divelab/Sys2Bench huggingface dataset:
Question: In how many ways can the letters of word CAREER be arranged such that all the vowels as well as all the Consonants always appear together?
Options:
A)3!*3!*2!
B)5!*4!
C)5!*5!
D)5!*4!*2!
E)6!*4!
Rationale: Since all the vowels and consonants have to be together there can only be there are 3! way to order the vowels and 3! to order the consonants. But they must be together either vowels come first or consonants so you multiply by 2.
So 3!3!2! (A)
Answer: A
Question: A major airplane manufacturer announced the sale of 150 small airliners at $125 million each, 75 medium sized airliners at $175 million each, and 60 large airliners at $220 million each. What percentage of the company's income came from large and medium airliners?
Options:
A)29%
B)41%
C)58%
D)69%
E)70%
Rationale: Answer is (money from mid and large plane)/(total money from all the planes)x 100
=(175∗75+220∗60)/(125∗150+175∗75+220∗60)∗100(175∗75+220∗60)/(125∗150+175∗75+220∗60)∗100
= 58.4%
you could just multiply add divide to get answer.
However sometimes its much better to make it easy we should see if we have any common terms
125*150=(5*5*5)*(2*3*5*5)
175*75=(5*5*7)*(3*5*5)
220*60=(2*2*11*5)*(2*2*3*5)
3*5*5 is common cancel it
Ans becomes
(175+176)/(176+175+250)*100 =~=~ 350/600*100=~=~7/12*100=60% >>> 58% is closest.
ANSWER:C
Answer: C
Question: The length of each side of an equilateral triangle having an area of 4√3 cm2 is?
Options:
A)1/8
B)1/9
C)1/5
D)1/23
E)1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
Answer: C
Answer: C
Question: A tank is filled by 3 pipes A,B,C in 7 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?
Options:
A)25hr
B)35hr
C)40hr
D)49hr
E)50hr
Rationale: Suppose pipe A alone take x hours to fill the tank
Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/7
7/x = 1/7
x = 49 hours
Answer is D
Answer: D
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Options:
A)1
B)3
C)4
D)2
E)6
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Answer: D
Question: In a psychology school the grade of the students is determined by the following method: At the end of the first year the grade equals to twice the age of the student. From then on, the grade is determined by twice the age of the student plus half of his grade from the previous year. If Joey’s grade at the end of the first year is 36, what will be his grade at the end of the third year?
Options:
A)44
B)56
C)62
D)75
E)61
Rationale: Cool question!
There's a lot of information given here, so let's eat slow here.
Joey scores a 36 at the end of his first year. That means that he's currently 16 years old (since given per instruction, after the first year one's grade is determined by doubling his/her age).
Now, come next year, or his second year at this psychology school, he's technically 17 years old. To find out the second year's grade, we want to double his age PLUS half of his previous grade.
Well, his second year is then going to be 17(2) + 16 = 50.
Now let's tackle the main question: what's his grade going to be the third year?
Well, he will be at an age of 22 on his third year at this school. Again, to find out his third year's grade, you're going to double his age (18x2), plus half of his previous year's grade (as calculated for his second year, his grade is 50; therefore, 50/2)
Having said that, the final answer would be 18(2) + 50/2 = 36 + 25 = 61 --> (E)
Answer: E
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Options:
A)165 ways
B)176 ways
C)197 ways
D)160 ways
E)162 ways
Rationale: Total number of persons in the committee
= 5 + 6 = 11
Number of ways of selecting group of eight persons
= ¹¹C₈
= ¹¹C₃ = (11 * 10 * 9)/(3 * 2) = 165 ways.
Answer:A
Answer: A
Question: A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
Options:
A)0
B)1/9
C)2/9
D)1/3
E)1
Rationale: Probability = (favorable cases)/(total number of cases)
Total number of ways in which a person can ride car = 3*3*3 = 27
(In first ride he has 3 options to sit, in second right again he has 3 seats available to sit and so on)
Number of favorable cases, i.e., when he rides on different cars;
He can choose seat car in 3 ways in his 1st ride.
He can choose seat car in 2 ways in his 2nd ride.
He can choose seat car in 1 ways in his 3rd ride.
So, 3*2*1 = 6 ways
Thus, probability of choosing different seats = 6/27 = 2/9
Answer: C
Answer: C
Question: In what ratio must tea at Rs.60 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.63 per Kg?
Options:
A)3 : 1
B)3 : 2
C)4 : 3
D)7 : 3
E)None
Rationale: Required ratio = 700 : 300 = 7 : 3
Answer D
Answer: D
Question: Mr. Hernandez, who was a resident of State X for only 9 months last year, had a taxable income of $42,500 for the year. If the state tax rate were 4 percent of the year’s taxable income prorated for the proportion of the year during which the taxpayer was a resident, what would be the amount of Mr. Hernandez’s State X tax for last year?
Options:
A) $900
B) $1275
C) $1200
D) $1300
E) $1060
Rationale: Total tax for the year = 42,500 x 4% = 1700
As stated Annual tax is prorated as per the duration of stay.
Prorated Tax = 1700 (9/12) = 1275
Answer B
Answer: B
Question: A train running at the speed of 120 km/hr crosses a pole in 12 seconds. What is the length of the train?
Options:
A)200 m
B)250 m
C)300 m
D)350 m
E)400 m
Rationale: Speed=(120 * 5/18) m/sec
= (100/3) m/sec Length of the train
= (Speed x Time)
= (100/3 * 12) m = 400 m.
Answer:E
Answer: E
Question: A and B started a partnership business investing some amount in the ratio of 6 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)4 : 9 : 8
B)5 : 7 : 4
C)12 : 10 : 5
D)7 : 9: 4
E)5 : 4 : 8
Rationale: Let the initial investments of A and B be 6x and 5x.
A : B : C = (6x x 12) : (5x x 12) : (5x x 6) = 72 : 60 : 30
= 12 : 10 : 5.
ANSWER :C
Answer: C
Question: If m is the product of all integers from 1 to 40, inclusive, what is the greatest integer p for which 10^p is a factor of m?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: The factors of 10 are 1, 2, 5, and 10.
To find what k is, find how many times you can make 10 with the numbers in 1-40.
First, find the 10's as they are going to be most restrictive. Only 10, 20, 30 and 40 have 10 as a factor. 4 total.
Next find 5's. 5, 15, 25 and 35 each have a 5, with 25 having 2. 5 total.
You don't need to find the twos as you know there are more than 5's.
Add the two you get 9.
ANSWER:C
Answer: C
Question: 7 men, 5 women and 8 children were given as assignment of distributing 2000 books to students in a school over a period of 3 days. All of them distributed books on the 1st day. One of the 2nd day 2 women and 3 children remained absent and on the 3rd day 3 men and 5 children remained absent. If the ratio of the no. of books distributed in a day by a man, a woman & a child was 5 : 4 : 2 respectively, a total of approximately how many books were distributed on the second day?
Options:
A)340
B)450
C)680
D)650
E)700
Rationale: Sol. Let the books distributed by man, a woman and a child be 5x, 4x and 2x respectively.
∴ No. of books distributed in 1st day
= 7×5x+5×4x+8×2x=71x
No. of books distributed in 1Ind day
=7×5x+3×4x+5×2x=57x
And no. of books distributed in IIIrd day
=4×5x+5×4x+3×2x=46x
71x + 57x + 46x = 2000, x = 2000/174
57x=2000/174×57=650
D
Answer: D
Question: A train 55 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)7
D)3
E)5
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [55 * 3/55] sec = 3 sec
Answer: D
Answer: D
Question: What is the greatest possible length which can be used to measure exactly the lengths 10 m 50 cm, 14 m 55 cm and 50 cm?
Options:
A)20 cm
B)24 cm
C)30 cm
D)10 cm
E)5 cm
Rationale: Required length = HCF of 1050 cm, 1455 cm, 50cm = 5 cm
Answer is E
Answer: E
Question: Which of the following is a prime number
Options:
A)18
B)20
C)19
D)16
E)24
Rationale: Clearly, 19 is a prime number.
Option C
Answer: C
Question: A right circular cylinder has a height of 23 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
Options:
A)500(π – 3)
B)575(π – 1.5)
C)500(π – 2)
D)500(π – 1.5)
E)500(π – 1)
Rationale: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
23*25*pi - 15*sqrt(50)^2
=575(π – 1.5)
B. 500(π – 1.5)
Answer: B
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 155 per Kg , the price of the third variety per Kg will be?
Options:
A)Rs. 147.50
B)Rs. 785.50
C)Rs. 177.50
D)Rs. 258.50
E)None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 155)
/ \
xâˆ’155 22.50
=>xâˆ’(155/22.50)=1.
=>xâˆ’155=22.50.
=>x= 177.50 Rs.
Answer : C
Answer: C
Question: A person borrows Rs.5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 7% p.a for 2 years. Find his gain in the transaction per year.
Options:
A)167.5
B)150
C)225
D)112.5
E)212.5
Rationale: Explanation :
The person borrows Rs. 5000 for 2 years at 4% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×4×2/100=400
He also lends it at 7% p.a for 2 years
Simple interest that he gets = PRT/100=5000×7×2/100=700
His overall gain in 2 years = Rs.700 - Rs.400 = Rs.300
His overall gain in 1 year = 300/2 = Rs.150
Answer : Option B
Answer: B
Question: $9,000 is deposited in a savings account that pays 14% annual interest compounded semiannually. To the nearest dollar, how much is in the account at the end of the year?
Options:
A)$11304.12
B)$12304.54
C)$11604.14
D)$10304.10
E)$9304.41
Rationale: this is the case of semi-annual compoundingso, multiply time period by 2 and divide rate by 2
So,
new time=2periods and new rate=14/2=7%
Now,
CA=9000(1+7/100)^2=$10304.10
Hence answer is D
Answer: D
Question: A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included ?
Options:
A)223
B)186
C)287
D)167
E)171
Rationale: Explanation:
When at least 2 women are included.
The committee may consist of 3 women, 2 men : It can be done in\inline \fn_jvn {\color{Black} 4C_{3}\times 6C_{2}} ways
or, 4 women, 1 man : It can be done in \inline \fn_jvn {\color{Black} 4C_{4}\times 6C_{1}} ways
or, 2 women, 3 men : It can be done in \inline \fn_jvn {\color{Black} 4C_{2}\times 6C_{3}} ways.
Total number of ways of forming the committees
= \inline \fn_jvn {\color{Black} 4C_{2}\times 6C_{3}+4C_{3}\times 6C_{2}+4C_{4}\times 6C_{1}}
= 6 x 20 + 4 x 15 + 1x 6
= 120 + 60 + 6 =186
Answer: B) 186
Answer: B
Question: A and B can do a piece of work in 9 days. With the help of C they finish the work in 6 days. C alone can do that piece of work in?
Options:
A)33
B)878
C)18
D)88
E)11
Rationale: C = 1/6 â€“ 1/9 = 1/18 => 18 days
Answer: C
Answer: C
Question: Pipe A can fill a pool in 12 hours at a constant rate. If Pipe A does the job for 8 hours and Pipe B does the rest of the job, which works at 1/3 constant rate of Pipe A. How long will it take for Pipe B alone to do the rest of the job?
Options:
A)12hrs
B)6hrs
C)8hrs
D)10hrs
E)24hrs
Rationale: Pipe A will do 8/12 in 8 hrs, so A does 2/3 of the work ..
Therefore, B will do the remaining 1/3 rd work alone..
As the speed of B is 1/3 rate of A, B will do the 1/3rd work in same time that A takes to complete full job...
ans 12
A
Answer: A
Question: If (x^2 + 1)y=6, which of the following is not a possible value for y?
Options:
A)3/2
B)2
C)1/3
D)2/13
E)13/2
Rationale: Its simple
equation is (x^2 +1)y = 6 ===> x^2 = (6/y) - 1 . As , in LHS, it is x^2 the value has to be positive or zero in RHS.
Hence, (6/y) - 1>= 0 ===> y =< 6. Now only option E has greater value of 'y' than 6.
Thus, correct ans is E
Answer: E
Question: If logx (base 27) +logx (base 9) +logx (base3) =11 then find the value of x?
Options:
A)3^4
B)3^3
C)3^5
D)3^6
E)3^9
Rationale: logx(base 3)=Y
Now logx(base27)=logx(3^3 base)=1/3 logx(base3)=1/3 Y
Also logx(base 9)=1/2 logx(base3)=1/2 Y
Now as given,
1/3 Y + 1/2 Y+ Y = 11
So 11/6 Y = 11
Or Y =6
So logx(base3)=6
X=3^6
Answer D
Answer: D
Question: What is the greatest possible length which can be used to measure exactly the lengths 10 m, 14 m 50 cm and 20 m 40cm cm?
Options:
A)20 cm
B)10 cm
C)25cm
D)50 cm
E)28 cm
Rationale: Required length = HCF of 1000 cm, 1450 cm, 2040 cm = 10cm
Answer is B
Answer: B
Question: If a, x, y, and z are positive integers and (x)×(y)×(z)=a^2, which of the following could be the values of x, y, and z?
Options:
A)3, 16, 25
B)9, 25, 24
C)2, 36, 32
D)2, 9, 16
E)8, 16, 36
Rationale: As it contains every no. 2 times
2
36=6*6
32=4*4*2
C is the answer
Answer: C
Question: If the radius of a circle is decreased 20%, what happens to the area?
Options:
A)10% decrease
B)20% decrease
C)36% decrease
D)40% decrease
E)50% decrease
Rationale: Area of Square = Pi* radius^2
New Radius = 4/5 * old radius
so new area = (4/5)^2 old area => 16/25 of old area => 64% old area
Answer : C
Answer: C
Question: Two numbers are respectively 12% and 60% more than a third number. The percentage that is first of the second is?
Options:
A)50%
B)60%
C)70%
D)80%
E)90%
Rationale: I II III
112 160 100
160----------112
100-----------? => 70%
Answer:C
Answer: C
Question: Tom read a book containing 480 pages by reading the same number of pages each day. If he would have finished the book 5 days earlier by reading 16 pages a day more, how many days did Tom spend reading the book?
Options:
A)10
B)12
C)15
D)16
E)18
Rationale: Say the number of days Tom spent reading the book was dd. Then:
The number of pages he read per day would be 480/d
The number of pages he would read per day with an increased speed would be 480/d−5
e are told that the number of pages for the second case was 16 pages per day more, so 480/d=480/d−5−16
At this point it's much better to plug answer choices rather than solve for dd. Answer choice CC fits: 480/15=32=480/15−5−16
Answer: C
Answer: C
Question: Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
Options:
A)Rs. 8828
B)Rs. 8821
C)Rs. 8818
D)Rs. 8819
E)Rs. 8820
Rationale: Explanation:
Amount = [8000 * (1 + 5/100)2]
= 8000 * 21/20 * 21/20
= Rs. 8820
Answer:E
Answer: E
Question: If the sides of a triangle are 52 cm, 48 cm and 20 cm, what is its area?
Options:
A)450 cm^2
B)470 cm^2
C)480 cm^2
D)420 cm^2
E)460 cm^2
Rationale: The triangle with sides 52 cm, 48 cm and 20 cm is right angled, where the hypotenuse is 52 cm.
Area of the triangle
= 1/2 * 48 * 20
= 480 cm^2
Answer: C
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
Options:
A)20/21
B)20/63
C)10/21
D)10/23
E)10/31
Rationale: Required probability = (5C2 . 4C2)/9C4 = (10 * 6)/126
= 10/21
Answer:C
Answer: C
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 424 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
Options:
A)1176
B)2209
C)2878
D)1210
E)1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+424)
(x-8)^2 = T+424 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 1176+424 = 1600 = 40^2 = (x-8)^2 Hence, x = 48.
Cross check by putting in eq (a) = x(x+1)/2 = T = > 48*49/2=1176
Hence, answer is A.
Answer: A
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 6-letter code words?
Options:
A)1 to 5
B)3 to 2
C)2 to 1
D)5 to 1
E)6 to 1
Rationale: Number of ways to form 5-letter code: 10!/5! = 10*9*8*7*6
Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5
Ratio: 1 to 5
Answer : A
Answer: A
Question: The expression xy+x is odd when the x and y are integers. Which of the following expressions must be even?
Options:
A)x
B)y
C)x + y
D)xy - x
E)x + y^2
Rationale: xy+x is odd
x and y are integers
If x were even xy+x would be even despite any value of y.
y can't be odd, so y must be even.
Ans : B
Answer: B
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person
Options:
A)11
B)66
C)28
D)30
E)99
Rationale: Let's take the present age of the elder person = x
and the present age of the younger person = x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30
Answer: D
Answer: D
Question: At an election 2 candidates are participated and a candidate got 45% of votes and defeated by 9000. and 83 votes are invalid. Find the total polled votes?
Options:
A)84512
B)78452
C)65893
D)90083
E)74502
Rationale: Winner votes = 100-45 = 55
polled votes = [(100*9000)/2*55-100]+83 = 90083
Answer is D
Answer: D
Question: If a rectangular billboard has an area of 91 square feet and a perimeter of 40 feet, what is the length of each of the shorter sides?
Options:
A)4
B)7
C)8
D)13
E)26
Rationale: This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 91 and a perimeter of 40. We're asked for the length of one of the SHORTER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 91, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square).
Let's TEST Answer b: 7
IF...
The shorter side = 7...
The area = 91....91/7 = 13 = the longer side
Perimeter = 7+7+13+13 = 40
B
Answer: B
Question: A train is 485 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length
Options:
A)20 seconds
B)30 seconds
C)40 seconds
D)50 seconds
E)None of these
Rationale: Explanation:
Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 485+140 = 625 meter
Time = Distance/speed
=625∗2/25=50seconds
Option D
Answer: D
Question: Pants, Shorts and Shirts in a dresser are in the ratio of 7: 7: 10. If there are 14 Pants, the number of Shirts in the dresser is:
Options:
A)14
B)7
C)20
D)70
E)35
Rationale: Explanation :
Let Pants = 7x, Shorts = 7x & Shirts = 10x. Now, 7x = 14 hence x = 2.
Number of Apples = 10x = 20.
Answer : C
Answer: C
Question: At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.75 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day?
Options:
A) 7
B) 8
C) 9
D) 10
E) 11
Rationale: After renting bowling shoes the person is left with $12.80-$0.5=$12.30, which is enough for 12.3/1.75=7.02 -> ~7.
Answer: A.
Answer: A
Question: Solution P is 20 percent lemonade and 80 percent carbonated water by volume; solution Q is 45 percent lemonade and 55 percent carbonated water by volume. If a mixture of PQ contains 72% percent carbonated water, what percent of the volume of the mixture is P?
Options:
A)48%
B)54%
C)60%
D)64%
E)68%
Rationale: 72% is 8%-points below 80% and 17%-points above 55%.
So the ratio of solution P to solution Q is 17:8.
Mixture P is 17/25 = 68% of the volume of mixture PQ.
The answer is E.
Answer: E
Question: If x and q are integers and 2x–q= 11, then 4x+ q CANNOT be
Options:
A) –5
B) 1
C) 13
D) 17
E) 551
Rationale: 2x-q=11....q=2x-11
4x+q=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both E CANNOT be solution=D
Answer: D
Question: A corporation that had $10 billion in profits for the year paid out $500 million in employee benefits. Approximately what percent of the profits were the employee benefits? (Note: 1 billion = 10^9)
Options:
A)50%
B)20%
C)5%
D)2%
E)0.2%
Rationale: required answer = [employee benefit/profit] *100
=[(500 million)/(10 billion)]*100
=[(500*10^6)/(10*10^9)]*100
=(50/1000)*100
=5%
So answer is (C)
Answer: C
Question: The captain of a cricket team of 11 members is 30 years old and the wicket keeper is 5 years younger. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average of the team?
Options:
A)20
B)23
C)32
D)19
E)29
Rationale: Let the average of the whole team be x years.
11x - (30 + 25) = 9(x - 1)
= 11x - 9x = 46
= 2x = 46 => x = 23
So, average age of the team is 23 years.
Answer:B
Answer: B
Question: If $5,000 is invested in an account at a simple annual rate of r percent, the interest is $250. When $18,000 is invested at the same interest rate, what is the interest from the investment?
Options:
A)$700
B)$750
C)$800
D)$850
E)$900
Rationale: -> 250/5,000=5% and 18,000*5%=900.
Thus, E is the answer.
Answer: E
Question: If the range of the set of numbers {140, 80, 135, 110, 175, 145, x, 123, 136} is 115, which of the following could be x?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: The range of the other 8 numbers is 175-80 = 95, so x must be either the smallest number or the largest number in the set.
Then x = 175-115 = 60 or x = 80+115 = 195
The answer is E.
Answer: E