divelab/Sys2Bench huggingface dataset:
Question: How many three letter words are formed using the letters of the word TIME?
Options:
A)28
B)21
C)26
D)24
E)29
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is ⁴P₃
= 4 * 3 * 2 = 24.
Answer: D
Answer: D
Question: Calculate the largest 6 digit number which is exactly divisible by 55?
Options:
A)999955
B)999900
C)999845
D)999790
E)999735
Rationale: Largest 4 digit number is 999999
After doing 999999 ÷ 55 we get remainder 44
Hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955
A
Answer: A
Question: A baseball team won 45 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
Options:
A)36
B)45
C)50
D)55
E)81
Rationale: Number of games won by baseball team in first 80 games = .45* 80 = 36
Total number of games = 80 + 82 = 162
% of wins required in 162 = 50
Number of wins required in 162 = 81
Number of wins required in remaining 82 games = 81 - 36 = 45
Answer B
Answer: B
Question: Barbie invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?
Options:
A)1250
B)3000
C)1000
D)3600
E)1200
Rationale: Let the additional invested amount for 8% interest be x;
Equation will be;
2400+0.05*2400+x+0.08x = 2400+x+0.06(2400+x)
0.05*2400+0.08x = 0.06x+0.06*2400
0.02x = 2400(0.06-0.05)
x = 2400*0.01/0.02 = 1200
Ans:E
Answer: E
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 10 points after 5 games, what is the least number of the remaining matches it has to win to reach the 45-point mark by the end of the tournament?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: To get 45 points as end of season we need another 35 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
Option B=7*3 + 8*1=29
Option C=8*3+7*1=31
Option D=9*3+6*1=33
Option E=10*3+5*1=35
hence option E-10
Answer: E
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 15 kmph and 25 kmph. When will they meet for the first time any where on the track if they are moving in the opposite direction ?
Options:
A)144
B)36
C)124
D)32
E)38
Rationale: Time taken to meet the first time = length of track/relative speed
= 400/ (15 +25) (5/18)
= 400/40 *(18/5) = 36 sec.
ANSWER:B
Answer: B
Question: A car takes 3hrs less than a truck to cover the distance frm Bombay to pune(192 km). The speed of the truck is 16km/hr slower than car.Find the speed of the car?
Options:
A)40.38
B)38.38
C)41.3
D)48
E)45
Rationale: Let the speed of car = x km/hrs
then that of truck = (x-16) km/hrs
According to the given condition
[192/(x-16)]- [192/x] = 3
on solving the equation we have x = 8[(sq-root of 17) + 1] =40.38
ANSWER:A
Answer: A
Question: If d=1/(2^3*5^11) is expressed as a terminating decimal, how many nonzero digits will d have?
Options:
A)One
B)Two
C)Three
D)Seven
E)Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^11)
= Multiply and divide by 2^8
=2^8/(2^3*2^8*5^11)
=2^8/10^11
=> non zero digits are 256=> Ans C
Answer: C
Question: What least number should be added to 1101, so that the sum is completely divisible by 24
Options:
A)A)4
B)B)1
C)C)2
D)D)3
E)E)5
Rationale: Explanation:
(1056 / 24) gives remainder 21
21 + 3 = 24, So we need to add 3.
Answer: Option D
Answer: D
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
A)2456
B)3456
C)4578
D)4290
E)5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: E
Question: If the average (arithmetic mean) of 2a+16, 3a-8 is 94, what is the value of a?
Options:
A)25
B)30
C)28
D)36
E)42
Rationale: AM of 2a+16, 3a-8=2a+16+ 3a-8 /2= 5a+8/2
Given that 5a+8 /2 = 94
a= 36
Answer is D
Answer: D
Question: Find the value of (875 233/899) × 899
Options:
A)786600
B)786650
C)786700
D)786750
E)786858
Rationale: (875 233/899) × 899
(786625 + 233)/899 × 899
786858/899 × 899
786858
E
Answer: E
Question: How many words can be formed by using all letters of the word ‘LONDON’ ?
Options:
A)120
B)320
C)420
D)620
E)720
Rationale: Solution
The word LONDON contains 6 different letters.
Required number of words = 6P6 = 6 ! = (6 x 5 x 4 x 3 x 2 x 1) = 720
Answer E
Answer: E
Question: Following an increase in prices, the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
Options:
A)11.
B)20.
C)13.
D)14.
E)14.5
Rationale: Price of candy before price increase= 20/1.25= 16
Price of soda before price increase= 6/1.5= 4
Total price = 16+4= 20
B is the answer
Answer: B
Question: The rate of Interest on a sum of money is 8% p.a. for the first 3 years, 4% p.a. for the next 4 years, and 5% for the period beyond 7 years. If the S.I, Occured on the sum for the total period of 8 years is Rs. 540/-, the sum is
Options:
A)1,200
B)2,000
C)2,100
D)2,250
E)2,540
Rationale: Explanation:
I1 = (P x 3 x 8)/100 = 6P/25
I2 = (P x 4 x 4)/100 = 4P/25
I3 = (P x 1 x 5)/100 = P/20
6P/25 + 4P/25 + P/20 = 540
9P/20 = 540
P = 1200
Answer: Option A
Answer: A
Question: A mail handler needs 3 hours to sort the mail. His assistant takes 6 hours to sort the mail. How many hours will it take for both of them working together to sort the mail?
Options:
A)3
B)2
C)1
D)2 1/2
E)1 1/5
Rationale: Work hrs=AB/(A+B)= 18/9 =2
Answer is B
Answer: B
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 0.5 minute each, how soon will the tank be filled?
Options:
A)1 hour 30 min
B)4 hours
C)3 hours
D)5 hours
E)6 hours
Rationale: in three minute 1/20+1/30-1/15=1/60 part is filled
1.5 min--------1/60 parts
x min--------- 1 part(full)
x=90 min =1 hour 30 min
ANSWER:A
Answer: A
Question: If the value of a piece of property decreases by 10% while the new tax rate on the property represent 110% of the original tax rate, what is the effect on the taxes?
Options:
A)taxes increase by 10%
B)taxes increase by 1%
C)there is no change in taxes
D)taxes decrease by 1%
E)taxes decrease by 10%
Rationale: Consider the value of property = 100, Original tax rate 10%, hence tax value = 100*10% = 10.
Decreased value of property = 90, New tax rate = 110% of 10 = 11%, hence tax value = 90*11% = 9.9
10-9.9 = decrease by 1%.
Answer D.
Answer: D
Question: ABCD is a parallelogram on xy rectangular coordinate plane, three of the four vertices of parallelogram are (5,15) , (5,55) and (-5,15). Which can be the coordinate of fourth vertex?
Options:
A)(15,55)
B)(5,15)
C)(-5,-25)
D)(-5,10)
E)(15,25)
Rationale: A(-5, 15)
B(5, 15)
C(5, 55)
X(-5, 55): Parallelogram=Square=AXCB, where AX||CB, AX=CB, XC||AB, XC=AB
Y(-5, 5): Parallelogram=AYBC, where AY||BC, AY=BC, AC||YB, AC=YB
Z(15, 55): Parallelogram=ACZB, where AC||ZB, AC=ZB, CZ||AB, CZ=AB
Ans:A
Answer: A
Question: Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
Options:
A)6:4
B)6:14
C)4:4
D)4:6
E)3:7
Rationale: let:
x = ounces taken from solution A (20% salt)
y = ounces taken from solution B (80% salt)
to prepare 50 ounce 50% salt.
first equation is simple:
x + y = 50
to get another equation so as to be able to solve, compute salt contents.
20% of x + 80% of y = 50% of 50 or
x/5 + 4/5 * y = 25 or
x+4y = 125
solve two equations to get:
x = 25
y = 25
so solutions has to mix in
1:1 oops 4:4
ANSWER:C
Answer: C
Question: Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now?
Options:
A)20 years
B)24 years
C)27 years
D)30 years
E)None
Rationale: Sol.
Present age of ( A + B) = ( 18 × 2 + 3 × 2) years = 42 years.
Present age of ( A + B + C) = (22 × 3) years = 66 years.
Therefore C’s age = (66 – 42) years
= 24 years.
Answer B
Answer: B
Question: A thief steals at a car at 2.30 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)2
B)78
C)5
D)6
E)7
Rationale: Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 5 p.m.
Answer: C
Answer: C
Question: The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along theboundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park is?
Options:
A)163600 m
B)178600 m
C)153600 m
D)163600 m
E)173600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: C
Question: If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?
Options:
A)4/5
B)1/4
C)3/10
D)1/5
E)1/10
Rationale: 10 + 10 + 55 = 75% 100 - 75 = 25% to all others
B
Answer: B
Question: If the price of sugar rises from Rs. 10 per kg to Rs. 11 per kg, a person, to have no increase in the expenditure on sugar, will have to reduce his consumption of sugar by
Options:
A)9%
B)20%
C)25%
D)30%
E)none
Rationale: Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 11 = x = 91 kg.
∴ Reduction in consumption = 9%.
Answer A
Answer: A
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 40 years now, the son's age five years back was?
Options:
A)16 years
B)15 years
C)18 years
D)19 years
E)25 years
Rationale: Let the son's present age be x years.
Then, (40 - x) = x
2x = 40 => x = 20
Son's age 5 years back = (20 - 5)
= 15 years.
Answer: B
Answer: B
Question: If q and r are both odd numbers N, which of the following must also be odd?
Options:
A)q – r
B)(q + r)^2
C)q(q + r)
D)(qr)^2
E)q/r
Rationale: We're told that q and r are both ODD numbers N. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
Answer: D
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
Options:
A)40 minutes
B)1 hour
C)1 hour 15 min
D)1 hour 30 min
E)none
Rationale: Solution
Rate downstream	= (1 / 10 x 60)km/hr
= 6 km / hr.
Rate upstream	= 2 km/hr.
Speed in still water	= 1 / 2(6 + 2)km/hr
= 4 km.
Required time	= (5 / 4) km/hr
= 1x 1/4 km/hr
= 1 hr 15 min.
Answer C
Answer: C
Question: If f(x)= 5x^3- 2x+8 and h(y)= 4y-4, then h(f(x)) =
Options:
A)11x^2+4x+4
B)11x^2-12x+44
C)8x^3-8x+32
D)30x^3+4x+4
E)20x^3-8x+28
Rationale: h(f(x)) = 4(f(x)) -4 = 4(5x^3- 2x+8) - 4 = 20x^3-8x+28 =>E
Answer: E
Question: The average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results?
Options:
A)24
B)25
C)48
D)50
E)None
Rationale: Answer
Sum of 100 result = sum of 60 result + sum of 40 result.
= 60 x 40 + 40 x 60
= 4800/100
Correct Option: C
Answer: C
Question: A question paper has 5 multiple choice questions. Each question has 2 choices with only one choice as the correct answer. What is the total number of ways in which a candidate will not get all the 10 answers correct?
Options:
A)19
B)85
C)120
D)624
E)1024
Rationale: A candidate can answer the test in 2^5 number of ways (each question has 2 choices and we have total of 5 questions). Now, out of these cases there will be only one case when the candidate answered all the 5 questions correct. Therefore the total number of ways in which a candidate will NOT get all the four answers correct is 5^4-1=624.
Answer: D.
Answer: E
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)4%
C)6%
D)3%
E)1%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: B
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 5 weeks have been $406, $413, $420, $436 and $395. What must his average (arithmetic mean) income over the next two weeks be to decrease his average weekly income to $400 over the 7-week period?
Options:
A)$350
B)$400
C)$365
D)$385
E)$375
Rationale: OFFICIAL SOLUTION:
(C) First, we need to add up the wages over the past 5 weeks: $406 + $413 + $420 + $436 + $395 = $2070.
To average $400 over 7 weeks, the salesman would need to earn: $400 × 7 = $2800.
Subtract $2070 from $2800 to determine how much he would need to earn, in total, over the next 2 weeks to average $400 for the 7 weeks: $2800 – $2070 = $730.
Dividing $730 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $730/2 = $365.
The correct answer is choice (C).
Answer: C
Question: The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?
Options:
A)0.5904
B)0.5914
C)0.5912
D)0.5916
E)1
Rationale: Explanation:
P(winning prize atleast on one ticket)
= 1 - P("Losing on all tickets")
= 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)
= (1.64)(0.36) = 0.5904
A)
Answer: A
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $12,000 imported car and ended up paying $1440 in taxes, what is the first tier's price level?
Options:
A)$1600
B)$6000
C)$6050
D)$1200
E)$8000
Rationale: Let T be the tier price, P be total price = 12000
Per the given conditions:
0.12T + 0.08(P-T) = 1440 ----> T= 12000. D is the correct answer.
Answer: D
Question: If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).
Options:
A)32/7
B)13/7
C)2/7
D)32/17
E)2/17
Rationale: . X/Y=3/4  (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2)
=(3+5)/(7/4)=32/7
ANSWER A 32/7
Answer: A
Question: In how many ways can 10 people, A, B, C, D, E, F, G, H, I, J be seated in a row such that C and D are not seated next to each other as well as A and B are not seated next to each other?
Options:
A)384
B)396
C)576
D)3628704
E)6960087
Rationale: Number of total arrangements = 10!
Restriction 1= ABCD not next to each other --> let say AB and CD are considered as one unit, respectively
Restriction 2= AB is not the same as BA + CD is not the same as DC --> the number will increase by 2*2
Total number of arrangements - Number out of restrictions = Result
10! - (4!*2*2) = 3628800 - (24*2*2) = 3628704
Answer D
Answer: D
Question: The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 20x + 25. If the sum of the perimeters of both squares is 36, what is the value of x?
Options:
A)3
B)5
C)7
D)9
E)11
Rationale: The areas are (x+5)^2 and (2x-5)^2.
The lengths of the sides are x+5 and 2x-5.
If we add the two perimeters:
4(x+5) + 4(2x-5) = 36
12x = 36
x = 3
The answer is A.
Answer: A
Question: What is the rate percent when the simple interest on Rs.810 amount to Rs.155 in 4 Years?
Options:
A)4.78
B)4.68
C)4.58
D)4.48
E)4.38
Rationale: 155 = (810*4*R)/100
R = 4.78%
Answer: A
Answer: A
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 5 ounces of corn syrup, how many ounces of water does it contain?
Options:
A)45
B)50
C)55
D)60
E)75
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 5*180/12 = 75 ounces of water
E
Answer: E
Question: In how many ways 5 different balls can be arranged in to 3 different boxes so that no box remains empty?
Options:
A)125
B)150
C)175
D)200
E)225
Rationale: 1. The total number of possibilities including empty boxes: 35=24335=243
2. Two of the boxes are empty: C32=3C23=3
3. One but not two of the boxes is empty: 3∗(25−2)=903∗(25−2)=90
4. the total number of possibilities excluding empty boxes: 243 - 3 - 90 = 150
ANS:B
Answer: B
Question: The percentage profit earned by selling an article for $1920 is equal to the percentage loss incurred by selling the same article for $1280. At what price should the article be sold to make 25% profit?
Options:
A)1000
B)3000
C)2000
D)4000
E)5000
Rationale: B
2000
Let C.P. be $x.
Then, (1920 - x)/x * 100 = (x - 1280)/x * 100
1920 - x = x - 1280
2x = 3200 => x = 1600
Required S.P. = 125 % of $1600 = 125/100 * 1600 = $2000.
Answer: C
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 39.6. The difference between the unit digit and hundreds digit of that number is :
Options:
A)a) 4
B)b) 3
C)c) 2
D)d) 1
E)e) 0
Rationale: Since the average increased by 39.6 and there were a total of 10 numbers, it means the incorrect number was 396 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 396
99c - 99a = 99(c - a) = 396
396 = 99*4 = 99(c - a)
So c - a = 4
Answer (A
Answer: A
Question: In a University the average age in an arts class is 21 and average age in technical class is 18. What is the age average of University if there are 8 arts classes and 5 technical classes?
Options:
A)18.75
B)19.85
C)20.32
D)20.9
E)21.0
Rationale: Average age of University= ((8x21)+(5x18))/13
=19.85
Answer: B
Answer: B
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 11 and 200, then the least and greatest integer on the card would be
Options:
A)3 and 15
B)3 and 20
C)4 and 13
D)4 and 14
E)5 and 14
Rationale: Given: 11<x(x+1)<200.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>11 --> so, the least value is 4. Test for the largest value: if x=15 then
x(x+1)=15*16=240>200 --> discard B.
Answer: A.
Answer: A
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 5 Ohms and y is 7 Ohms?
Options:
A)3/5
B)1/7
C)12/35
D)31/12
E)35/12
Rationale: 1/R = 1/x + 1/y
1/R = 1/5+1/7 = 12/35
R = 35/12
The answer is E.
Answer: E
Question: How many real roots does the equation x^2y+15xy+64y=0 have if y < 0?
Options:
A)0
B)1
C)2
D)3
E)Infinite
Rationale: x^2y+15xy+64y=0
=> y ( x^2 + 15x + 64) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-7
So although there are 2 factors , they are the same x=-7 .
The equations has 2 distinct real root .
Answer C
Answer: C
Question: A fruit-salad mixture consists of apples, peaches, and grapes in the ratio 6:5:4, respectively, by weight. If 60 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?
Options:
A)15
B)12
C)8
D)6
E)4
Rationale: We can first set up our ratio using variable multipliers. We are given that a fruit-salad mixture consists of apples, peaches, and grapes, in the ratio of 6:5:4, respectively, by weight. Thus, we can say:
apples : peaches : grapes = 6x : 5x : 4x
We are given that 60 pounds of the mixture is prepared so we can set up the following question and determine a value for x:
6x + 5x + 4x = 60
15x = 60
x = 4
Now we can determine the number of pounds of apples and of grapes.
pounds of grapes = (4)(4) = 16
pounds of apples = (6)(4) = 24
Thus we know that there are 24 - 16 = 8 more pounds of apples than grapes.
Answer is C.
Answer: C
Question: If the personal income tax rate is lowered from 40% to 33%, what is the differential savings for a tax payer having an annual income before tax to the tune of $45000?
Options:
A)$3500
B)$5000
C)$3150
D)$7000
E)$10000
Rationale: Saving = (40-33)% of 45000 = 3150.
Answer:C
Answer: C
Question: E is the set of all positive integers x such that x^2 is a multiple of both 27 and 375. Which of the following integers must be a divisor of every integer x in E?
I. 9
II. 15
III. 27
Options:
A)I only
B)II only
C)I and II only
D)I and III only
E)I, II, and III
Rationale: Ans: C
E->{x} where x^2 is a multiple of both 27 and 375 means 3^3 and (5^3)*3
means x must contain 3^2 and 5^2
so with these conditions we know that 9=3^2 and 15=3*5 both have required factors for the divisibility of lowest int for x which is 9*25
but 27 is not a divisor because it can't divide 9*25 fully.
so Ans : C
Answer: C
Question: The first three terms of a proportion are 2, 10 and 20. The fourth term is?
Options:
A)105
B)102
C)190
D)100
E)134
Rationale: (10*20)/2 = 100
Answer:D
Answer: D
Question: A bag contains 6 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)3/4
B)7/13
C)1/7
D)1/8
E)4/3
Rationale: Let number of balls = (6 + 7) = 13.
Number of white balls = 7.
P (drawing a white ball) =7/13
Option B.
Answer: B
Question: Apple Street begins at Peach Street and runs directly east for 3.2 kilometers until it ends when it meets Cherry Street. Apple Street is intersected every 200 meters by a perpendicular street, and each of those streets other than Peach Street and Cherry Street is given a number beginning at 1st Street (one block east of Peach Street) and continuing consecutively (2nd Street, 3rd Street, etc...) until the highest-numbered street one block west of Cherry Street. What is the highest-numbered street that intersects Apple Street?
Options:
A)14th
B)15th
C)16th
D)17th
E)18th
Rationale: 3.2 km / 200 m = 16.
However, the street at the 3.2-km mark is not 16th Street; it is Cherry Street.
Therefore, the highest numbered street is 15th Street.
The answer is B.
Answer: B
Question: When the integer n is divided by 17, the quotient is x and the remainder is 5. When n is divided by 23, the quotient is y and the remainder is 13. Which of the following is true?
Options:
A) 23x + 17y =19
B) 17x –23y = 8
C) 17x +23y =19
D) 14x + 5y = 6
E) 5x – 14y = -6
Rationale: From the problem it follows:
n=17x+5
n=23y+13
So, 17x+5=23y+13
17x-23y=8
The answer is B
Answer: B
Question: f(x) = x! g(x)=x^10 h(x)= 10^x for large values of x which is greater?
Options:
A)f(x)
B)g(x)
C)h(x)
D)both
E)none
Rationale: let x=100
then g(x)=100^10=10^20
h(x)=10^100
so h(x) is greater
ANSWER:C
Answer: C
Question: If (2^x)(3^y) = 108, where x and y are positive integers, then (2^x-1)(3^y-2) equals:
Options:
A)6
B)24
C)48
D)96
E)144
Rationale: So I would start attacking this problem by quickly performing the prime factorization of 288. With that it is easy to count the 5 twos and the 2 threes that are the prime factors. So x=2, y=3. now quickly 2^1(3^1)=6. Than answer should be number 1.
A
Answer: A