = 50
From this equation we can’t get the required ratio
Answer D
Answer: D
Question: How many five digit numbers can be formed by using the digits 0,1,2,3,4,5 such that the number is divisible by 4?
Options:
A)288
B)173144
C)144
D)297
E)2181
Rationale: Explanation:
If a number has to be divisible by 4, the last two digit of that number should be divisible by 4.
So _ _ _ x y. Here xy should be a multiple of 4.
There are two cases:
Case 1: xy can be 04, 20 or 40
In this case the remaining 3 places can be filled in 4×3×2 = 24. So total 24×3 = 72 ways.
Case 2: xy can be 12, 24, 32, 52.
In this case, left most place cannot be 0. So left most place can be filled in 3 ways. Number of ways are 3×3×2 = 18. Total ways = 18×4 = 72.
Total ways = 144
Answer:C
Answer: C
Question: Which of the following CANNOT be a product of two distinct positive integers c and d?
Options:
A)c
B)d
C)3d + 2c
D)d - c
E)dc
Rationale: In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with
take c = 1 and d = 2 and work with the options
cd = 2
A) c take c =2, d = 1
B) d take c = 1 d = 2
C) 3d + 2c Seems tricky, lets see other options and then come back to it.
D) d - c take d = 1 and c = 2 --> d - c = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them?
E) dc Always true
You don't even have to worry what C is !
ans D
Answer: D
Question: How much time will it take for an amount of 450 to yield 81 as interest at 4.5% per annum of simple interest?
Options:
A)5 years
B)8 years
C)2 years
D)4 years
E)9 years
Rationale: D
4 years
Time = (100 x 81)/(450 x 4.5) years = 4 years.
Answer: D
Question: A straight pipe 1 meter in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a meter?
Options:
A) 1/6 and 1/4 only
B) 1/4 and 1/3 only
C)1/12, 1/6 and 1/4
D) 1/6, 1/4, and 1/3
E) 1/12, 1/6, and 1/3
Rationale: Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3
Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12
Now comine : 0,3,4,6,8,9,12
Now find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.
Answer - C
Answer: C
Question: A train 125 m 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)33
B)50
C)88
D)26
E)23
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x = 50 km/hr.
Answer: B
Answer: B
Question: A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share?
Options:
A)Rs.12
B)Rs.18
C)Rs.15
D)Rs.21
E)Rs.25
Rationale: Explanation :
Face value of each share = Rs.20
Dividend per share = 9% of 20 = 9×20/100=9/5
He needs to have an interest of 12% on his money
ie, Money Paid for a share 9×12/100=9/5
Money Paid for a share=9/5×100/12=15
ie, Market Value of the share = Rs.15
Answer : Option C
Answer: C