divelab/Sys2Bench huggingface dataset:
Question: If each data point in a certain set Q is increased by a factor of 8, what happens with the set's standard deviation?
Options:
A)Doesn't Change
B)Decreases by Factor 8
C)Increases by Factor 8
D)Increases by 8
E)Can't be determined
Rationale: Standard deviation questions will always be conceptual in nature, because the GMAT does not require that you be able to calculate standard deviation.Veritasteaches a concept known as themapping strategyfor data sufficiency, which helps make a problem like this easily understandable. The mapping strategy is just looking at data sufficiency with sets of numbers like you would look at a map. Moving left and right on the map does not change the map's scale (which represents standard deviation in this analogy), just as adding or subtracting the same value in all numbers of a set does not change that set's standard deviation. For example, the set: 2, 5, 8, 11 has the same standard deviation of that same set after adding 5 to each number: 7, 10, 13, 16. Multiplying and dividing the entire set by a number other than 1, however, does affect standard deviation, and it does so proportionately. Multiplying by a number with an absolute value greater than 1 is like zooming in on a map...the standard deviation increases. Consider that same set multiplied by 2: 4, 10, 16, 22....this has a larger standard deviation than 2, 5, 8, 11. The opposite goes for division - dividing each number in a set of numbers by a number with an absolute value greater than 1 will reduce standard deviation, like zooming out on a map reduces the map's scale. Here because each number was multiplied by a factor of 8, the standard deviation will increase proportionately, giving us answer choice C.
Answer: C
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/4 the number of cans that Karen collected and 1/9 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
Options:
A) 1/5
B) 1/3
C) 2/5
D) 1/2
E) 1/9
Rationale: John = (1/4)Karen --> Karen = 4(John)
John = 1/9(Luke) --> Luke = 9(John)
Total = 36(John)
Karen/Total = 4/36 = 1/9
Answer: E
Answer: E
Question: the cost of a tv is rs.2400 which is 20% below the marked price.If it is sold at a discount of 16% on the marked price,then find its marked price,selling price and profit ?
Options:
A)2520,120
B)2520,110
C)2520,130
D)2420,120
E)2620,120
Rationale: Let the marked price be x
SP is 20% below x
Then x*80/100 = 2400
4x/5 = 2400
4x = 12000
x = 3000
For 16% discount on x, SP ll be
SP = 3000*84/100 => CP = 2520
Profit = 2520 - 2400 = 120
Marked Price : 3000
Selling Price : 2520
Profit : 120
ANSWER:A
Answer: A
Question: If A father said to his elder son, "I was as old as you are at the present at the time of your birth". If the father's age is 25 years now, what was the son's age four years back?
Options:
A)7.5
B)8.5
C)9
D)9.5
E)10
Rationale: Let son's present age be a years. Then,
(25−a)=a
⇒2a=25
⇒a=25/2=12.5
Son's age 4 years back =12.5-4=8.5
ANSWER:B
Answer: B
Question: The equation r = 2y2 + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at r = -5, the equation for l is
Options:
A)+ y + 15 = 0
B)- 3x - 11 = 0
C)+ y - 16.5 = 0
D)- y - 7 = 0
E)+ y + 13.5 = 0
Rationale: Is optionC: -3r + y -6.5= 0=C
Answer: C
Question: SECTION-1 If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
Options:
A)22
B)99
C)787
D)66
E)11
Rationale: Explanation:
If men is fixed,work is proportional to time. If work is fixed, then time is inversely proportional to men therefore, (M1*T1/W1)=(M2*T2/W2) From the above formula i.e (m1*t1/w1)=(m2*t2/w2) so (9*6*88/1)=(6*8*d/1) on solving, d=99 days.
Answer: B
Answer: B
Question: A train 300 m long passed a pole in 30 sec. How long will it take to pass a platform 650 m long?
Options:
A)28 sec
B)89 sec
C)85 sec
D)16 sec
E)95 sec
Rationale: Speed = 300/30= 10 m/sec.
Required time = (300 + 650)/10
= 95 sec.
Answer:E
Answer: E
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.30 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)160
B)175
C)180
D)200
E)210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.30 + X x 3.20 = 432
X = 20.
Hence, total hours of work = (160 + 20) = 180.
answer :C
Answer: C
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
Options:
A)55 years
B)44 years
C)33 years
D)Data inadequate
E)None of these
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
From (1) and (2), we cannot find b.
Answer:D
Answer: D
Question: if xy+z=x(y+z) which of the following must be true?
Options:
A)x=2 or z=0
B)x=1 or z=0
C)x=1 or z=1
D)x=0 or z=0
E)x=0 or z=0
Rationale: xy+z=xy+xz
z=xz
xz-z=0
z(x-1)=0
Means;
either z=0
OR
x-1=0 i.e. x=1
Answer B
Answer: B
Question: How much time will it take for an amount of Rs. 400 to yield Rs. 100 as interest at 5% per annum of simple interest?
Options:
A)5 years
B)4 years
C)7 years
D)6 years
E)2 years
Rationale: Explanation:
Time = (100 x 100)/(400 x 5) years
= 5 years.
Answer: A
Answer: A
Question: In a certain country 1/3 of 4 = 8. Assuming the same proportion, what would be the value of 1/8 of 4 ?
Options:
A)2
B)6
C)5
D)4
E)3
Rationale: E
3
Answer: E
Question: A man spends Rs. 1700 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
Options:
A)2025
B)2125
C)2225
D)2325
E)2425
Rationale: Explanation:
Total expenditure for the first 3 months = 3 Ã— 1700 = 5100
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 5100 + 6200 + 9000 + 5200 = Rs. 25500
So, Average monthly income = 25500/12 = Rs. 2125
Answer B
Answer: B
Question: Peter rolls two dice at the same time. What is the probability that he will not roll a double?
Options:
A)a) 1/12
B)b) 1/36
C)c) 1/6
D)d) 1/6
E)e) 5/6
Rationale: We can have 6 different outcomes on a dice.
Total outcomes on two dices = 6*6
We need only the cases when Peter rolls a double, that means only the outcomes in which the numbers on both the dices are same
They can be {1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {6, 6}.
A total of 6 outcomes
Number of outcomes where he will not roll a double = 36-6 = 30
Probability = favorable outcomes/ total outcomes = 30/36 = 5/6.
Option E
Answer: E
Question: Length of a rectangular plot is 50 mtr more than its breadth. If the cost of fencin g the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
Options:
A)46 m
B)60 m
C)58 m
D)75 m
E)80 m
Rationale: Let breadth = x metres.
Then, length = (x + 50) metres.
Perimeter = 5300/26.5 m = 200 m.
2[(x + 50) + x] = 200
2x + 50 = 100
2x = 50
x = 25.
Hence, length = x + 50 = 75 m
D
Answer: D
Question: The simple interest on a sum in 2 years is Rs. 96 and the compound interest on the same sum for the sametime is Rs. 99. Find the sum and the rate.
Options:
A)3.25%
B)5.25%
C)6.25%
D)4.25%
E)7.25%
Rationale: P(r/100)^2 =3, ie) pr^2 =30000 S.I =P*2*R/100=96 ie) pr =4800 pr^2/pr =30000/4800 r =6.25% Answer : C
Answer: C
Question: The no of revolutions a wheel of diameter 40cm makes in traveling a distance of 176m is
Options:
A)122
B)140
C)287
D)128
E)112
Rationale: distance covered in 1 revolution =
= 2 *(22/7) *20 = 880/7 cm
required no of revolutions = 17600 *(7/880)
= 140
Answer: B
Answer: B
Question: A and B can do a work in 6 days.They both started the work and after three days A left the work.B finished the remaining work in 15 days.In how many days will A finish the work?
Options:
A)7 days
B)7.5 days
C)8.5 days
D)9.5 days
E)6.5 days
Rationale: A and B'S 1 DAY WORK i.e A+B =1/6
WORK COMPLETED AFTER THREE DAYS=3*1/6=1/2
REMAINING WORK 1/2 i.e 50 percentage completed by B in 15 days,so B can finish work in 30 days.. b's 1 day work 1/30
a's 1 day work=1/6-1/30=4/30
so a can finish work 30/4=7.5 days
ANSWER:B
Answer: B
Question: Rs.1600 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5%?
Options:
A)1100
B)1200
C)1300
D)1400
E)1700
Rationale: (x*5*1)/100 + [(1600 - x)*6*1]/100 = 85
5x/100 + (9600 – 6x)/100 = 85
=> x = 1100
ANSWER:A
Answer: A
Question: A pharmaceutical company received $4 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?
Options:
A)8%
B)15%
C)45%
D)52%
E)58%
Rationale: Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 4/20= 1/5
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (4/20) x 60 = 12
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 12 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 12)/12] x 100
-175/3 x 100
At this point we can stop and consider the answer choices. Since we know that 175/3 is just a bit less than ½, we know that -175/3 x 100 is about a 58% decrease.
Answer E.
Answer: E
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 10 and 12. The larger of the two numbers is:
Options:
A)276
B)299
C)322
D)345
E)395
Rationale: Clearly, the numbers are (23 x 10) and (23 x 12).
Larger number = (23 x 12) = 276.
Answer: Option A
Answer: A
Question: How many ways can 7 friends be arranged around a circular dinner table?
Options:
A)120
B)720
C)3280
D)5040
E)5660
Rationale: The number of ways to order 7 people is 7!
However, around a circular table, each pattern would be repeated 7 times.
So the number of ways to seat 7 friends around a circular table is 6! = 720
The answer is B.
Answer: B
Question: A bat is bought for Rs.400 and sold at a gain of 30% find its selling price.
Options:
A)A)Rs.460/-
B)B)Rs.470/-
C)C)Rs.480/-
D)D)Rs.500/-
E)E)Rs.520/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
130 % ------> 520 (130 * 4 = 520)
Selling price = Rs.520
Answer : E
Answer: E
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 9 p.c?
Options:
A)36400
B)29000
C)37000
D)38000
E)40000
Rationale: Option B
Explanation:
CP + CP/8 = 45000
CP = 40000
SP = 40000*(91/100) = 36400
Option A
Answer: A
Question: Think of a number, divide it by 5 and add 8 to it. The result is 61. What is the number thought of?
Options:
A)24
B)77
C)297
D)265
E)29
Rationale: Explanation :
61-6 = 53
53 x 5 = 265
Answer : D
Answer: D
Question: At what price must an article costing Rs.51.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
Options:
A)60.5
B)69.5
C)67.5
D)67.7
E)22.5
Rationale: CP = 51.50
SP = 51.50*(125/100) = 64.375
MP*(95/100) = 64.375
MP = 67.7
Answer:D
Answer: D
Question: If the salary of an employee is first increased by 20% and the decreased by 12%, then what is the change in his salary in percent?
Options:
A)5.9 % increase
B)5.6 % increase
C)4.6 % increase
D)1.6 % increase
E)5.7 % increase
Rationale: Explanation:
Let the first change be denoted by ‘x’ and the second by ‘y’.
The net change is given by {x + y + (x*y)/100}%
Therefore, the net change in salary is {20 + (-12) + (20*(-12))/100}
= 8 – 2.4
= 5.6% (as the sign is +ve, the change is increase)
ANSWER: B
Answer: B
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.19
B)7.17
C)7.19
D)7.15
E)7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Answer: D
Question: Reena took a loan of 1500 with simple interest for as many years as the rate of interest. If she paid 735 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)7
C)18
D)Cannot be determined
E)None
Rationale: Explanation: Let rate = R% and time = R years.
Then, (1500 x R x R)/100 = 735
15RÂ² = 735
RÂ² = 49
R = 7.
Answer: Option B
Answer: B
Question: A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $65,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
Options:
A) $27,500
B) $35,000
C) $37,500
D) $40,000
E) $50,000
Rationale: let x be the average of 40 customers
40*x + 10* 65000 = 50*45000
solving this we have x= 40000
Answer is D.
Answer: D
Question: If 20% of certain quantity of work is done by A and the rest 80% by B, the work is completed in 20 days. If 80% of the work is done by A and the remaining 20% by B, then the work is completed in 30 days. How many days are required to complete the work , if A and B work together .
Options:
A)11 1/9
B)10 1/9
C)12
D)15
E)Source: TIME material.
Rationale: Use algebra:
0.2/A + 0.8/B = 20
1/A + 4/B = 100
0.8/A + 0.2/B = 30
4/A+ 1/B = 150
15/B = 250
B = 3/50 work per day
A = 3/100 work per day
Combined rate = 3/40 + 3/100 = 9/100
Time taken when working together = 100/9 = 11(1/9) days
Answer (A)
Answer: A
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $55,000?
Options:
A)$38,796.
B)$40,000.
C)$38,976.
D)$39,679.
E)$53,592.
Rationale: 55,000 *1.16*.84= 53,592
Answer E
Answer: E
Question: The integer n is formed by writing the integers 1 through 333 in order as shown below.
n=123456789101112.......331332333
counting from the left, what is the 333rd digit of n?
Options:
A)0
B)1
C)3
D)7
E)8
Rationale: the other way you can approach this is:
add zeroes as follows:
123456789....
make a pair of 3 by making each number a 3 digit number
000
001
002
003
004
005
006
007
008
009
010.... and so on
....by doing this we can make that every other 30th digit will be a 9
and for doing this we are adding 1*3+2*9+1*90=112 zeroes...therefore 333rd digit now will be 333+111=444 th digit
now 30*15=450....therefore 450th digit will be 9
and 15 th series will be of 141,142....149
so ........147148149.....in this 9 is the 450th digit therefore 444 th will be 7
hence the answer is 7 answer is D
Answer: D
Question: Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1600 item. Peter has twice as much money as John. Quincy has $40 more than Peter. Andrew has 10% more than Quincy. If they put all their money together and spend the $1600, they will have $14 left. How much money does Peter have?
Options:
A)$400
B)$560
C)$425
D)$380
E)$455
Rationale: P= 2J ; Q= P+40 ; A= 1.1(Q)
P+J+Q+R-1600=14
P+0.5P+P+40+1.1(P+40) = 1614
P+0.5P+P+40+1.1P+44=1614
P+0.5P+P+1.1P+84=1614
P+0.5P+P+1.1P=1530
3.6P=1530
P=425
Answer:C
Answer: C
Question: Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 80% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
Options:
A)$1000
B)$1100
C)$1200
D)$1300
E)$1400
Rationale: 0.8(x-600)=0.6(x-400)
0.2x=480-240
x=1200
The answer is C.
Answer: C
Question: Calculate the percentage gain if a trader bought a bicycle for Rs.440 and sold it for Rs.610?
Options:
A)38.64%
B)39.64%
C)31.64%
D)35.64%
E)34.64%
Rationale: C.P. = 440
S.P. = 610
Gain = 610-440 ---- 170
% Gain => 170/440*100 => 38.64%
Answer:A
Answer: A
Question: A ladder 22 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 3 feet, how many feet will the bottom of the ladder slip?
Options:
A)12.86
B)15
C)18
D)19
E)25
Rationale: 22^2-7^2=435
it means that the height is equal to 20.85.
since the top of the ladder slips down 4 feet, then the height of the wall =20.85-3=17.85
the bottom =sqrt(22^2-17.85^2)=sqrt(484-318.62)=12.86
ans is A
Answer: A
Question: A circular mat with diameter 14 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat?
Options:
A)5/12
B)2/5
C)1/5
D)3/4
E)5/6
Rationale: SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(7)(7)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(41/24)
I hope this is easy to follow, so with some simplification i get (1/8)(12/7) =3/14= (1/5) Answer is C
Answer: C
Question: Which part of an atom has no electrical charge?
Options:
A)q1
B)22
C)72
D)27
E)28
Rationale: Answer: Option B
Answer: B
Question: The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)Rs. 2400
B)Rs. 2200
C)Rs. 2300
D)Rs. 2500
E)Rs. 2600
Rationale: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
A
Answer: A
Question: A company sells two products, L and M. Last year, seventy percent of the units sold were product L, and the price of product L was 25 percent greater than the price of product M. Approximately what percent of the total revenue the company received last year was from the sale of product L?
Options:
A)15%
B)25%
C)35%
D)65%
E)74%
Rationale: Percentage of total units that is product L = 70 %
Price of product L = 25 percent greater than price of product M.
Now , we can consider this as a weighted average scenario .
If the price of both the products L and M was equal , then contribution of product L to total sales would be = 70%
But since , price of product L is greater than M , then contribution of product L to total sales will be greater than 70%
The only option is 74%
Answer E
Answer: E
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 5. The numbers are
Options:
A)12, 24, 30
B)12, 24, 38
C)12, 24, 362
D)5, 10, 15
E)12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 5
\inline \fn_jvn \therefore The numbers are 5, 10, 15
Answer: D) 5, 10, 15
Answer: D
Question: In how many no. between 10 and 40 exactly Two of the digits is 4?
Options:
A)10
B)15
C)35
D)1
E)45
Rationale: It's simple can be solved by elimination of answer choices.
Option B and C are too large, not possible. Even AE are large to have correct choice.
Ans : D
Answer: D
Question: From given equation find the value of x: 2x² + 9x − 5
Options:
A)1
B)1/2
C)1/3
D)2/3
E)2/5
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or −5
B
Answer: B
Question: A garrison of 2000 men has provisions for 40 days. At the end of 20 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement?
Options:
A)1888
B)2766
C)2999
D)2000
E)1712
Rationale: 2000 ---- 40
2000 ---- 20
x ----- 10
x*10 = 2000*20
x = 4000
2000
-------
2000
Answer: D
Answer: D
Question: What is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1?
Options:
A)60
B)70
C)80
D)90
E)100
Rationale: Since 200=2^3*5^2 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200.
We then need to eliminate the 20 numbers that end with 5, that is 5, 15, 25,...,195.
There are a total of 100 - 20 = 80 such numbers between 1 and 200.
The answer is C.
Answer: C
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 4), the remainder is also D. If P/Q = 1020.75 and P/(Q + 4) = 816.6, then which of the following gives the correct set of {D, Q}?
Options:
A){6, 12}
B){6, 15}
C){12, 16}
D){9, 15}
E){15, 24}
Rationale: p/q= d=p/q+4
d= .75 q
d= .6(q+4)
we get d = 12 and q = 16. Answer = C.
Answer: C
Question: A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance T between the two cities?
Options:
A)48
B)72
C)96
D)120
E)192
Rationale: Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance T to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E
Answer: E
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 520. If one of the numbers is 480, then the other is:
Options:
A)13
B)18
C)21
D)24
E)38
Rationale: Other number =	(12 x 520)/480 = 13.
ANSWER :A
Answer: A
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
Options:
A)19
B)18.7
C)19.9
D)21.7
E)22.8
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 36 Paise is given as tax
=> Total tax incurred = 36 Paise = Rs.36/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−36/100−x)6/100 = 36/100
⇒ 6(25 −0.36 −x) = 36
⇒ (25 − 0.36 − x) = 6
⇒ x = 25 − 0.36 − 6 = 18.7
B)
Answer: B