divelab/Sys2Bench huggingface dataset:
Question: What should be the minimun mark up percentage such that after giving the discount of 200/3% ., there will neither a loss nor a profit ?
Options:
A)133.3%
B)100%
C)neither gain nor loss
D)200%
E)120%
Rationale: Let CP = 100.
Discount = 200/3%.
Let 200% was the mark up.
MP = 100 + 200% of 100 = 300.
Now, after discount
300 - (200/3)% of 300
= 300 - 200 = 100.
So, in transaction neither gain nor loss occurs.
ANSWER - OPTION C
Answer: C
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20% ?
Options:
A)30 %
B)25 %
C)15 %
D)20 %
E)23 %
Rationale: Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
ANSWER IS D
Answer: D
Question: If a population of women in a town is 60% of men . What is the population of men as a % of population of women ?
Options:
A)A)200%
B)B)100%
C)C)50%
D)D)65%
E)E)166%
Rationale: We're told that the number of Women in a town is equal to 60% of the number of Men in that town.
IF....
Men = 10
Women = 6
We're asked for the number of Men, as a percentage of the number of Women.
M/W = 10/6 = 5/3 = 166%
Answer is E
Answer: E
Question: In the set of positive integers from 1 to 100, what is the sum of all the odd multiples of 5?
Options:
A)180
B)245
C)320
D)405
E)500
Rationale: reduce 1 - 100
5 - 15 - 25 - 35 - 45 --55--65--75--85--95 are valid multiples. Add them -->500
E
Answer: E
Question: What is the unit digit in (632)^179×(615)^316×(341)^476
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: unit digit in (632)179
= unit digit in (4)1797
= unit digit in [(42)898 × 4]
= unit digit in [16898 × 4]
= unit digit in (6 × 4)
= 4
unit digit in (615)316
= unit digit in (5)316
= 5
unit digit in (341)476
= unit digit in (1)476
= 1
Hence, unit digit in (6324)1797 × (625)316 × (341)476
= unit digit in [4 × 5 × 1]
= 0
A
Answer: A
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
A)33/96
B)33/91
C)33/67
D)33/28
E)33/19
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is
= ¹²C₄/¹⁵C₄
= (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12)
= 33/91
Answer: B
Answer: B
Question: Find the sum of all 2 digit numbers divisible by 3.
Options:
A)16387
B)26787
C)1267
D)1665
E)1781
Rationale: Explanation:
No explanation is available for this question!
ANSWER:D
Answer: D
Question: If the simple interest on a certain sum of money after 3 1⁄8 years is 1⁄4 of the principal, what is the rate of interest per annum?
Options:
A)6%
B)4%
C)8%
D)5%
E)12%
Rationale: Explanation :
Let the the sum of money(P) be Rs.x
Time(T) = 3 1⁄8 Years = 25⁄8 Years
Simple interest (SI) = x⁄4
Rate of interest per annum(R) = 100×SI/PT=100×x/4/x × 25/8
=100× x ×8/4× x × 25
=8%
Answer : Option C
Answer: C
Question: If 0.75 : x :: 5 : 8, then x is equal to:
Options:
A)1.25
B)1.62
C)2.0
D)1.21
E)1.2
Rationale: (x x 5) = (0.75 x 8)
x = 6/5 = 1.20
ANSWER E
Answer: E
Question: The difference between the place values of 6 and 1 in the number 527631 is
Options:
A)596
B)587
C)533
D)568
E)599
Rationale: Sol.= (Place value of 6) – (place Value of 1)= (600 - 1)= 599 Answer E
Answer: E
Question: Enrollment in City College in 1980 was 83 1/3 percent of enrollment in 1990. What was the percent increase in the college’s enrollment from 1980 to 1990?
Options:
A)10%
B)16 2/3 %
C)20%
D)25%
E)183 1/3%
Rationale: Let 100 is the enrollment in 1990.
Enrollment in 1980= 83.3
% increase= (Increase from 1980 to 1990)/Enrollment in 1983
=>16.7*100/83.3 =20%
ANSWER:C
Answer: C
Question: Mary is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of white, 3 morsels of wheat, and 1 morsel of rye. The pattern repeats after she leaves the morsel of rye. If Mary drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
Options:
A)rye − white − white
B)white − white − wheat
C)wheat − rye − white
D)wheat− wheat − wheat
E)wheat − wheat− rye
Rationale: In a single round Mary drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Answer: A
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Options:
A)32 years
B)36 years
C)40 years
D)48 years
E)45 years
Rationale: let the age be x
2/5x=x (2/5 the age of son = mothers age)
after 8 yrs
2/5x+8=x+8/2
4=x/10
x=40.
ANSWER:C
Answer: C
Question: Express a speed of 36 kmph in meters per second?
Options:
A)10 mps
B)14 mps
C)18 mps
D)19 mps
E)11 mps
Rationale: 36 * 5/18 = 10 mps
Answer: A
Answer: A
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)9:9
B)9:8
C)9:4
D)9:1
E)9:2
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: B
Question: How many different possible arrangements D can be obtained from the letters G, M, A, T, I, I, and T, such that there is at least one character between both I's?
Options:
A)360
B)720
C)900
D)1800
E)5040
Rationale: Total ways for arranging without restriction = 7!/ (2!2!) { 2! is becoz of two T's and other 2! for two I's)
Restriction : atleast one character between I's = Possible ways - both I's together i.e.o character between I's
_ _ _ _ _ (I I)
Both I's Together = 6! (Assuming 2 I's as one unit) /2!(for 2 T's) * 2! (No of arrangements of 2 I's)/2! (for 2 I's)
=6!/2!
Therefore ans D= 7!/ (2!2!) -6!/2! = 900
HENCE C.
Answer: C
Question: Each of the integers from 1 to 14 is written on the a seperate index card and placed in a box. If the cards are drawn from the box at random without replecement, how many cards must be drawn to ENSURE that the product of all the integers drawn is even?
Options:
A)19
B)12
C)11
D)10
E)8
Rationale: Out of the 14 integers: 7 are odd and 7 are even.
If we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number. In the worst case:
1. we will end up picking odd numbers one by one, so we will pick all 7 odd numbers first
2. 8th number will be the first even number
So we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even.
So, answer will be 8. (E)
Answer: E
Question: A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel 1.1 km long. How many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
Options:
A)1.0
B)1.2
C)1.4
D)1.6
E)1.8
Rationale: 72 km/hr = 1.2 km/min
The total distance is 1.2 km.
1.2 / 1.2 = 1 minute
The answer is A.
Answer: A
Question: A tour group of 25 people paid a total of $620 for entrance to a museum. If this price included a 5% sales tax, and all the tickets cost the same amount, what was the face value of each ticket price without the sales tax?
Choices
Options:
A)$22
B)$23.56
C)$24
D)$25.20
E)$30
Rationale: B.
Answer: B
Question: Will is 7 years older than Judy while George is 5 years younger than Judy. What is the age of Judy, If the sum of all of their ages is 32 years?
Options:
A)17 years
B)20 years
C)10 years
D)15 years
E)19 years
Rationale: Let Judy's age be x, Will's age be x+7 and George's age be x-5
x + x+7 + x-5 = 32
x = 10
Judy's age is 10 years
Answer : C
Answer: C
Question: Which of the numbers 1, 2, 3, 4, or 5 is nearest in value to the sum
2007/2999+8001/5998+2001/3999=?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The sum is a little more than (2/3) + (8/6) + (2/4) = 2.5.
correct answer C
Answer: C
Question: A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Options:
A)Rs.4000
B)Rs.1000
C)Rs.1250
D)Rs.2000
E)Rs.3000
Rationale: Explanation:
P(11/10)4 - P(6/5)2 = 482
P = 2000
ANSWER IS D
Answer: D
Question: If in a triangle, the area is numerically equal to the perimeter, then the radius of the inscribed circle of the triangle is
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Solution
Radius = Area / Semi perimeter
= [Area x 2 / Area]
= 2.
Answer B
Answer: B
Question: A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?
Options:
A)66 days
B)88 days
C)24 days
D)55 days
E)77 days
Rationale: B = 1/8 – 1/2 = 1/24 => 24 days
Answer:C
Answer: C
Question: A seven-digit phone number is divisible by 9. After adding the two digits of the area code the number is not divisible by 9, which of the following cannot be the area code?
Options:
A)07.
B)06.
C)05.
D)04.
E)09.
Rationale: Given that 7 digit number is divisible by 9
we know any number will not be divisible by 9 if the sum of all digits of the number is not the multiple of 9.
Hence looking at the option we can say that the number that should be added to the seven digit number must be 09 as adding it will make it divisible by 9... hence answer is E
Answer: E
Question: A chair is bought for Rs.200/- and sold at Rs.310/- find gain or loss percentage
Options:
A)15% loss
B)20% gain
C)25% gain
D)30% gain
E)55% gain
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (310- 200)/200= 55% gain
E
Answer: E
Question: If the average (arithmetic mean) of x + 1, x + 5, and x + 9 is 0, then x =
Options:
A)–5
B)–4
C)–2
D)–1
E)0
Rationale: (x+1 + x+5 + x+9)/3 = 0
=>3x + 15 = 0
=>x = -5
Answer A
Answer: A
Question: If each of 3 digit code is formed of integers from 1 to 30, inclusively, and each of the digits are different, how many possible codes are there?
Options:
A)22896
B)25423
C)26980
D)24698
E)24360
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 30 possibilities
Second digit can have 29 possibilities
Third digit can have 28 possibilities
Total number of possible codes = 30*29*28 = 24360
Answer: E
Answer: E
Question: One side of a triangle has length 6 and a second side has length 5. Which of the following could be the area of the triangle?
I. 20
II. 15
III. 5
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I, II and III
Rationale: The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 6 and 5 are the base and height of triangle .
Area = 1/2 * 6 * 5 = 15
There is no lower limit on the area of any triangle whose only 2 sides are known.
Then 0 < Area <= 15
The answer is D.
Answer: D
Question: a is the product of each integer from 1 to 50, inclusive and b=100^k, where k is an integer . What is the greatest value of k for which y is a factor of a?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*50 = 50!
No. of trailing zeros in 50! = 50/5 + 50/5^2 = 10+2 = 12
100^k = 10^2k → k = 12/2 = 6
A
Answer: A
Question: On what sum will the compound interest for 2 1⁄2 years at 10% amount to Rs. 31762.5?
Options:
A)Rs.5000
B)Rs.20000
C)Rs.25000
D)Rs.30000
E)Rs.50000
Rationale: Explanation:
P(1+10/100)^2×(1+1/2×10/100))=31762.5
P(11/10)^2×(21/20)=31762.5
P=31762.5×20×10×10/21×11×11=1512.5×20×10×10/11×11
=137.5×20×10×10/11
=12.5×20×10×10=Rs. 25000
Answer : Option C
Answer: C
Question: If 10,000 microns = 1 decimeter, and 1,000,000angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)100
B)10,000
C)100,000
D)0.01
E)0.0001
Rationale: 10,000 microns = 1 decimeter, and 1,000,000angstroms = 1 decimeter
10,000 microns = 1,000,000 angstroms
1 micron = 100
Answer : A
Answer: A
Question: What least number must be subtracted from 2000 to get a number exactly divisible by 17 ?
Options:
A)9
B)8
C)5
D)11
E)15
Rationale: On dividing 2000 by 17, we get 11 as remainder.
Required number to be subtracted = 11
Answer D
Answer: D
Question: In how many ways can the letters of the word RAVES be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)60
B)30
C)120
D)240
E)90
Rationale: Two letters can be arranged in 2! ways.
only one combination EIU is required.
5 letters can be arranged in 5! ways.
thus 5!/ 2! * 1 = 60.
A
Answer: A
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)320$
B)380$
C)411$
D)450$
E)480$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 50 ) = 21 + 390 => 411
Hence answer will be (C) 411
Answer: C
Question: If the function Q is defined by the formula Q = 5w/(4d(z^2)), by what factor will Q be multiplied if w is quadrupled, d is doubled, and z is tripled?
Options:
A)1/9
B)2/9
C)4/9
D)3/9
E)2/27
Rationale: We just need to find the factor thats all,
w -> quadrupled -> 4w
d-> doubled -> 2d
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
W is in numerator, and d*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B
Answer: B
Question: Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 25 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes riding at 15 km per hour?
Options:
A)20
B)40
C)60
D)80
E)100
Rationale: Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 25 minutes, Sam rides 5 km so Sam will be 3 km ahead.
It will take Annie 60 minutes to catch Sam.
The answer is C.
Answer: C
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 3, and 6, if the digits are allowed to repeat within a number?
Options:
A)6660
B)7770
C)8880
D)9990
E)10,110
Rationale: The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 3, and 6 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(333) + 9(666) = 9,990
The answer is D.
Answer: D
Question: A shop owner sells 100 lemons and gains SP of 40 lemons. Find the gain %?
Options:
A)62 2/3%
B)64 2/3%
C)66 2/3%
D)66 5/3%
E)68 2/3%
Rationale: Gain=40 lemonsTotal 100 lemonsCP 100-40=60(40/60)*100=66 2/3%Ans C
Answer: C
Question: James went on a diet 12 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 190 pounds?
Options:
A) 3
B) 3.5
C) 4
D) 4.5
E) 5
Rationale: 222 - 198 = 24 pounds lost in 12 months
24/12 = 2, so Joe is losing weight at a rate of 2 pounds per month.
...in approximately how many months will he weigh 190 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 196 lbs
In 2 months: 194 lbs
In 3 months: 192 lbs
In 4 months: 190 lbs
Answer: C
Answer: C
Question: You and your friend spent a total of $17 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?
Options:
A)$9
B)$3
C)$4
D)$10
E)$5
Rationale: My lunch = l, my friends lunch = l+3
(l)+(l+3)=17
l+l+3-3=17-3
2l=14
l=7
My friends lunch l+3 = 7+3=$10, the answer is D
Answer: D
Question: There are 4 red chips and 2 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
Options:
A)A)10
B)B)12
C)C)24
D)D)50
E)E)100
Rationale: Using anagram method:
6_5_4_3_2_1
R_R_R_R_B_B
so..
6!/Number of repeated letters (4!)(2!) = 5
ANS:D
Answer: D
Question: If a is a positive integer and a^2 is divisible by 12, then the largest positive integer that must divide a ^3 is
Options:
A) 2^3
B) 2^6
C) 3^3
D) 6^3
E) 12^2
Rationale: Since a is an integer so a cannot have a 2 and sqrt 3 (because squaring this will give us a 2^2 and 3 (making the product as 12, and making a^2 as a multiple of 12))
a^2 is divisible by 12 (12 = 2*2*3), So, a should have at least one 2 and one 3 so that a^2 has a 2^2 and two 3
So, a will have a 2 and a 3. Or a will be a multiple of 6
So, largest possible integer than should divide a^3 is 6^3
So, Answer will be D
Answer: D
Question: Andy has 20 pairs of matched gloves. If he loses 15 individual gloves, which of the following is NOT a possible number of matched pairs he has left?
Options:
A)9
B)11
C)13
D)14
E)15
Rationale: We can solve this is second. The question isSelect an answer choice where there is no possibility of having a number as a matched pair
Case1: If 15 gloves are gone the maximum probability of losing maximum gloves is 15 pairs of gloves out of 20. This means i m having 5 pairs of gloves. [Minimum number of gloves i can have is 5 pairs]
Case2: If 15 gloves are gone the maximum probability of losing minimum gloves is 15/2 = 7.5 means i can lose 8 glove. in this scenario i will be having 12 gloves.
Hence10 < Available Glove Pair < 13
any given time I cant possess 13 glove pair for the above mentioned scenario. And thats the answer. C.
Answer: C
Question: By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .
Options:
A)20%
B)30%
C)40%
D)50%
E)60%
Rationale: (SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%
ANSWER D
Answer: D
Question: Mrs. Rodger got a weekly raise of $149. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A)$140
B)$141
C)$142
D)$149
E)$145
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 149.
So after completing the 1st week she will get $ (x+1495).
Similarly after completing the 2nd week she will get $ (x + 149) + $ 149.
= $ (x + 149 + 149)
= $ (x + 298)
So in this way end of every week her salary will increase by $ 149.
correct answer D)$149
Answer: D
Question: R is the set of positive odd integers less than 200, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
Options:
A) None
B) Two
C) Four
D) Five
E) Seven
Rationale: R is the set of positive odd integers less than 200, and S is the set of the squares of the integers in R.
How many elements does the intersection of R and S contain?
R=1,3,5,7,9,11,13,15...
S=1,9,25,49,81...
Numbers: 1, 9, 25, 49, 81, 121, and 169 are odd integers (less than 200) that are in both sets.
Solution: Seven
Answer: E
Answer: E
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
A)Rs.345
B)Rs.270
C)Rs.275
D)Rs.324
E)Rs.325
Rationale: I = (500*9*6)/100 = 270
Answer :B
Answer: B
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
Options:
A)15 5/15%
B)18 2/11%
C)16 2/3%
D)30%
E)40%
Rationale: Explanation:
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer IS B
Answer: B
Question: If a(a - 6) = 27 and b(b - 6) = 27, where a ≠ b, then a + b =?
Options:
A)6
B)−2
C)−48
D)46
E)48
Rationale: i.e. if a =-3 then b = 9
or if a = 9 then b =-3
But in each case a+b = -3+9 = 6
Answer: option A
Answer: A
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
Options:
A)2:00pm, 206 km
B)2:00pm, 220 km
C)2:00pm, 200 km
D)2:00pm, 208 km
E)2:00pm, 230 km
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed
= 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50
= 200 km away from Mumbai.
Answer: C
Answer: C
Question: One day when Ram was walking on the street, one boy requested him to donate for cancer patients welfare fund. He gave him a rupee more than half the money he had. He walked a few more steps. Then came a girl who requested him to donate for poor people's fund for which he gave two rupees more than half the money he had then. After that, again a boy approached him for an orphanage fund. He gave three rupees more than half of what he had. At last he had just one rupee remaining in his hand.How much amount did Ram have in his pocket when he started?
Options:
A)Rs.72
B)Rs.58
C)Rs.35
D)Rs.42
E)Rs.52
Rationale: Last he had 1 rupee,when he gave to boy 3 rupees more than half so it written as (1+3)*2 similarly remaining
i.e. (((1+3)2+2)2+1)2=42
ANSWER:D
Answer: D
Question: A positive number x is multiplied by 2, and this product is then divided by 4. If the positive square root of the result of these two operations equals x, what is the value of x ?
Options:
A) 9/4
B) 3/2
C) 4/3
D) 2/3
E) 1/2
Rationale: We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^2
3x^2 – 2x = 0
x(3x – 2) = 0
x = 0 or
3x – 2 = 0
3x = 2
x = 9/4
Because x is positive, x = 9/4. The answer is A.
Answer: A
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
Options:
A)1 : 1
B)2 : 3
C)5 : 2
D)4 : 3
E)9 : 5
Rationale: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 4 and 2 parts, respectively.
This will give us in the final mixture (5 + 4) : (3 + 2), which means 9:5
Answer E.
Answer: E
Question: A company has 4 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?
Options:
A)500
B)120
C)4500
D)25
E)55
Rationale: atleast one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(4c1*5c4) + (4c2*5c3) + (4c3*5c2) = 120;
Hence B.
Answer: B
Question: A group of five women and three men have tickets for seven adjacent seats in one row of a theatre. If the three men will not sit in three adjacent seats, how many possible different seating arrangements are there for these 8 theatre-goers?
Options:
A) 7! – 2!3!2!
B) 7! – 4!3!
C) 8! - 6!3!
D) 7 × 2!3!2!
E) 2!3!2!
Rationale: 8 people can sit in 8! different ways. But because 3 men cannot sit together, we take them as a unit.
This unit of men, among themselves can sit in 3! ways.
Hence, 8! - 3!.
This unit of men along with 5 women can sit in 6! different ways which also needs to be eliminated.
Hence 8! - 6!3!
C
Answer: C
Question: (2+√3+√5)^2-(√3+√5)^2=?
Options:
A)1+2√3+2√5
B)4+4√3+4√5
C)1-√3+√5
D)1+√3-√5
E)√3+√5
Rationale: (2+√3+√5)^2-(√3+√5)^2
(2+√3)^2 + 5 +2 (2+√3) (√5) - ( 3 +5 + 2√3√5)
4+ 3+ 4√3 +5 +4 √5 + 2 √15 - 3-5 -2√15
4+4√3+4√5
B is the answer
Answer: B