divelab/Sys2Bench huggingface dataset:
Question: For each of her sales, a saleswoman receives a commission equal to 20 percent of the first $500 of the total amount of the sale, plus 45 percent of the total amount in excess of $500. If the total amount of one of her sales was $800, the saleswoman’s commission was approximately what percent of the total amount of the sale?
Options:
A)22%
B)24%
C)25%
D)29%
E)28%
Rationale: Total sales =800
Comission = (20/100)*500+ (45/100)*300
=100 + 135
=235
%Comission =(235/800)*100=29.4~ 29%
Answer is D
Answer: D
Question: A meeting has to be conducted with 5 employees.Find the number of ways in which the employees may be selected from among 8 employees,if 2 employees will not attend the meeting together.
Options:
A)1.35
B)2.91
C)3.12
D)4.126
E)5.36
Rationale: 8 employees, but two of them cannot attend the meeting together.
We can split it into two cases.
1. Meeting without these two employees in it. That would mean selecting 5, from the remaining 6 which is 6C5 = 6
2. Meeting with one of the two employees. select 1 employees from two, and then select 4 from the remaining 6, which is 2C1 X 6C4 = 15.
So, answer is 30 + 6 = 36.
Answer : E
Answer: E
Question: 2.3.4.15.12
3.4.5.28.20
4.5.6.45.30
5.6.7.a .42
6.7.8.91.56
Value of a ?
Options:
A)65
B)66
C)67
D)68
E)69
Rationale: 2.3.4.15.12
3.4.5.28.20
4.5.6.45.30
5.6.7.a .42
6.7.8.91.56 so check each colounm u will find the increasing diff...in 'a' coloumn the diff is of 4..means 15...then 28 diff is of 13..then next term can b find out by adding 4 in 13..means add 17 to 28 u get 45 then same way keep on...
ANSWER:B
Answer: B
Question: Vijay bought 160 shirts at the rate of Rs. 235 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)Rs. 297
B)Rs. 270
C)Rs. 277.5
D)Rs. 285
E)None of these
Rationale: Total CP per shirt = 235 + 1400/160 + 1.75 + 320/160 = Rs. 247.5
SP = CP[(100 + profit%)/100]
= 247.5 * [(100 + 20)/100] = Rs. 297.
ANSWER:A
Answer: A
Question: When is |x-3| = 3-x?
Options:
A)x<=3
B)x=3
C)x>3
D)x=0
E)x< 0
Rationale: When is |x-3| = 3-x?
Choice A: X=3, it is true but X cannot be always 3
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>3, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=3, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is A.
Answer: A
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance (in km) is :
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Sol.
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60 ⇔ 47x/60 = 47/60 ⇔ x = 1.
∴ total distance = (3*1) km = 3km.
Answer C
Answer: C
Question: What least value should be replaced by * in 2631*4 so the number become divisible by 3
Options:
A)3
B)4
C)5
D)2
E)7
Rationale: Explanation:
Trick: Number is divisible by 3, if sum of all digits is divisible by 3, so (2+6+3+1+*+4) = 16+* should be divisible by 9,
16+2 will be divisible by 2,
so that least number is 2.
Answer: Option D
Answer: D
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 11,000, how many purple chips were selected?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 11,000 = 1*5^3*8*11
The factor of 8 must come from the purple point value, so there is 1 purple chip.
The answer is A.
Answer: A
Question: Which of the following CANNOT be the median T of the four consecutive positive integers w, x, y, and z, where w < x < y < z ?
Options:
A)(w+x)/2 - 1
B)(w+z)/2
C)(x+y)/2
D)(y+z)/2 -1
E)(w+x+y+z)/4
Rationale: Using the properties of consecutive positive integers we could right away eliminate B,C and E.
(B) - The average of first and last terms is the median
(C) - For even number of integers, the median is the average of middle terms
(E) - The average is equal to median if the integers are consecutive
Remaining answer choices are A and D.
For A, the average of first two consecutive numbers (w,x) will definitely be less than x making it impossible to be a median T.
Answer (A)
Answer: A
Question: 39! is divided by 41 then what is the remainder?
Options:
A)1
B)2
C)4
D)6
E)7
Rationale: Substituting p = 41 in the wilson's theorem, we get
40!+141=0
40×39!+141=0
−1×39!41=−1
Cancelling -1 on both sides,
39!41=1
A
Answer: A
Question: Rajeshâ€™s school bus is facing North when reaches his school. After starting from Rajeshâ€™s house, it turning twice and then left before reaching the school. What direction the bus facing when it left the bus stop in front of Rajeshâ€™s house?
Options:
A)East
B)North
C)South
D)West
E)East-West
Rationale: West
ANSWER D
Answer: D
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.5400. How much third person will get?
Options:
A)2400
B)277
C)2789
D)2669
E)2123
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 54000 = 2400.Answer: A
Answer: A
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
Options:
A)80/9
B)80/7
C)80/2
D)80/1
E)80/3
Rationale: Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
Answer: B
Question: In a Quiz the points in each round for the first,second and third were 1000,50,20 . No other points were given. Sam participated in several rounds in the competition and the product of his score was 50000. In How many rounds did he participate?
Options:
A)Cannot be determined
B)43
C)3
D)6
E)10
Rationale: Correct answer is A because we are given that there won't be any points awarded for rounds other than 1st three position.
Thus, it may happen that he played 100 rounds out of only 7 rounds were there in which he was awarded some points.
Answer: A
Question: A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)118
B)88
C)90
D)42
E)22
Rationale: SP of 1m of cloth = 8925/85 = Rs. 125
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 125 - Rs. 7 = Rs. 118
Answer:A
Answer: A
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 20% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
Options:
A)17% less than N
B)25% less than N
C)equal to N
D)20% greater than N
E)25% greater than
Rationale: Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 20% it becomes price2=P/N*1.20
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.20) i.e. N/1.20 i.e. .83*
Answer: A
Question: f, b, and c are positive integers. If f, b, and c are assembled into the six-digit number fbcfbc, which one of the following must be a factor of fbcfbc?
Options:
A) 16
B) 13
C) 5
D) 3
E) none of the above
Rationale: Plug in some values and check -
fbcfbc = 123123
Not divisible by 16 and 5
let fbcfbc = 125125
Not divisible by 3
Only option (B) and (E) is left in both the cases...
Check once more to marke (B) as correct answer
let fbcfbc = 135135
Again divisible by 13
So, mark answer as (B) 13
Answer: B
Question: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.70 per glass on the first day, what was the price per glass on the second day?
Options:
A)$0.15
B)$0.20
C)$0.30
D)$0.40
E)$0.46
Rationale: On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.
We are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.
Say the price of the glass of the orangeade on the second day was $x then 2*0.7=3*x --> x=$0.46.
Answer: E.
Answer: E
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability E that N is divisible by 3?
Options:
A)1/3
B)¼
C)9/25
D)5/16
E)0
Rationale: Prime digits are: 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Answer: D
Question: In a certain school, the ratio of boys to girls is 5 to 17. If there are 72 more girls than boys, how many boys are there?
Options:
A)27
B)36
C)45
D)72
E)108
Rationale: The ratio of b to G is 5:13 and the other data point is G are more than boys by 72...
Looking at the ratio we can say that the 12(17-5) extra parts caused this diff of 72. so 1 part corresponds to 72/8=9 and so
5 parts correspond to 12*9 = 108.
E
Answer: E
Question: A certain collage has total of 450 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
Options:
A)130
B)80
C)75
D)60
E)50
Rationale: Answer is A.
Six majors are as follows: a + b + c + d + e + f
Each has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20
4 of the majors have 300 seniors: a + b + c +d = 300
There are a total of 450 seniors.
So e + f = 150. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 130.
A
Answer: A
Question: Calculate the average mark scored by Adam if he had the following scores in an examination: 85, 67, 52, 69, 56, 62, and 59 marks (out in 100) in Spanish Language, Mathematics, Biology, Physics, French Language,Fine art and Chemistry respectively?
Options:
A)64.3
B)62.1
C)65.2
D)57.4
E)67.1
Rationale: Explanation:
Average mark = 85+67+52+69+56+62+59/7=64.3
Answer: Option A
Answer: A
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
Options:
A)99
B)98
C)97
D)96 answer
E)95
Rationale: The square roots of all numbers from answer choices are between 9 and 10, so the product of primes of the number we are looking should be less then 9, so this number should have only 2-s, only 3-s, only 5-s, or only 2-s and 3-s as its primes. Only 96 satisfies this.
Answer: D.
Answer: D
Question: Find the surface area of a10cm x 4cm x 3cm brick
Options:
A)84
B)124
C)164
D)180
E)120
Rationale: Explanation:
surface area = [2(10 x 4 + 4 x 3 + 10 x 3)]cm2 = 164 cm2
Answer: C
Answer: C
Question: Which of the following is closest to the difference between sum E of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
Options:
A)2.82
B)2.72
C)1.82
D)1.72
E)0.82
Rationale: Sum E of all proper fractions (fractions less than 1) in the form 1/x, where x is a positive digit:
1/1 + 1/2 + 1/3 +.....+ 1/9
This is a harmonic progression. Harmonic progression is inverse of arithmetic progression.
Approximate sum of a harmonic progression with even number of terms = number of terms * (average of middle 2 terms)
Approximate sum of a harmonic progression with odd number of terms = number of terms * (middle term)
The actual sum will be slightly more than the approximation.
Here we have 9 terms (odd).
Sum = 9 * 1/5
= 9/5
Product of all proper fractions in the form y/(y+1), where y is a positive digit:
1/2 * 2/3 * 3/4 *.....*9/10
We will be left with 1/10.
Required = 9/5 - 1/10
= 1.8 - 0.1
= 1.7
Closest is 1.72
Answer (D).
Answer: D
Question: A number is doubled and 5 is added. If the resultant is trebled, it becomes 123. What is that number?
Options:
A)12
B)29
C)27
D)18
E)99
Rationale: Explanation:
Let the number be x.
Therefore,
3(2x + 5) = 123
6x + 15 = 123
6x = 108
x = 18
ANSWER:D
Answer: D
Question: The timing of a college is from 12 p.m to 4.10 p.m. Five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students. Find the duration of each lecture.
Options:
A)52 minutes
B)45 minutes
C)46 minutes
D)48 minutes
E)44 minutes
Rationale: Explanation:
Total time a student spends in college = 4 hours 10 minutes = 250 minutes
As there are 5 lectures, the number of breaks between lectures is 4. Total time of the break = 20 minutes
Hence, the duration of each lecture is = (250 â€“ 20)/5
= 46 minutes
ANSWER C
Answer: C
Question: If 15 toys cost Rs. 545, what do 37 toys cost ?
Options:
A)Rs. 1344
B)Rs. 1349
C)Rs. 1346
D)Rs. 1341
E)Rs. 1343
Rationale: Explanation:
Let the required cost be Rs. x.
More toys, More cost (Direct proportion)
Therefore 15 : 37 :: 545 : x
(15 * x) = (37 * 545)
x = (37*545)/15
= 1344.33
Hence, the cost of 37 toys is Rs. 1344.33
ANSWER: A
Answer: A
Question: If it takes 10 kids 6 hours to wear out their teacher, how long would it take 15 kids?
Options:
A)5 hours
B)4 hours
C)3 hours
D)2 hours
E)1 hour
Rationale: 10 * 6 = 15 * x
x = 4
Answer: B
Answer: B
Question: The Arnolds purchased 550 square feet of Kentucky Gem sod at $1.59 per square foot and 270 square feet of Zelzea Blue sod at $1.38 per square foot. What was the approximate average price per square foot paid for all the sod?
Options:
A)$1.63
B)$1.40
C)$1.68
D)$1.72
E)$1.76
Rationale: Average price = (550*1.59)+(270*1.38)/550+270=1.40 (Approx)
Answer B
Answer: B
Question: The fourth proportional to 5, 8, 15 is
Options:
A)18
B)19
C)20
D)24
E)None
Rationale: Sol.
Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : : 15 : x ⇔ 5x = (8x15)
⇔ x = (8x15) / 5 = 24.
Answer D
Answer: D
Question: A motorcyclist goes from Bombay to Pune, a distance of 128 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
Options:
A)1:3
B)1:5
C)1:4
D)1:1
E)1:8
Rationale: T = 128/32 = 4 h
T = 4 - 3 = 1
Time Ratio = 4:1 = 4:1
Speed Ratio = 1:4
Answer: C
Answer: C
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
Options:
A)15 hours
B)13 hours
C)14 hours
D)12 hours
E)19 hours
Rationale: Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
Answer:C
Answer: C
Question: A can run 4 times as fast as B and gives B a start of 72 m. How long should the race course be so that A and B might reach in the same time?
Options:
A)70 m
B)60 m
C)80 m
D)65 m
E)96 m
Rationale: Speed of A:Speed of B=4:1
means in a race of 4m A gains 3m.
then in a race of 72m he gains 72*(4/3)
I.e 96m
ANSWER:E
Answer: E
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)7
B)8
C)2
D)9
E)6
Rationale: Explanation:
Total number of letters = 8
Using these letters the number of 8 letters words formed is = 8.
Answer: B
Answer: B
Question: How many integers n are there such that 1< 5n + 4 < 24?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: 1< 5n + 4 < 24
We first subtract 4 from all three parts of the inequality, and we obtain:
-3 < 5n < 20
Next, we divide both sides of the inequality by 5 and we get:
-3/5 < n < 4
The answer is D
Answer: D
Question: The value of (34.31*0.473*1.567)/(0.5*23.25*7.57) is close to
Options:
A)2
B)1.15
C)2.05
D)0.29
E)2.35
Rationale: (34.31*0.473*1.567)/(0.5*23.25*7.57) = 25.4303/88.00125
= 0.29
ANSWER:D
Answer: D
Question: The radius of a semi circle is 6.3 cm then its perimeter is?
Options:
A)32.8
B)32.4
C)32.1
D)32.2
E)32.9
Rationale: 36/7 r = 6.3
= 32.4
Answer:B
Answer: B
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability W that Jane will be on the same committee as Albert?
Options:
A) 12%
B) 20%
C) 33%
D) 40%
E) 50%
Rationale: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability W= (8/20) *100 =40%.
+1 for me.. :D
Answer: D
Question: Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
Options:
A)2/5
B)2/7
C)33/83
D)99/250
E)100/249
Rationale: The number of integers from 101 to 350, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 100/250=2/5.
Answer: A.
Answer: A
Question: A man can row 7 ½kmph in still water. If in a river running at 1.5 km an hour, it takes him 50 minutes to row to a place and back, how far off is the place?
Options:
A)3 km
B)4 km
C)5 km
D)6 km
E)None
Rationale: Sol.
Speed downstream = (7.5 + 1.5) kmph = 9 kmph;
Speed upstream = (7.5 - 1.5) kmph = 6 kmph.
Let the required distance be x km. Then,
x/9 + x/6 = 50/60 ⇔ 2x + 3x = [5/6 * 18] ⇔ 5x = 15 ⇔ x =3.
Hence, the required distance is 3 km.
Answer A
Answer: A
Question: The perimeter of a square is 24 m. Find the area of the square.
Options:
A)161 mÂ².
B)36 mÂ².
C)46 mÂ².
D)169 mÂ².
E)33 mÂ².
Rationale: Perimeter of square = 24 m
But perimeter of square = 4 Ã— side
Therefore, 4 Ã— side = 24 m
Therefore, side= 24/4 m = 6m
Now, the area of the square = (side Ã— side)
Therefore, area of the square = 6 Ã— 6 mÂ² = 36 mÂ².
ANSWER : OPTION B
Answer: B
Question: There are 84 supermarkets in the FGH chain. All of them are either in the US or Canada. If there are 10 more FGH supermarkets in the US than in Canada, how many FGH supermarkets are there in the US?
Options:
A)20
B)31
C)42
D)47
E)64
Rationale: x + (x - 10) = 84 --> x = 47.
Answer: D.
Answer: D
Question: What is the sum of the multiples of 5 from 80 to 140, inclusive?
Options:
A)560
B)780
C)990
D)1008
E)1200
Rationale: The formula we want to use in this type of problem is this:
Average*Total Numbers=Sum
First, find the average by taking the sum of the F + L number and divide it by 2:
A = (F + L)/2
Second, find the total numbers in our range by dividing our F and L numbers by 5 and add 1.
(140/5) - (80/5) + 1
Multiply these together so what we show Average*Total Numbers=Sum
(80 + 140)/2 * (140/5) - (80/5) + 1 = Sum
110 * 9 = 990
C
Answer: C
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
Options:
A)35
B)37
C)39
D)41
E)44
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x—10)
hence x=39.
Present age of B = 39 years
Option C
Answer: C
Question: Jim’s Taxi Service charges an initial fee of $2.45 at the beginning of a trip and an additional charge of $0.35 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
Options:
A)$3.15
B)$4.45
C)$4.80
D)$5.05
E)$5.6
Rationale: Let the fixed charge of Jim’s Taxi Service = 2.45 $
and charge per 2/5 mile(.4 mile) = .35$
Total charge for a trip of 3.6 miles = 2.45 + (3.6/.4) * .35
= 2.45 + 9*.35
= 5.6 $
Answer E
Answer: E
Question: If x and y are prime numbers such that x > y > 4, then x^2 − y^2 must be divisible by which one of the following numbers?
Options:
A) 7
B) 8
C) 5
D) 9
E) 13
Rationale: If x=7 and y=5, then x^2-y^2=24 and 24 is divisible only by 8 from the options, thus it must be correct.
Answer: B.
Answer: B
Question: A university needs to select a nine-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 5 students hold membership in both organizations, how many different committee are possible?
Options:
A)140
B)180
C)220
D)260
E)300
Rationale: student government + the student advisory board consists of 9 + 8 = 17 members.
5 students hold membership in both, so they were counted twice.
The total number of people to choose from is 17 - 5 = 12
The number of ways to choose 9 members from 12 is 12C9 = 220
The answer is C.
Answer: C
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.655 in all. Find the share of B?
Options:
A)130
B)120
C)218
D)140
E)136
Rationale: A+B+C = 655
A = 3B
3B+B+B-25 = 655
5B = 680
B = 136
Answer: E
Answer: E
Question: If the average (arithmetic mean) of five consecutive negative integers is 2k – 1, what is the difference E between the greatest and least of the five integers?
Options:
A)4K
B)4k^2 -4k
C)4-4k
D)4
E)4k+4
Rationale: (n-2 + n - 1 + n + n + 1 + n + 2)/5 = 2k - 1
=> n = 10k - 5
Greatest = n + 2 = 10k - 5 + 2 = 10k - 3
Least = n - 2 = 10k - 5 - 2
=> Difference E= 10k - 3 - (10k - 7)
= 4
Answer - D
Answer: D
Question: A birthday child reaches into a bag filled with toys (1 yo-yo, 1 ball, 1 whistle, and 1 box crayons). If the child randomly picks three toys, what is the probability the child will pick the yo-yo and a ball as two of the three toys?
Options:
A)1/3
B)1/2
C)1/4
D)1/5
E)2/5
Rationale: Combination Formula: nCr = n!/(r!(n - r)!), where n is the population/set, and r is the sample/subset.
Total number possible = 4C3 - 4!/(3!(4 - 3)!) = 4
Number yo-yo possible = 1C1 = 1
Number ball possible = 1C1 = 1
Number other possible = 2C1 = 2
Probability Formula: P(A) = (Number Favorable Outcomes)/(Total Number Possible Outcomes)
P(YB) = (1C1)(1C1)(2C1)/4C3 = 2/4 = 1/2
Answer: B
Answer: B
Question: Two airplanes take off from one airfield at noon. One flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour. Approximately how many miles apart are the airplanes at 2 p.m.?
Options:
A)412
B)332
C)400
D)483
E)566
Rationale: A
In two hours:
the plane flying East will be 412 miles away from airport.
the other plane will be 566 miles away from airport.
566/412 = ~1.4 = ~sqrt(2)
This means that planes formed a right isocheles triangle => sides of such triangles relate as 1:1:sqrt(2) => the planes are 412 miles apart.A
Answer: A
Question: In a city, the bus route numbers consist of a natural number less than 100, followed by one of the letters A,B,C,D,E and F. How many different bus routes are possible?
Options:
A)500
B)594
C)588
D)700
E)600
Rationale: The number can be any one of the natural numbers from 1 to 99.
There are 99 choices for the number.
The letter can be chosen in 6 ways.
Number of possible bus routes are 99Ã—6=99Ã—6= 594
ANSWER B
Answer: B
Question: If x > 7, which of the following is equal to (x^2 - 8x + 16)/(x^2 - 16) ?
Options:
A)(x + 4)/(4(x - 4))
B)(x - 4)/(x + 4)
C)(x - 2)/(x + 4)
D)(x + 4)/(x - 4)
E)(x - 8)/(x - 4)
Rationale: (x^2 - 8x + 16)/(x^2 - 16)
= (x - 4)(x - 4) / (x + 4)(x - 4)
=(x - 4)/(x + 4)
B. (x - 4)/(x + 4)
Answer: B