divelab/Sys2Bench huggingface dataset:
Question: In a secondary school the seats for Maths, physics and social studies are in the ratio 8 : 5 : 7. there is a proposal to increase these seats by 75%, 40% and 50% respectively. What will be the new ratio?
Options:
A)5 : 3 : 4
B)4 : 2 : 3
C)10 : 7 : 9
D)1 : 3 : 4
E)None of these
Rationale: Explanation :
Solution: Originally, let the number of seats for Maths, physics and social studies be 8x, 5x and 7x respectively.
Number of increased seats are (175% of 8x), (140% of 5x) and (150% of 7x).
i.e. (175*7x/100), (140*5x/100) and(150*7x/100) i.e. 14x, 7x and 21x/2.
.'. Required ratio = 14x : 7x : 21x/2 = 28x : 14x : 21x = 4 : 2 : 3
Answer : B
Answer: B
Question: X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Find the time in which they can complete the work together?
Options:
A)15 days
B)16 days
C)17 days
D)18 days
E)19 days
Rationale: If X can complete work in x days and y can complete work in 3x days.
Then 2x = 40
x= 20 days.
so X can complete work in 20 days and y can complete work in 60 days.
they can complete the work together in 1/(1/20 + 1/60) = 1/ (4/60) = 15 days
ANSWER:A
Answer: A
Question: The C.P of 10 pencils is equal to the S.P of 12 pencils. Find his gain % or loss%?
Options:
A)18 2/3%
B)58 2/3%
C)16 2/3%
D)46 2/3%
E)6 2/3%
Rationale: Option C
Explanation:
10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer: C
Question: Of the 100 athletes at a soccer club, 40 play defense and 66 play midfield. If at least 20 of the athletes play neither midfield nor defense, the number of athletes that play both midfield and defense could be any number between
Options:
A)10 to 20
B)10 to 40
C)26 to 40
D)30 to 70
E)40 to 70
Rationale: First of all notice that since only 40 athletes play defense, then the number of athletes that play both midfield and defense cannot possibly be greater than 40.Eliminate D and E.
{Total} = {defense} + {midfield} - {both} + {neither}
100 = 40 + 66 - {both} + {neither}
{both} = {neither} + 6.
Since the least value of {neither} is given to be 20, then the least value of {both} is 20+6=26.Eliminate A and B.
Answer: C.
Answer: C
Question: A and B started a business investing Rs. 21,000 and Rs. 28,000 respectively. Out of a total profit of Rs. 14,000, B’s share is :
Options:
A)7600
B)7700
C)7800
D)7900
E)8000
Rationale: Ratio of their shares = 21000 : 28000 = 3 : 4.
B’s share = Rs. 14000 * 4/7
= Rs. 8000
ANSWER:E
Answer: E
Question: When positive integer N is divided by positive integer J, the remainder is 10. If N/J = 205.08, what is value of J?
Options:
A)125
B)100
C)75
D)150
E)50
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 205.08
Here 205 is the quotient.
Given that Remainder = 10
So, 205.08 = 205 + 10/J
So, J = 125
Answer: A
Answer: A
Question: A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
Options:
A)18
B)24
C)42
D)81
E)90
Rationale: Explanation:
Let the ten's and unit's digit be x and 8/x respectively.
Then,
(10x + 8/x) + 18 = 10 * 8/x + x
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2
So, ten's digit = 2 and unit's digit = 4.
Hence, required number = 24.
ANSWER IS B
Answer: B
Question: For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 1*/4* ?
Options:
A)5
B)5/4
C)4/5
D)1/4
E)1/5
Rationale: When dealing with 'Symbolism' questions, it often helps to 'play with' the Symbol for a few moments before you attempt to answer the question that's asked. By understanding how the Symbol 'works', you should be able to do the latter calculations faster.
Here, we're told that K* is the PRODUCT of all the fractions of the form 1/T, where T is an integer between 1 and K, inclusive.
Based on this definition....
IF....
K = 2
K* = (1/1)(1/2) = 1/2
IF....
K = 3
K* = (1/1)(1/2)(1/3) = 1/6
We're asked to find the value of 5*/4*
Now that we know how the Symbol 'works', solving this problem shouldn't be too difficult. You can actually choose to do the math in a couple of different ways....
5* = (1/1)(1/2)(1/3)(1/4)(1/5)
Don't calculate this just yet though....since we're dividing by 4*, many of those fractions will 'cancel out.'
4* = (1/1)(1/2)(1/3)(1/4)
We're looking for the value of:
(1/1)(1/2)(1/3)(1/4)(1/5) / (1/1)(1/2)(1/3)(1/4)
Since the first four fraction in the numerator and denominator cancel out, we're left with just one fraction:
4/5
A
Answer: A
Question: Amber works 28 days a month at d dollars per day for m months out of the year. Which of the following represents her monthly pay?
Options:
A)m/(20d)
B)20d
C)10md/6
D)28d
E)20md
Rationale: ANSWER: D The passage states that she works 28 days a month at d dollars per day, so 28 d is her monthly pay
Answer: D
Question: A certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 11 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
Options:
A)42
B)70
C)140
D)165
E)385
Rationale: Ans: 385
7C1 * 11C2
Answer E)
Answer: E
Question: At a florist shop on a certain day, all corsages sold for either $20 or $30. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 10 percent. What was the store's actual revenue from corsages that day?
Options:
A)$200
B)$400
C)$600
D)$800
E)$1000
Rationale: Let, No. of corsages @ $20 = x, no. of corsages @ $30 = y and revenue= r
so, 20x+30y=r.........(1)
Now,
Given the situation, 20(x+8) + 30(y-8)= r-.1r
=> 20x+160+30y-240 = .9r
=> 20x+30y = .9r+80............(2)
so, r = .9r+80
=> r = 800
The answer is D.
Answer: D
Question: After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount.
Options:
A)22%
B)18%
C)24%
D)17%
E)20%
Rationale: Let the first discount be x%
Then,87.5% of (100-x)% of 150= 105
=	87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80
x=(100-80)=20
first discount = 20%
Answer is E.
Answer: E
Question: How many times digit 6 is used while writing numbers from 100 to 1100?
Options:
A)648
B)320
C)252
D)225
E)26
Rationale: There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have calculated 190.
The total now comes to 280. The nearest to which is 320. Hence B.
Answer: B
Question: Find large number from below question The difference of two numbers is 1355. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1234
B)1265
C)1350
D)1467
E)1623
Rationale: Let the smaller number be x. Then larger number = (x + 1355).
x + 1355 = 6x + 15
5x = 1340
x = 268
Large number = 268+1355 = 1623
E
Answer: E
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability that the worker is under 25 years old?
Options:
A)0.3
B)0.25
C)0.45
D)0.7
E)0.9
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old = .7
Answer D
Answer: D
Question: For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 2 is in the set , which of the following must also be in the set ?
a) 4
b) -4
c) -5
Options:
A)a only,
B)b only,
C)c only,
D)a and b only
E)b and c only
Rationale: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.
Since 2 is in the set, then so must be 2-3=-1. Similarly, since -1 is in the set, then so must be -1-3=-4. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.
Answer: B.
Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: B
Question: The area of Circle O is added to its diameter. If the circumference of Circle O is then subtracted from this total, the result is 4. What is the area of Circle O?
Options:
A)2/π
B)2
C)8
D)4
E)4π
Rationale: area+diameter-circumference=4
pi*r^2+2r=4+2pi*r
isolate r and get r(pi*r+2)=4+2pi*r
r=(4+2pi*r)/(pi*r+2) =>2(2+pi*r)/(pi*r+2)
r=2
Area = pi * r^2 => pi * 4
E
Answer: E
Question: Suppose that AB = AC = CD and
AD = BD. What is the measure of
6 ADC in degrees?
Options:
A)24
B)28
C)32
D)36
E)40
Rationale: Let be the measure of \ADC. Then since ADC is isosceles, we obtain that
the measures of \CAD and \DCA are and 180 􀀀 2, respectively. It follows that
\ACB has measure 2. Since ACB is isosceles, we obtain that the measures of \CBA
and \BAC are 2 and 180 􀀀 4, respectively. Since ADB is isosceles, we deduce that
the measures of \CBA and \BAD are the same. This gives that 2 = (180 􀀀 4) +
which implies 5 = 180. Therefore, = 36.
correct answer D
Answer: D
Question: In the coordinate plane, Line A has a slope of -1 and an x-intercept of 2. Line B has a slope of 5 and a y-intercept of -10. If the two lines intersect at the point (a,b), what is the sum a+b?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The equation of Line A is y = -x + 2
The equation of Line B is y = 5x - 10
5x - 10 = -x + 2
x = 2
y = 0
The point of intersection is (2,0) and then a+b = 2.
The answer is C.
Answer: C
Question: If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?
Options:
A)2
B)5
C)100/21
D)110/20
E)9/4
Rationale: Last months revenue can be calculated as 220x / 1.10 = 200x
Now consider the next statement - > if the price of ticket is hiked by 5% the new price is 1.05 x.
So the new revenue when only 200 tickets are sold = 200 * 1.05x = 210x.
We need to find the percentage difference ; so we have (new-old/new*100) 210x-200x/210x*100 = 100/21
Answer: C
Answer: C
Question: The ratio of 2 numbers is 1:2 and their H.C.F. and L.C.M are 10 and 20. Find the numbers.
Options:
A)20, 10
B)10, 20
C)20, 30
D)30, 20
E)10, 10
Rationale: Let the numbers be x and 2x
Their H.C.F. = 10
L.C.M = 20
ie) 2x^2 = 200
x^2 = 100, x = 10 t The numbers are x and 2x , ie)10, 20 respectively.
Answer is B
Answer: B
Question: By how much is two-fifth of 500 greater than five - seventh of 210 ?
Options:
A)50
B)75
C)120
D)None of these
E)Cannot be determined
Rationale: Solution
2/5of 500 - 5/7 of 210 = 50.
Answer A
Answer: A
Question: The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest?
Options:
A)80 years
B)70 years.
C)20 years.
D)30 years.
E)20 years.
Rationale: Present total age of the members = 26(5) = 130 years.
Present age of the youngest member = 10 years
Present total age of the remaining four members = 130 -10 = 120 years
Their average age at the time of the birth of the youngest member = [120 - (4 * 10)] / 4 = 30 - 10 = 20 years.
Answer: C
Answer: C
Question: If m and n are positive integers, and m=2n and k=2m, then -
Options:
A)2m is a factor of k.
B)m/2 is a factor of k.
C)3m is a factor of k/2.
D)k is a factor of m.
E)k is a factor of m/2.
Rationale: m=2n --> m is even.
k=2m --> m is factor of k, thus m/2 = integer must also be a factor of k.
Answer: B.
Answer: B
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A?
Options:
A)240
B)288
C)266
D)216
E)123
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
Answer: A
Answer: A
Question: If |x^2 − 12| = x, which of the following could be the value of x?
Options:
A)-4
B)-3
C)1
D)2
E)3
Rationale: |x2−12|=x|x2−12|=x
|x2−12||x2−12|cannot be negative; anything that comes out of mod is always positive
so |x2−12|>0|x2−12|>0
Out of our options A= -4 B= -3 cannot be the right answer because none of them are greater than 0
Now only Option C=1 or D=2 or E=3 are contenders for right answers.
A quick Cursory crude calculation will tell you that E is the right choice
|−32−12|=3|−32−12|=3
|9−12|=3|9−12|=3
|−3|=3|−3|=3
3=33=3
ANSWER IS E
Answer: E
Question: If log 27 = 1.437, then the value of log 9 is:
Options:
A)0.934
B)0.945
C)0.954
D)0.958
E)0.998
Rationale: log 27 = 1.437
log (3cube ) = 1.437
3 log 3 = 1.437
log 3 = 0.479
log 9 = log(3square ) = 2 log 3 = (2 x 0.479) = 0.958.
Answer: Option D
Answer: D
Question: P can do the work in 12 days and Q can do the same work in 15 days. If they work together for 4 days, what is the fraction of work that is left?
Options:
A)1/5
B)2/5
C)7/15
D)11/15
E)23/30
Rationale: 4/12 + 4/15 = 1/3 + 4/15 = 9/15 = 3/5 (completed work)
The work that is left is 1 - 3/5 = 2/5
The answer is B.
Answer: B
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
Options:
A)10,000 square meters
B)20,000 square meters
C)30,000 square meters
D)40,000 square meters
E)50,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer B
Answer: B
Question: A merchant marks his goods up by 40% and then offers a discount of 10% on the marked price. What % profit does the merchant make after the discount?
Options:
A)8%
B)14%
C)26%
D)15%
E)17%
Rationale: Let the price be 100.
The price becomes 140 after a 40% markup.
Now a discount of 10% on 126.
Profit=126-100
26%
answer C
Answer: C
Question: A committee of 6 is chosen from 6 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
Options:
A)275
B)700
C)1404
D)2620
E)3510
Rationale: The only cases possible are :
1. 2 men and 4 women : 6C2 * 5C4 = 75
2. 3 men and 3 women: 6C3*5C3 = 200
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 75+200 = 275. Thus A is the correct answer.
Answer: A
Question: The ratio of a to b is 4 to 5, where a and b are positive. If x equals a increased by 25 percent of a, and m equals b decreased by 40 percent of b, what is the value of m/x?
Options:
A)2/5
B)3/4
C)4/5
D)5/4
E)3/5
Rationale: a/b = 4/5
m/x = (3/5)*5 / (5/4)*4 = 3/5
The answer is E.
Answer: E
Question: A and B can do a piece of work in 6 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
Options:
A)40 days
B)16 days
C)6 days
D)5 days
E)40 days
Rationale: C
6 days
C = 1/3 – 1/6 = 1/6 =>6 days
Answer: C
Question: Sheela deposits Rs. 3400 in bank savings account. If this is 15% of her monthly income. What is her monthly income in?
Options:
A)22666
B)20000
C)25000
D)22235
E)None of these
Rationale: Explanation :
15% of income = Rs. 3400
100% of income = 3400 X 100/15 = Rs. 22666
Answer : A
Answer: A
Question: In a box, there are 2 yellow, 4 grey and 4 white pencils. One pencil is picked up randomly. What is the probability that it is neither yellow nor grey?
Options:
A)2/5
B)1/5
C)3/5
D)4/5
E)5/6
Rationale: Explanation :
Neither yellow nor grey means the pencil drawn is white.
Total number of outcomes = (2+4+4) = 10.
Number of Favourable outcomes = 4 = Number of white pencils.
Hence, Probability of the event = 4/10 = 2/5.
Answer : A
Answer: A
Question: Which is the following is divisible by 11
Options:
A)A)4305
B)B)4825
C)C)6594
D)D)4905
E)E)4906
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 11(11 + 1)//2 = 11 x 6 = 66
Sum of first 99 natural numbers = 111(111 + 1)//2 = 111 x 60 = 6660
6660 - 66 = 6594
Answer: Option C
Answer: C
Question: A bag contains 2 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag. Find the probability that one ball is red and one is green.
Options:
A)19/20
B)17/20
C)21/25
D)8/10
E)9/40
Rationale: Let A be the event that ball selected from the first bag is red and ball selected from second bag is green.
Let B be the event that ball selected from the first bag is green and ball selected from second bag is red.
P(A) = (2/5) x (6/10) = 6/25.
P(B) = (3/5) x (4/10) = 6/25.
Hence, the required probability is P(A) + P(B) which is nothing but 21/25.
ANSWER:C
Answer: C
Question: If an object travels at five feet per second, how many feet does it travel in one hour?
Options:
A)1700
B)1900
C)1400
D)1600
E)1800
Rationale: If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour.
Answer = 1800
Answer is E.
Answer: E
Question: 1/(4-√15)=?
Options:
A)4+√15
B)9-4√5
C)9+2√5
D)9-2√5
E)4+9√5
Rationale: This question requires us to rationalize (fix) the denominator.
For more on this technique, seehttps://www.gmatprepnow.com/module/gmat ... video/1044
Given: 1/(4-√15)
Multiply top and bottom by the CONJUGATE of 4-√15, which is 4+√15
So, 1/(4-√15) = (1)(4+√15)/(4-√15)(4+√15)
= (4+√15)/(1)
= 4+√15
=
A
Answer: A
Question: Which of the following options is an appropriate approximate value in the following equation’? 625.3 of 165.83+42% of 1560= ? - 625.7
Options:
A)104875.3
B)12825.3
C)1034825.3
D)104425.3
E)104825.3
Rationale: 625.3 of 165.83+42% of 1560= ? - 625.7
103693.5+506.1= ? - 625.7
103693.5+506.1 + 625.7= ?
≈ 104825.3
Answer E
Answer: E
Question: 9 neighbors are to split the cost of topsoil. The cost of the 5 truck loads of dirt was $690.47. What is the least amount of money (in whole number of dollars) that they must add to bill if they wants to split this money evenly among his nine neighbors?
Options:
A)690.48
B)690.49
C)690.5
D)690.51
E)690.52
Rationale: If the bill was $690.47 dollars, how much money should be removed with 1 cent as the smallest unit?
This is equivalent to finding the first number that is divisible by 9 that occurs after 690.47.
In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 6+9+0+4+7 = 26. If you add 1 , the number is divisible by 9 (26 +1). 27 is divisible by 9.
Hence, we need to add 1 cent from this number for it to be divisible by 9.
Correct Option : A
Answer: A
Question: A hiker walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked at 7 miles per hour for 2 hours. How many miles in total did she walk?
Options:
A)24
B)52
C)58
D)60
E)62
Rationale: First day - 18 miles with 3 miles per hours then total - 6 hours for that day
Second day - 4 miles per hour and 5 hours - 20 miles
Third day - 7 miles per hour and 2 hours - 14 miles
Total 18+20+14 = 52
Answer: option B.
Answer: B
Question: At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 60 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
Options:
A)20%
B)25%
C)30%
D)33.33%
E)40%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
60 = 20 + b + 20b/100
b = 33.33
Answer (D)
Answer: D
Question: A man can row upstream at 60 kmph and downstream at 90 kmph, and then find the speed of the man in still water?
Options:
A)75 kmph
B)65 kmph
C)30 kmph
D)73 kmph
E)65 kmph
Rationale: US = 60
DS = 90
M = (60 + 90)/2 = 75
Answer:A
Answer: A
Question: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is negative, y must be negative
III. If x is positive, y must be positive
Options:
A)I only
B)II only
C)III only
D)I and II
E)II and III
Rationale: If x-y=8, which of the following must be true?
I. Both x and y are positive
II. If x is positive, y must be positive
III. If x is negative, y must be negative
1. x and y can be negative, for instance, -2 - (-10) = 8 =>Eliminate A and D
2. x can be positive and y can be negative, for instance, 2 - (-6) = 8 => Eliminate B and E
A) I only
B) II only
C) III only
D) I and II
E) II and III
Answer B
Answer: B
Question: Six years back, a father was 42 years older than his son. At present the father is 4 times as old as the son. How old will the son be three years from now?
Options:
A)20 years
B)19 years
C)18 years
D)17 years
E)16 years
Rationale: Using linear equations to convert the word problem:
** F = fathers current ageS = sons current age
#1 Six years back, a father was 42 years older than his son: F-6 = 42 + (S - 6)
#2 At present the father is 4 times as old as the son: F = 4*S
How old will the son be three years from now?: S + 3 = ?
With two variables and two linear equations we are able to solve the problem:
(S*4) - 6 = 42 +S -6
3S=42
S = 14
S + 3 = 14 + 3 = 17
Answer: D
Answer: D
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1904?
Options:
A)1700
B)2777
C)2889
D)27670
E)2771
Rationale: 1904 = P [1 + (5*12/5)/100]
P= 1700.Answer:A
Answer: A
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 340 m long?
Options:
A)56 sec
B)42 sec
C)45 sec
D)48 sec
E)50 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 340 = 700 m
Required time = 700 * 2/25 = 56 sec
ANSWER:A
Answer: A
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he
Options:
A) broke even
B) lost 4 cents
C) gained 4 cents
D) lost 10 cents
E) gained 10 cents
Rationale: 20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
The answer is (A)
Answer: A