divelab/Sys2Bench huggingface dataset:
Question: Some of the people in Town V are left-handed, some are tall, some are both, and some are neither. In Town Y, three times as many people are left-handed > as are left-handed in Town V, three times as many people are tall as are tall in Town V, three times as many people are both as are both in Town V, but no one is neither. If the total number of people in Town V is four times greater than the total number of people in Town Y, which of the following could be the number of people in Town V who are neither left-handed nor tall?
Options:
A) 23
B) 39
C) 72
D) 143
E) 199
Rationale: Yes, correct answer is indeed D.
{V}={Left} + {Tall} - {Both} + {Neither};
{Y} = 3*{Left} + 3*{Tall} - 3*{Both};
Since the total number of people in Town V is four times greater than the total number of people in Town Y, then:
{Left} + {Tall} - {Both} + {Neither}=4*(3*{Left} + 3*{Tall} - 3*{Both});
{Neither}=11*({Left} + {Tall} - {Both}), which means that # of people in Town V who are neither left-handed nor tall must be a multiple of 11.
Only answer choice D, is a multiple of 11: 143=11*13.
Answer: D.
Answer: D
Question: There are 1000 buildings in a street. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will he need?
Options:
A)190
B)191
C)192
D)193
E)194
Rationale: divide as (1-100)(100-200)....(900-1000)
total 192
ANSWER:C
Answer: C
Question: Seven years ago the average age of a family of 2 members was 22 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
Options:
A)30years
B)33years
C)35years
D)37years
E)40years
Rationale: Explanation:
Average of the family of two numbers
7 years ago = 22
= (22+ 7) * 2 = 36 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 - 36 = 33 years
Answer: Option B
Answer: B
Question: Mr. Sane invested a total amount of 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was 3,620, what was the amount invested in scheme B?
Options:
A)8,000
B)8,600
C)8,150
D)Data inadequate
E)None of these
Rationale: % interest on total amount per annum
= 3620×100/16500×2=362/33%
Now, use Alligation method.
Hence, ratio of amount invested in schemes A and B
= (12 - 362⁄33) : (362⁄33 - 10) = 17 : 16
Hence, amount invested in B = 16×16500/(17+16)=8000
Answer A
Answer: A
Question: A circular box kept around a circular place. If the difference between the circumference of the outer circle and the inner circle is 44m, find the width of the box?
Options:
A)5 m
B)6 m
C)4 m
D)7 m
E)8 m
Rationale: Let radius of the outer circle be R and radius of the inner circle be r.
Circumference of the outer circle =
Circumference of the inner circle =
But,
or, R - r =
Thus, width of the road = 7 m
D
Answer: D
Question: If a number is 35% more than the another, how much % is the smaller number less than the first ?
Options:
A)24%
B)28%
C)16(1/3)%
D)16(4/3)%
E)26%
Rationale: Take a number 100,
Then the other number is 135
% the smaller number is less than the first = [(35/(135)) x 100]% = 26%.
ANSWER:E
Answer: E
Question: Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 12 days. How many additional pipes Q, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
Options:
A) 6
B) 9
C) 10
D) 12
E) 15
Rationale: This is an inverse proportional problem......
5 pipes in 12 days; So for 4 days, it will be = 12 x 5 / 4 = 15
So, Q=15-5 = 10.C
Answer: C
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
Options:
A)65 ways
B)54 ways
C)88 ways
D)14 ways
E)30 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in 3C2 ways.
3 consonants and 2 vowels can be selected in 5C2 .3³C2 ways i.e., 10 * 3
= 30 ways.
Answer:E
Answer: E
Question: If 2 tables and 3 chairs cost Rs, 3500 and 3 tables and 2 chairs cost Rs. 4000, then how much does a table cost ?
Options:
A)500
B)1000
C)1500
D)2000
E)3000
Rationale: Explanation:
Let the cost of a table and that of a chair be Rs. x and Rs, y respectively.
Then, 2x + 3y = 3500 ...(i)
and 3x + 2y = 4000 .....(ii)
solving (i) and (ii) we get x = 1000, y = 500
ANSWER IS B
Answer: B
Question: A boat can move upstream at 25 kmph and downstream at 30 kmph, then the speed of the current is?
Options:
A)5
B)6
C)7
D)2.5
E)9
Rationale: US = 25
DS = 30
M = (35 - 25)/2 = 2.5
Answer: D
Answer: D
Question: Ron has had 3 pay cuts in her salary in the past 6 months. If the first pay cut was 5%, the second pay cut was 10% and the third was 15%. What will be the percentage decrease, if the salary is decreased in a single shot?
Options:
A)29.33%
B)27.33%
C)17.33%
D)27.99%
E)29.33%
Rationale: Let Rs.100 be initial salary.
Salary After 1st decrease, 5% = 95
Salary After 2nd decrease, 10% = 85.5 i.e. reduced by 10 percent of 95
Salary After 3rd decrease, 15% = 72.675 i.e. reduced by 15 percent of 85.5
So if its decreased in single shot =
i = ( ( b - a ) /b ) * 100
=27.33%
ANSWER:B
Answer: B
Question: tipli and pikli are a married couple (dont ask me who he is and who she is)
They have two children, one of the child is a boy. Assume safely that the probability of each gender is 1/2.
What is the probability that the other child is also a boy?
Hint: It is not 1/2 as you would first think.
Options:
A)1/1
B)1/2
C)1/3
D)1/4
E)1/5
Rationale: Solution:
1/3
This is a famous question in understanding conditional probability, which simply means that given some information you might be able to get a better estimate.
The following are possible combinations of two children that form a sample space in any earthly family:
Boy - Girl
Girl - Boy
Boy - Boy
Girl - Girl
Since we know one of the children is a boy, we will drop the girl-girl possibility from the sample space.
This leaves only three possibilities, one of which is two boys. Hence the probability is 1/3
Answer C
Answer: C
Question: Find the sum of the following series,
1,4/5,16/25,64/125 ……………..
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: It is a G.P with infinite terms. The common ratio is (4/5) and this is less than 1. The sum to infinity of a series with first term ‘a ‘ and common ratio ‘r’ =[ a/( 1-r) ], The sum to infinity = 1/ (1 – 4/5 ) = 5
ANSWER:C
Answer: C
Question: Evaluate combination
97C95=97/(95)!(2)!
Options:
A)4656
B)5176
C)4176
D)3176
E)None of these
Rationale: Explanation:
nCr=n!/(r)!(n−r)!
97C95=97!/(95)!(2)!
=97*96*95!/(95)!(2)!
=97*96/2∗1
=4656
Option A
Answer: A
Question: A sum of money is to be distributed among A, B, C, D in the proportion of
5 : 2 : 4 : 3. If C gets Rs. 500 more than D, what is A's share?
Options:
A)Rs. 2500
B)Rs. 1000
C)Rs. 1500
D)Rs. 2000
E)NOne
Rationale: Sol.
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 500 ⇔ x = 500.
∴ A's share = Rs. 5x= Rs. (5x500) = Rs. 2500.
Answer A
Answer: A
Question: How many four letter words are formed using the letters of the word SHORT?
Options:
A)95
B)100
C)115
D)110
E)120
Rationale: The number of letters in the given word is five.
The number of four letter words that can be formed using these five letters is 5P4
= 5 * 4* 3* 2 = 120.
Answer: E
Answer: E
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 80, what is the value of c âˆ’ a?
Options:
A)25
B)70
C)90
D)140
E)It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=160 --2
subtracting 1 from 2 we have
c-a=70;
ANSWER:B
Answer: B
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Options:
A)Rs. 4991
B)Rs. 4993
C)Rs. 4997
D)Rs. 4999
E)Rs. 5000
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
Option A
Answer: A
Question: On increasing the number of lines in a page by 110, they become 240. What is the % of increase in the no. of lines in the page?
Options:
A)20%
B)305
C)50%
D)55%
E)84.6%
Rationale: Explanation : Number of pages increased = 110
Now , the number of pages of book = 240
Number of pages of the books before increase = 240 – 110 = 130
% increase in the number of pages in the book = 110 /130
x 100% = 84.6%
E
Answer: E
Question: The amount of principal Rs.8000 at compound interest at the ratio of 5% p.a. for 3 years is
Options:
A)Rs.9621
B)Rs.6921
C)Rs.9261
D)Rs.6261
E)Rs.6361
Rationale: c.i=p(1+r/100)^n
=8000(1+5/100)^3
=8000(21/20*21/20*21/20)
=Rs9261
ANSWER:C
Answer: C
Question: The present worth of Rs.676 due in 2 years at 4% per annum compound interest is
Options:
A)Rs.150.50
B)Rs.154.75
C)Rs.156.25
D)Rs.625
E)None
Rationale: Solution
Present Worth	= Rs.[676/(1+4/100)²]
= Rs.(676x25/26x25/26)
= Rs.625
Answer D
Answer: D
Question: If 0.75: x :: 5:6, then x is equal to:
Options:
A)1.12
B)1.16
C)1.2
D)0.9
E)None of these
Rationale: Explanation:
(x * 5) = (0.75 *6)
X=4.5/5 = 0.9
Answer: D
Answer: D
Question: A 40-liter solution of alcohol and water is 5 percent alcohol. If 5.5 liters of alcohol and 4.5 liters of water are added to this solution, what percent of the solution produced is alcohol?
Options:
A)9%
B)11%
C)13%
D)15%
E)17%
Rationale: The percent of alcohol in the solution is (0.05(40) + 5.5) / 50 = 7.5/50 = 15%
The answer is D.
Answer: D
Question: If a-b= 3 and a^2+b^2=29, find the value of ab
Options:
A)10
B)12
C)15
D)18
E)19
Rationale: 2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
=> ab = 10.
ANSWER:A
Answer: A
Question: A sum of money deposited at C.I. amounts to Rs.2560 in 3 years and to Rs.2989 in 4 years. Find the rate percent?
Options:
A)30%
B)10%
C)20%
D)16%
E)50%
Rationale: 2560 --- 429
100 --- ? => 16%
Answer: D
Answer: D
Question: Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 15 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 15 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 15jars?
Options:
A)15n/225-mn
B)m
C)n
D)m+n
E)M-n
Rationale: working rate p = 15/m ; working rate pq =( 1/p +1/q)* n =15 or mn/15 +n/q =15 0r n/q = 15-mn/15 = 225-mn/15
q = 15n/225-mn
A
Answer: A
Question: Mike earns $14 per hour and Phil earns $12 per hour. Approximately how much less, as a percentage, does Phil earn than Mike per hour?
Options:
A)25%
B)32.5%
C)14%
D)37.5%
E)40%
Rationale: What % less of 14 is 12
let it be x % less ,then
=14(1-x/100)=12
1-x/100=12/14
x=100/7
x=14%
Ans C
Answer: C
Question: How many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph?
Options:
A)22 sec
B)27 sec
C)25 sec
D)24 sec
E)11 sec
Rationale: Explanation:
D = 100 + 120 = 220
S = 36 * 5/18 = 10 mps
T = 250/10 = 22 sec
Answer: Option A
Answer: A
Question: A certain industrial loom weaves 0.13 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 15 meters of cloth?
Options:
A)114
B)115
C)116
D)117
E)118
Rationale: Let the required number of seconds be x
More cloth, More time, (direct proportion)
Hence we can write as
(cloth) 0.13 : 15 :: 1 : x
=>0.13*x=15
=>x=15/0.13
=>x=115
ANSWER:B
Answer: B
Question: 25 onions on a scale weigh 5.12 kg. When 3 onions are removed from the scale, the average weight of the 22 onions is 200 grams. What is the average weight (in grams) of the 3 onions which were removed?
Options:
A)200
B)220
C)240
D)260
E)280
Rationale: 22*200=4400.
The other 3 onions weigh a total of 720 grams.
The average weight is 720/3 = 240 grams.
The answer is C.
Answer: C
Question: What approximate value should come in place of the question mark (?) in the following equation?
2.542 × 2408.69 + 1134.632 = ?
Options:
A)4600
B)4800
C)5200
D)6400
E)7200
Rationale: Explanation 6100 + 1100 = 7200
Answer E
Answer: E
Question: From the sale of sleeping bags, a retailer made a gross profit of 14% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
Options:
A)3.0
B)3.36
C)24.56
D)25.0
E)31.36
Rationale: Cost price * 1.14 = Selling price --> Cost price * 1.14 = $28 --> Cost price = $24.56.
Answer: C.
Answer: C
Question: 275, 132, 462, 396, 327, 891, 121
Options:
A)327
B)228
C)2768
D)028
E)272
Rationale: Explanation:
In each number except 327, the middle digit is the sum of the other two.
ANSWER: A
Answer: A
Question: When 3 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
Options:
A)32
B)81
C)60
D)27
E)90
Rationale: Explanation:
Let the number be
3 + 1/2[1/3(a/5)] = a/15
=> 3 = a/30 => a = 90
Answer:E
Answer: E
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)280
B)999
C)277
D)277
E)288
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer: A
Answer: A
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
Options:
A)12 1/2
B)12 1/5
C)12 1/9
D)12 1/3
E)12 1/1
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 1/2 years.Answer: A
Answer: A
Question: A group of four Womens and three Mens have tickets for seven adjacent seats in one row of a theater. If the three mens will not sit in three adjacent seats, how many possible different seating arrangements are there for these 7 theatre-goers?
Options:
A)7! – 5!3!
B)7! – 4!3!
C)7 × 2!3!2!
D)7! – 2!3!
E)2!3!2!
Rationale: There are 3 boys and 4 girls , we want to calculate the seating arrangements if three mens do not sit together, like MMM.
Let's calculate the # of arrangements when they SIT together and subtract from total # of arrangements of these 7 persons without restriction. Thus we'll get the # of arrangements asked in the question.
1. Total # of arrangements of 7 is 7!.
2. # of arrangements when 3 mens are seated together, like MMM;
Among themselves these 3 boys can sit in 3! # of ways,
Now consider these 3 boys as one unit like this {MMM}. We'll have total of 5 units: {MMM}{W}{W}{W}{W}. The # of arrangements of these 5 units is 5!.
Hence total # of arrangements when 3 men sit together is: 3!5!.
# of arrangements when 3 mens do not sit together would be: 7!-3!5!.
Answer: A).
Answer: A
Question: In an election between two candidates first candidate got 60% of votes polled and second Candidate got 240 votes. The total number of votes polled was?
Options:
A)votes
B)votes
C)votes
D)votes
E)votes
Rationale: Total = 100 %,
First person got 60%
second person got remaining 40 % of votes.
than 40 % = 240
40% = 40×7 = 240
100% =100×7 =700 votes
A)
Answer: A
Question: Thirty percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the women are science majors if 40% of the class are men?
Options:
A)2%
B)5%
C)28%
D)30%
E)45%
Rationale: 3/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have - 0.3 * 60 = 18
[Non-Science-Women] will have - 42
[Science-Men] will have = 20-18 = 2
S0 18/60 * 100 = 30%
Answer - D
Answer: D
Question: The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160.The time after which it is due is :
Options:
A)6 months
B)8 months
C)9 months
D)10 months
E)None
Rationale: Solution
P.W = Rs.(1760 - 160)= Rs.1600. ∴ S.I. on Rs.1600 at 12% is Rs.160. ∴ Time =(100x160/1600x12 ) = 5/6years = ( 5/6x12) months = 10 months
Answer D
Answer: D
Question: Albert invested amount of 24000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Albert will get on the maturity of the fixed deposit
Options:
A)Rs. 8510
B)Rs. 26460
C)Rs. 8730
D)Rs. 8820
E)None of these
Rationale: Explanation:
=>(24000×(1+5/100)2)
=>24000×21/20×21/20
=>26460
Option B
Answer: B
Question: In a business A and C invested amounts in the ratio 2 : 1. Whereas the ratio between amounts invested by A and B was 3 : 2. If 1,57,300 was their profit, how much amount did B receive?
Options:
A)72,600
B)48,400
C)36,300
D)24,200
E)None of these
Rationale: Ratio A : B = 3 : 2 and A : C = 2 : 1
\ A : B : C = 6 : 4 : 3
Profit share of B = 4 × 1,57,300 = 48400
Answer B
Answer: B
Question: On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out
sand-dunes, 1 has treasure and only 3 out of 5 sand dunes formed have lucky coupons. Find
the probability that the blown-out sand dune will contain both the things.
Options:
A)2/25
B)4/75
C)7/75
D)3/5
E)4/5
Rationale: Probability of sand dune blown out = 2/3
Probability that it has treasure = 1/5
Probability that it has lucky coupon = 3/5
total probability = 2/3 * 1/5 * 3/5 = 2/25
ANSWER:A
Answer: A
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Options:
A)111.12
B)188.93
C)111.17
D)111.89
E)131.12
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9
= 888.88 m.
B can give C = 1000 - 888.88
= 111.12 m.
Answer:A
Answer: A
Question: Angelina walked 840 meters from her home to the grocery at a constant speed. She then walked 480 meters to the gym at double the speed. She spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym?
Options:
A)2
B)3
C)4
D)16
E)30
Rationale: let the speed be X...
so time taken from home to grocery= 840/x..
the speed to gym = 2x..
so time taken = 480/2x=240/x..
its given 840/x-240/x=40..
600/x=40..
x=15m/secs..
so grocery to gym=2*15=30m/s...
E
Answer: E
Question: A radio station has to choose seven days of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?
Options:
A)9
B)15
C)1
D)35
E)56
Rationale: Behind the story, we are really being asked to evaluate 7C7. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C7, the third entry of the seventh row, is 1. Answer = C.
Answer: C
Question: A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. Whatis the profit %?
Options:
A)120%
B)145%
C)145.6%
D)166.66%
E)167%
Rationale: Let the cost price of 1 litre pure milk be Re.1, then
\inline{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}{6litres(milk)→CP=Rs.62litres(water)→CP=Rs.0}\rightarrow CP=Rs.6 only
and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16
Profit %= 166.66%
D
Answer: D
Question: Given that m/m < 1, and both m and n are positive integers, which one of the following must be greater than 1?
Options:
A)m/n^2
B)m^2/n
C)m^2/n^2
D)n/m
E)√(m/n)
Rationale: Since m/n is a fraction n must always be > 1
Given -
Which one of the following must be greater than 1
We can get the result one only when the denominator in m/n ( Which is less than 1 ) becomes numerator..
Among the given options only (D) has the required characteristic we are looking for...
Hence answer will be (D)
Answer: D
Question: A ball is bought for Rs.400 and sold at a gain of 20% find its selling price?
Options:
A)Rs.480/-
B)Rs.490/-
C)Rs.500/-
D)Rs.520/-
E)Rs.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
A
Answer: A
Question: A rectangular box has two sides whose
lengths are 3 centimeters and 9 centimeters
and a volume of 135 cm3. What is the area
of its largest side?
Options:
A)27 cm2*square
B)36 cm2*square
C)39 cm2*square
D)45 cm2*square
E)48 cm2*square
Rationale: The box has dimensions of 3 and 9 and a volume of 135, so plug these values into the
formula for the volume of a box:
V=lwh=>
135=(3)(9)h=>
135=27h=>
5h
So the remaining dimension of the box is 5. The two longest dimensions are 5 and 9, so the
area of the largest side is 5 × 9 = 45
correct answer D)45 cm2*square
Answer: D
Question: Abinaya had 100 currency notes in all, some of which are of Rs 80 denomination and the remaining of Rs 50 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 50?
Options:
A)96
B)90
C)98
D)100
E)95
Rationale: Let the number of 50-rupee notes = x
Then, the number of 80-rupee notes = (100 – x)
50x + 80(100 – x) = 5000 : x = 100
ANSWER:D
Answer: D
Question: Father’s age is three years more than three times the son’s age.
After three years, father’s age will be ten years more than twice the son’s age.
What is the father’s present age.
Options:
A)31
B)32
C)33
D)34
E)35
Rationale: F = 3S +3
F+3 = 10 + 2*(S+3)
3S+3 +3 = 10+2S+6
S = 10 yrs
F= 3+30=33 years
ANSWER:C
Answer: C
Question: Find the simple interest on $10000 at 6% per annum for 12 months?
Options:
A)$410
B)$500
C)$600
D)$710
E)$1000
Rationale: P = $10000
R = 6%
T = 12/12 YEARS = 1 YEAR
S.I. = P*R*T/100 = 10000*6*1/100 = $600
Answer is C
Answer: C
Question: The juice stall at the circus stocked just 2 brands of orange juice tetra packs. Brand A costs $1 per pack and brand B costs $1.5 per pack. Last week , brand A contributed to x% of stall’s revenue and accounted for y% of sales of juice tetra packs. Which of the following expresses x in terms of y?
Options:
A)100y/(150 – y)
B)200y/(250-y)
C)200y/(300-y)
D)250y/(400-y)
E)300y/(500-y)
Rationale: 1. Let the number of units sold be 100. Then y units of A are sold and (100-y) units of B are sold.
Total revenue= Revenue due to A + Revenue due to B
= (No.of units of A sold * Cost/unit of A) + (No.of units of B sold * cost/unit of B)
= y *1 + (100-y) *1.5
= y + (150-1.5y) --- (1)
2. But we know, revenue due to A = x%. of the total revenue --- (2)
3. To express x in terms of y we need to relate (1) and (2)
4. x% = y / ( y + (150-1.5y))
or x= 100y / 150-0.5y = 200y/(300-y)
C
Answer: C
Question: In a hostel there were 100 students. To accommodate 45 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
Options:
A)A)Rs.5800
B)B)Rs.5480
C)C)Rs.2900
D)D)Rs.5900
E)E)Rs.5430
Rationale: 100x + 400
= 145(x – 5)
x = 25
100 * 25 + 400
= 2900
Answer:C
Answer: C
Question: If log10 2 = 0.3010, the value of log10 80 is:
Options:
A)1.903
B)1.603
C)1.758
D)1.205
E)1.3056
Rationale: log10 80	= log10 (8 x 10)
= log10 8 + log10 10
= log10 (2^3 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER A
Answer: A
Question: If x = 3^9 and x^x = 3^k, what is k?
Options:
A)3^11
B)3^13
C)3^25
D)3^27
E)3^81
Rationale: Solution:
We know that x=3^9
which implies x^x = (3^9)^(3^9) = 3^(9 * 3^9) [because (x^y)^z = x^(y*z))]
so 3^(3^2 * 3^9) = 3^(3^(2+9)) [because x^a * x^b = x^(a+b)]
therefore x^x = 3^(3^11)
Given that x^x=3^k
so 3^(3^11) = 3^k
Since the base is same the exponent will also be same
therefore k = 3^11
Answer: A
Answer: A
Question: Robert's salary was decreased by 20% and subsequently increased by 20%. how much percentage does he lose?
Options:
A)4%
B)20%
C)25%
D)30%
E)50%
Rationale: let original salary be $100
Salary after decreasing 20% = 100 - 100 x 20/100 = $80
Salary after increasing 20% on $80 = 80 + 80 x 20/100 = $96
Percentage of loss = 100 - 96 = 4%
Answer : A
Answer: A