divelab/Sys2Bench huggingface dataset:
Question: A shopkeeper sells 10% of his stock at 20% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)20000
B)16000
C)18000
D)17000
E)15000
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/10 * x * 6/5 = 6x/50
The SP of 80% of the stock = 9/10* x * 0.95 = 171x/200
Total SP = 24x/200+171/200= 49x/50
Overall loss = x - 195/20050 = 5x/200
5x/200 = 400 => x = 16000
Answer:B
Answer: B
Question: Find the ratio of speed of truck to train if truck covers 550m in 1 minute and train covers 33 km in 45 min.
Options:
A)3:9
B)8
C)3:2
D)3:4
E)3:1
Rationale: Explanation:
Using the formula, speed=distance/time
Speed of truck = 550/60 m/s
Speed of train= 33000/(45*60) m/s
Ratio of speed of truck to train= (550/60 ) / [33000/(45*60)]
=3:4
Hence, the ratio is 3:4
ANSWER: D
Answer: D
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 12 lighbulbs, how many different samples can be chosen?
Options:
A)6
B)24
C)36
D)66
E)72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
12!/2!(12-2)!
12!/2!*10!
12*11/2*1
=66
ANSWER:D
Answer: D
Question: The population of a city increases by 5% per year but due to migration it decrease by 1% per years. What will be the percentage increase in population in 3 years?
Options:
A)9%
B)9.27%
C)27%
D)12.48%
E)None of these
Rationale: Actual increase in population=4%
Let, earlier population=100 then the population after 3 years
=100(1+4/100)^3=112.4864
∴Required percentage=12.48%
ANSWER:D
Answer: D
Question: A wheel that has 12 cogs is meshed with a larger wheel of 21 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
Options:
A)12
B)10
C)6
D)8
E)7
Rationale: Explanation :
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
21:12::21:x => 21 * x = 21 * 12
=> x = (21 * 12)/21
=> x = 12
Answer : A
Answer: A
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 39000, then the share of B is?
Options:
A)A)34500
B)B)24000
C)C)24098
D)D)19007
E)E)18000
Rationale: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 39000
Share of B = 6/13 (39000)
= Rs. 18000
Answer:E
Answer: E
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
Options:
A)Rs. 5400
B)Rs. 7200
C)Rs. 8400
D)Rs. 9600
E)Rs. 8600
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
ANSWER:C
Answer: C
Question: A student took 6 courses last year and received an average (arithmetic mean) grade of 100 points. The year before, the student took 5 courses and received an average grade of 70 points. To the nearest tenth of a point, what was the student’s average grade for the entire two-year period?
Options:
A)79
B)89
C)95
D)86.36
E)97.2
Rationale: Let the 6 courses that were taken last year be A1 , A2, A3 , A4 , A5 , A6
A1+A2+A3+A4+A5+A6 = 100*6 = 600
The year before , the 5 courses be B1, B2 , B3 , B4 , B5
B1+B2+B3+B4+B5 = 70*5 = 350
Student's average = (600+350)/11 = 86.36
Answer D
Answer: D
Question: A man said to his son, "I was two-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son?
Options:
A)28.9
B)28.0
C)28.4
D)28.8
E)28.1
Rationale: Present age of the son be P, he was born P years ago.
The age of the man was: (48 - P).
His age when the son was born should be equal to 2/3 of P.
(48 - P) = 2/3 P
5P = 144 => P = 28.8
Answer: D
Answer: D
Question: Insert the missing number
17, 7, 24, 19, 9, 28, ..., 8, 31
Options:
A)20
B)21
C)18
D)23
E)25
Rationale: 17+7=24
19+9=28
x+8=31
therefore x=23
ANSWER:D
Answer: D
Question: In what ratio should a variety of rice costing Rs. 6 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
Options:
A)5/6
B)5/9
C)5/2
D)5/1
E)5/8
Rationale: Explanation:
Let us say the ratio of the quantities of cheaper and dearer varieties = x : y
By the rule of allegation, x/y = (87.5 - 7.50) / (7.50 - 6) = 5/6
Answer: A
Answer: A
Question: What is the remainder of Q= 3^19 when divided by 10?
Options:
A)0
B)1
C)5
D)7
E)9
Rationale: I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, Q=when divided by 10, the remainder must be 7.D
Answer: D
Question: If Samson's home is 100 meters to his workplace and he trek's to work everyday, which of the following could be true?
I. Samson treks at least a distance of 200 meters everyday.
II. In 3 days, Samson would have covered a distance of 600 meters.
III. Daniel's work place is less than 100 meters from Samson's home.
Options:
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III
Rationale: Let's Check each Statement.
Statement I: Samson treks at least a distance of 200 meters everyday. He treks 100 meters to work and 100 meters back to work. 100meters + 100 meters = 200 meters, in which case Statement I is True.
Statement II: In 3 days, Samson would have covered a distance of 600 meters. Each day he treks 200 meters. 3 days will be 200 meters * 3 = 600 meters, in which case Statement II is TRUE.
Statement III: Daniel's work place is less than 100 meters from Samson's home. Distance from work to school is equal to distance from school to work, in which case Statement III can NEVER BE TRUE.
Only Statement I and II are True. So, the Correct answer is B
Answer: B
Question: A man has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)33
B)38
C)135
D)90
E)28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 720
⇒ 16x = 720
∴ x = 45.
Hence, total number of notes = 3x = 135
Answer:C
Answer: C
Question: When asked what the time is,a person answered that the amount of time left is 4/8 of the time already completed.what is the time.
Options:
A)2 PM
B)9 PM
C)4 PM
D)8 PM
E)6 PM
Rationale: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x)
24−x=4/8x⇒x=20
Time is 4 PM
Answer:C
Answer: C
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw Fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their Investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second Year, Alice and Bob each earned a 20 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, And Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
Options:
A)99%
B)97%
C)100%
D)107%
E)120%
Rationale: Say Arthur's fortune was $100. Then:
A = 20*1.5*1.2 = 36
B = 20*1.5*1.2 = 36
C = 20*1.5*0.4 = 12
D = 20*0.6*1.25 = 15
E = 0
Total 39 + 39 + 12 + 15 = 99.
Answer: A.
Answer: A
Question: If .08216 and 68.01 are multiplied to give x as product , how many digit to the right of the decimal point does x have?
Options:
A)8
B)7
C)6
D)8
E)9
Rationale: Product of .08216 and 68.01 is 5.5877016.
Therefore number of digits to right of decimal point is 7
Answer is B.
Answer: B
Question: The sum of ages of 4 children born at the intervals of 10 years each is 80 years. What is the age of the youngest child?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 10) + (x + 20) + (x + 30) = 80
4x = 20
x = 5.
Age of the youngest child = x = 5 years.
Answer:B
Answer: B
Question: A CAN FINISH A WORK IN 9 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
Options:
A)3
B)5 1/2
C)6
D)8
E)NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (9*1/3)=3 DAYS.
CORRECT OPTION:A
Answer: A
Question: Stuart bought a sweater on sale for 30% off the original price and another 25% off the discounted price. If the original price of the sweater was $40, what was the final price of the sweater?
Options:
A)$25.75
B)$35.75
C)$15.75
D)$ 21
E)$16.75
Rationale: The price with 30% off
40 - 30% of 40 = 40 - (30 / 100) *40 = 40 - 12 = 28
The price with another 25% off
28 - 25% of 28 = 28 - (25/100)* 28
= $21
correct answer D
Answer: D
Question: Which number is the odd one out?
159
248
963
357
951
753
Options:
A)143
B)269
C)358
D)486
E)753
Rationale: E
753
In the rest there is the same difference between each digit, eg:7 (Ã¢â‚¬â€œ2)5 (Ã¢â‚¬â€œ2)3
Answer: E
Question: When 21 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: This means that 18 must be a multiple of k.
The factors of 18 are 1, 2, 3, 6, 9, and 18.
Out of these, k can be 6, 9, and 18.
The answer is C.
Answer: C
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability F that the team will have exactly 2 women?
Options:
A)1/14
B)1/7
C)2/7
D)3/7
E)1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2* 3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: D
Question: If the sides of a cube are in the ratio 4:3. What is the ratio of their diagonals?
Options:
A)4:3
B)4:8
C)4:1
D)4:2
E)4:7
Rationale: a1:a2 = 4:3
d1:d2 = 4:3
Answer:A
Answer: A
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
Options:
A)30/90 kmph
B)80,40 kmph
C)24,98 kmph
D)30,54 kmph
E)45.98 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph
Answer:B
Answer: B
Question: A student has to obtain 33% of the total marks to pass. He got 175 marks and failed by 89 marks. The maximum marks are?
Options:
A)450
B)300
C)800
D)610
E)175
Rationale: Let the maximum marks be x
Then, 33% of x = 175+89
33x/100 = 264
x = 800
Answer is C
Answer: C
Question: A $500 investment and a $1,500 investment have a combined yearly return of 8.5 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1 ,500 investment have?
Options:
A)9%
B)10%
C)10 5/8%
D)11%
E)12%
Rationale: The ratio of investments is 500:1,500 = 1:3.
The deviation from the average return from $500 investment and $1,500 investment must be in the ration 3:1.
$500 investment return has the deviation from the mean of 8.5-7=1.5%, thus $1,500 investment return must have the deviation from the mean equal to 0.5%, which means that $1 ,500 investment has 8.5+0.5=9% yearly return.
Answer: A.
Answer: A
Question: A wolf eats 5.5 Kg of meat in 3 days. A baby tiger eats 3 Kg of meat in 4 days. How much meat can the two combined eat in three days?
Options:
A)10.
B)9.
C)8.
D)7.75
E)6.
Rationale: 3/3*5.5+3/4*3=7.75 kg
D
Answer: D
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)3.6
B)6
C)18
D)22
E)25
Rationale: Let rate = R% and time = R years.
Then, (1200 x R x R)/100	= 432
12R^2 = 432
R^2 = 36
R = 6.
Answer: Option B
Answer: B
Question: When the positive integer e is divided by 11, the quotient is f and the remainder 3. When e is divided by 19, the remainder is also 3. What is the remainder when f is divided by 19?
Options:
A)4
B)3
C)2
D)1
E)0
Rationale: Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r
where k = LCM (d1,d2)
In this case the divisors are 1119 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also e =d1q+3 ; which means d1q=209d1=11 therefore q=19
And ( f divided by 19)19/19 leaves remainder 0.
Answer is E
Answer: E
Question: What is the units digit of 23^2 * 17^2 * 39^2?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The units digit of 23^2 is the units digit of 3*3 = 9 which is 9.
The units digit of 17^2 is the units digit of 7*7 = 49 which is 9.
The units digit of 39^2 is the units digit of 9*9 = 81 which is 1.
The units digit of 9*9*1 = 81 is 1.
The answer is A.
Answer: A
Question: John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: (x+x1+...x14)/15 = 40
50
Option A
Answer: A
Question: A merchant has selected two items to be placed on sale, one of which currently sells for 20 percent less than the other. If he wishes to raise the price of the cheaper item so that the two items are equally priced, by what percentage must he raise the price of the less expensive item?
Options:
A)23 %
B)24%
C)25%
D)26%
E)27%
Rationale: Expensive item = $100;
Cheap item = $80;
We must increase $80 to $100, so by $20, which is 25% increase: (100-80)/80 = 1/4 = 0.25
Answer: C.
Answer: C
Question: Country X taxes each of its citizens an amount equal to 15 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
Options:
A)$40,000
B)$50,000
C)$64,000
D)$66,667
E)$80,000
Rationale: Equation is correct, so math must be a problem.
0.15*40,000+0.2*(x-40,000)=8,000 --> 6,000+0.2x-8,000=8,000 --> 0.2x=10,000 --> x=50,000.
Answer: B.
Answer: B
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of $600 per sq. metre.
Options:
A)$12375
B)$13575
C)$16575
D)$14575
E)$18575
Rationale: A
Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = $600
Hence, total cost
=5.5×3.75×600= $12375
A
Answer: A
Question: If the price of petrol increases by 25% and Benson intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
Options:
A)8%
B)7%
C)10%
D)6%
E)None of these
Rationale: Explanation :
Assume that the initial price of 1 Litre petrol = Rs.100 ,Benson spends Rs.100 for petrol,
such that Benson buys 1 litre of petrol
After the increase by 25%, price of 1 Litre petrol = 100 × (100+25)/100 = Rs.125
Since Benson spends additional 15% on petrol,
amount spent by Benson = 100×(100+15)/100 = Rs.115
Hence Quantity of petrol that he can purchase = 115/125 Litre
Quantity of petrol reduced = 1 − (115/125) Litre
Percentage Quantity of reduction =(1−115/125)1×100
=(10/125) × 100 = (10/5) × 4 = 2×4 = 8%
Answer : Option A
Answer: A
Question: A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.340 less than the sum lent. What was the sum lent?
Options:
A)Rs.400
B)Rs.450
C)Rs.550
D)Rs.500
E)Rs.650
Rationale: Explanation:
P - 340 = (P*4*8)/100
P = 500
ANSWER IS D
Answer: D
Question: What is the x-intercept of a line that passes
through the point (3, 4) and has a slope of 2?
Options:
A)-2
B)-1
C)0
D)1
E)2
Rationale: First, plot the point (3, 4) on a graph. A slope of 2 means “up 2, over 1,” so plot this point
on a graph, too. Here’s the resulting graph:
y over 1
up 2
(1, 0)
(2, 2)
(3, 4)
(4, 6)
x
The line passes through the x-axis at 1, making the correct answer D)1
Answer: D
Question: Which of the following is the Highest Common Factor of 18, 24 and 36?
Options:
A)8
B)10
C)6
D)14
E)12
Rationale: Ans is :C
actors of 18 = {1 , 2 , 3 , 6 , 9 , 18} Factors of 24 = {1 , 2 , 3 , 4 , 6 , 8 , 12 , 24} Factors of 36 = {1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36} => the Highest Common Factor is 6
Answer: C
Question: A, B and C can do a piece of work in 24 days, 30 days and 60 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
Options:
A)10 days
B)11 days
C)13 days
D)21 days
E)31 days
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/60 = 11/120 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
ANSWER:B
Answer: B
Question: If one-third of one-fourth of the number is 10, then two-fifth of that number is
Options:
A)80
B)70
C)60
D)None of these
E)56
Rationale: Explanation:
None of these
Answer: Option D
Answer: D
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent F of the interns report no feelings of tiredness during their shifts?
Options:
A)6
B)14
C)19
D)20
E)81
Rationale: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired F= 5 + 14 = 19.
Answer: C.
Answer: C
Question: Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Z in miles per hour for the entire trip?
Options:
A)26.7
B)Z=30.0
C)Z=40.0
D)Z=53.3
E)60.0
Rationale: VERITAS PREPOFFICIAL SOLUTION
Correct Answer: C
Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.
Answer choice C is correct.
Answer: C
Question: Find the odd one out
Options:
A)ctyugg
B)crusade
C)campaign
D)cruise
E)expedition
Rationale: Explanation:
Cruise = a sea voyage for pleasure.
All other words are related to ‘journey on land, sea with an aim’
Answer: D)
Answer: D
Question: (1/35)+(1/36)+……+(1/65)+(1/66) is including in which of the following ranges?
Options:
A)2
B)1
C)2~ 3
D)1/2~1
E)1/2
Rationale: Number of terms in the given series = 32.
The lowest term is 1/65 , the largest being 1/35.
Thus, the sum of the given series will be more than
1/65 + 1/65.....1/65 (32 times)
---> 32*(1/65) = 32/65
less than 1/35 + 1/35...... 1/35 (32 times)
---> 32*(1/35) = 32/35 = 1 (approx)
D is thus the correct answer.
Answer: D
Question: The sides of a triangle are in the ratio 5: 12: 13 and its perimeter is 300 m, its area is?
Options:
A)3000 sq m
B)2887 sq m
C)6296 sq m
D)2587 sq m
E)5854 sq m
Rationale: 5x + 12x + 13x = 300 => x = 10
a = 50, b = 120, c = 130
S = (50 + 120 + 130)/2 = 150
3000 sq m
Answer: A
Answer: A
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time, how many books of the special collection were loaned out during that month?
Options:
A)20
B)30
C)35
D)40
E)55
Rationale: I didn't understand How did we get 100?
Total = 75 books.
65% of books that were loaned out are returned --> 100%-70%=30% of books that were loaned out are NOT returned.
Now, there are 63 books, thus 76-63=12 books are NOT returned.
{loaned out}*0.30=7 --> {loaned out}=40.
Answer: D.
Answer: D
Question: A man purchases 2 watches for $ 600. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
Options:
A)$ 260 and $ 300
B)$210 and $ 350
C)$240 and $360
D)$560 and $560
E)$224 and $ 350
Rationale: x + y = 600 --- (1)
1.15x + 0.9y = 600 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*120)/(3*120) = 240/360
Answer: C
Answer: C
Question: In a lottery, there are 8 prizes and 24 blanks. A lottery is drawn at random. What is the probability of getting a prize?
Options:
A)1/4
B)1/8
C)1/12
D)1/16
E)1/24
Rationale: P(winning a prize) = 8 / (8+24) = 8/32 = 1/4
The answer is A.
Answer: A
Question: Lines y=√2·x+5 and y=3√2·x−1 intersect at what height above the x axis?
Options:
A)-8√2
B)0
C)7√2
D)8
E)4√2
Rationale: Solve two equations for y
y=√2·x+5
y=3√2·x−1
Set the two equations equal to each other and solve for x
√2·x+5 = 3√2·x−1
6 = 2√2·x
6/(2√2) = x
3/√2 = x
Plug x = 3/√2 into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=√2·x+5
y=√2·(3/√2)+5
y = 3 + 5
y = 8
Final answer:
D) 8
Answer: D
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares?
Options:
A)310
B)320
C)305
D)315
E)325
Rationale: Average of the two areas =7002=350
one-fifth of the average of the two areas=3505=70
⇒ Difference of the two areas =70
Let area of the smaller part =x hectares.
Then, area of the larger part =x+70 hectares.
x+(x+70)=700⇒2x=630⇒x=315
Answer is D.
Answer: D
Question: If s / t is an integer, which of the following statements must be true?
Options:
A)s = nt where n is an integer
B)both s and t are integers
C)either s or t is negative
D)t is an integer
E)s / t is an integer
Rationale: Let s = 1/4; t = 1/8 -->s/t = 2
s= nt where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: A
Answer: A
Question: A bus trip of 210 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: The time is the distance/speed. The time difference is 1 hour.
210/V - 210/(V+5) = 1
210(V+5) - 210V = (V)(V+5)
1050 = (V)(V+5)
30*35 = (V)(V+5)
V = 30 mph
The answer is B.
Answer: B
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first z stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits z + a stories in a month earn than a writer who submits z+ b stories?
Options:
A)(a – b)( a + b + z)
B)a – b
C)a^2 – b^2
D)z( a – b)
E)az + bz – az
Rationale: total earned for z+a stories =a + a(a+b)
total earned for z+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Answer: C
Question: A basketball is dropped from a height of 40 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.
Options:
A)50
B)55
C)110
D)75
E)80
Rationale: Initial distance = 40 feet
first bounce = 20 feet up + 20 feet down = 40 feet
second bouche = 10 feet up + 10 feet down = 20 feet
third bounce = 5 feet up and 5 feet down= 10 feet
total distance covered = 40+40+20+10= 110
ANSWER IS C
Answer: C