divelab/Sys2Bench huggingface dataset:
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at
Options:
A)6 %
B)6.1 %
C)6.2 %
D)6.3 %
E)6.4 %
Rationale: Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (E)
Answer: E
Question: There are 6 boxes numbered 1, 2, ... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
Options:
A)5
B)6
C)21
D)33
E)60
Rationale: 6 Green - 1 way
5 green - 2 ways
4 green - 3 ways
3 green - 4 ways
2 green - 5 ways
1 green - 6 ways
total = > 21 ways
Answer C
Answer: C
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 15 men in 3 days?
Options:
A)65mtr.
B)52mtr
C)70mtr.
D)78mtr.
E)42mtr.
Rationale: 20 men is 6 days can build 112 metres
15 men in 3 days can build = 112*(15/20)x(3/6)
= 42 meters
Answer: E.
Answer: E
Question: A palindrome is a number that reads the same forward and backward, such as 242. How many even thirteen-digit numbers are palindromes?
Options:
A)40
B)400
C)500
D)5,000
E)40,000,000
Rationale: if the palindrome must be even, it must begin and end in 2,4 6 and 8 ( 4 ways) e.g 22122,44144.
The middle number in the thirteen-digit could be 0-9 ( 10 ways), e.g 2222225222222, 2864228224682
The 2nd and fourth numbers , the 3rd and 5th, 4th and 6th, 5th and 7th must also be same i.e 0-9( 10 ways)
we thus have, 4 *10*10*10*10 *10*10= 4000000.E
Answer: E
Question: A rectangular table seats 8 people on each of two sides, with every person directly facing another person across the table. If 16 people choose their seats at random, what is probability that person P directly faces person Q?
Options:
A)1/14
B)3/7
C)1/16
D)2/11
E)1/15
Rationale: Person P will be seated somewhere at the table.
Each of the other 15 people has an equal chance of sitting opposite person P.
The probability that person Q sits across is 1/15.
The answer is E.
Answer: E
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 8 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
Options:
A)258
B)584
C)774
D)624
E)523
Rationale: Pretty simple actually
Number of 1 letter symbols = 8
Number of 2 letter symbols = 8*8
Number of 3 letter symbols = 8*8*8
The answer is sum of the 3. =584
So the answer is B.
Answer: B
Question: What approximate value should come in place of the a in the following equation?
10% of 6275 + 20% of 7584 = a
Options:
A)2180
B)2160
C)2140
D)2130
E)2120
Rationale: a = 10% of 6275 + 20% of 7584
a = 10/100* 6275 + 20/100* 7584
a =2144.3
≈ 2140
Answer C
Answer: C
Question: The mark up between "normal plan" price and "premium plan" price is 30 percent of the "normal plan" price. The markup is what percent of the "premium plan" price ?
(markup = difference between normal and premium price plans)
Options:
A) 8%
B) 20%
C) 33 1/3%
D) 45%
E) 56 2/3%
Rationale: A = price for normal plan
B = price for premium plan
MP = 0.5 A
B = A + 0.5 A = 1.5 A
hence Markup = B-A = 0.5/1.5 B = 1/3 B. Hence MP is 33.33% of B
Answer C
Answer: C
Question: Car X began traveling at an average speed of 35 miles per hour. After 72 minutes, car Y began traveling at an average speed of 42 miles per hour. When both cars had traveled the same distance, both cars stopped. How many miles did car X travel from the time car Y began traveling until both cars stopped?
Options:
A)105
B)140
C)175
D)210
E)245
Rationale: In 72 minutes, car X travels 42 miles.
Car Y gains 7 miles each hour, so it takes 6 hours to catch car X.
In 6 hours, car X travels 210 miles.
The answer is D.
Answer: D
Question: The ratio between the school ages of Neelam and Shaan is 5:6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age of 5:9, then what is the school age of Shaan?
Options:
A)17
B)16
C)18
D)15
E)19
Rationale: Let the school ages of Neelam and Shaan be 5x and 6x years respectively.
Then, (1/3 * 5x)/(1/2 * 6x) = 5/9
15 = 15
Thus, Shaan's age cannot be determined.
Answer:D
Answer: D
Question: let p be the product of the positive integers between 1 and 7 inclusive. How many distinct prime factors does p have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: There are 4 primes between 1 and 7, inclusive: 2, 3, 5, and 7, therefore p=1*2*...*7=7! has 4 distinct prime factors.
Answer: D.
Answer: D
Question: The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 5 months, find for how much time did Q invest the money?
Options:
A)19 months
B)10 months
C)11 months
D)81 months
E)12 months
Rationale: 7*5: 5*x = 7:10
x = 10
Answer: B
Answer: B
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 40 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)27%
E)28%
Rationale: Total sales =800
Comission = (20/100)*500+ (40/100)*300
=100 + 120
=220
%Comission =(220/800)*100=27.5~ 28%
Answer is E
Answer: E
Question: If abc ≠ 1 and the sum of the reciprocals of a, b, and c equals the reciprocal of the product of a, b, and c, then a =
Options:
A)(1 + bc)/(b + c)
B)(1 – bc)/(b + c)
C)(1 + b + c)/(bc)
D)(1 – b – c)/(bc)
E)(1 – b – c)/(b + c)
Rationale: Answer is C though it took me around 4 minutes to get that.
Answer: C
Question: g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(z) is divisible by 4^11, what is the smallest possible value for z?
Options:
A) 22
B) 24
C) 28
D) 32
E) 44
Rationale: g(z)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Answer: B
Question: A certain list of 300 test scores has an arithmetic mean of 75 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 301 test scores with a standard deviation less than d?
Options:
A) 75 and 80
B) 80 and 85
C) 70 and 75
D) 75 and 75
E) 74 and 74
Rationale: Deviation means spreading of the numbers from one median point value..
as the set is already established and we need to add only two numbers, this means we can only add numbers which are closer to the median to reduce the deviation.
so 75 and 75 are the most close numbers and they will increase the number of elements in the set without changing the median value.
D
Answer: D
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/9 + 9^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
Options:
A)1/4
B)1/5
C)1/6
D)1/7
E)1/2
Rationale: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/2
Answer E
Answer: E
Question: If s and t are positive integers such that s/t = 64.15, which of the following could be the remainder when s is divided by t ?
Options:
A)2
B)4
C)8
D)20
E)45
Rationale: The remainder is 0.15 or 15/100. You can go one step further and say that X/Y=12/100, where X and Y are whole numbers. Plug in all the answer choices for X and see which one makes Y a whole number.
One thing that jumps out at me is that A, B, C, and D are all even. E on the other hand is odd. Why? Maybe I'll start plugging in here first.
45/Y=15/100
15Y=4500
Y=300
Answer: E.
Answer: E
Question: In Town X, 96 percent of the population are employed, and 24 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)25%
C)32%
D)75%
E)52%
Rationale: Total employed people 96%, out of which 24 are employed males, hence 72% are employed females.
(employed females)/(total employed people)=72/96=3/4=75%
Answer: D.
Answer: D
Question: On Charlie's cell phone plan, he signed up for 8GB of data per 4 week period. If he went over the 8GB per month, it would cost him an extra $10.00 per GB.
In the first week, he used 2 GB; in the 2nd week, he used 3 GB; in the 3rd week, he used 5 GB; and in the 4th week, he used a whopping 10GB.
How much extra did Charlie need to pay on his cell phone bill?
Options:
A)$120
B)$40
C)$80
D)$100
E)$140
Rationale: To determine how much extra he would need to pay, you have to add all 4 weeks of GB usage (2+3+5+10 = 20).
To determine the extra amount of GB usage, you have to subtract the the original amount of GB (8) allowed on his plan. 20-8 = 12
To determine the extra cost on his cell phone plan, you have to multiply $10.00 per extra usage (12) for a total of $120.00.
The correct answer is A
Answer: A
Question: The ratio between the speeds of two trains is 3: 4. If the second train runs 400 kms in 6 hours, then the speed of the first train is ?
Options:
A)50.01 km/hr
B)51.01 km/hr
C)40.01 km/hr
D)52.01 km/hr
E)None of these
Rationale: Explanation:
Let the speeds of two trains be 3X and 4X km/hr.
4/X=400/6=>X=16.67 Km/hr
So speed of first train is 16.67*3 = 50.01 km/hr
Option A
Answer: A
Question: In how many different number of ways 6 men and 2 women can sit on a shopa which can accommodate persons?
Options:
A)A)160
B)B)170
C)C)190
D)D)1680
E)E)230
Rationale: 8p4 = 8 x 7 × 6 × 5 = 1680
Option 'D'
Answer: D
Question: If 2994 Ã· 14.5 = 173, then 29.94 Ã· 1.45 = ?
Options:
A)17.1
B)17.3
C)17.5
D)17.7
E)17.2
Rationale: 29.94/ 1.45 = 299.4/14.5
= (2994/14.5) x 1/10) [ Here, Substitute 173 in the place of 2994/14.5 ]
= 173/10
= 17.3
Answer is B.
Answer: B
Question: 1764 can be expressed as a product of primes as
Options:
A)2 × 2 × 3 × 3 × 7 × 7
B)2 × 3 × 3 × 3 × 7 × 7
C)2 × 2 × 2 × 3 × 3 × 7
D)2 × 3 × 3 × 3 × 3 × 7
E)None of these
Rationale: Explanation:
It is clear that 1764 = 2 × 2 × 3 × 3 × 7 × 7
Answer: Option A
Answer: A
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 35% play football, how many play both?
Options:
A)120
B)150
C)200
D)180
E)60
Rationale: n(A) = 75*600/100 = 450
n(B) = 35*600/100 = 210
n(AUB) = 600
n(AnB) = 450+210-600 = 60
Answer is E
Answer: E
Question: A volume of 10936 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres?
Options:
A)2812
B)8231
C)2734
D)4222
E)4254
Rationale: a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 10936l can be kept in (10936/4) hemispheres
ans.2734
ANSWER:C
Answer: C
Question: The unit digit in the product (624 * 708 * 913 * 463) is:
Options:
A)2
B)7
C)6
D)8
E)1
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*8*3*3) = 8
ANSWER: D
Answer: D
Question: In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:1, If Rs 60000 was their profit, how much amount did C receive.
Options:
A)10000
B)20000
C)15000
D)61000
E)26000
Rationale: Explanation:
A:B = 3:1 = 3:1
=> A:C = 3:2 = 3:2
=> A:B:C = 3:1:2
C share = (2/6)*60000= 20000
Option B
Answer: B
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?
Options:
A)11
B)86
C)66
D)55
E)44
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86
Answer:B
Answer: B
Question: 3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?
Options:
A)7
B)8
C)6
D)5
E)3
Rationale: Let 1 woman's 1 day work = x.
Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4.
So, (3x/2 + 4x + + 6x/4) = 1/7
28x/4 = 1/7 => x = 1/49
1 woman alone can complete the work in 49 days.
So, to complete the work in 7 days, number of women required = 49/7 = 7.
Answer: A
Answer: A
Question: If GAVE is coded as 4657 and RAT is coded as 333. How is GATE coded?
Options:
A)4673
B)4367
C)4637
D)4763
E)4376
Rationale: g-4 a-6 e-7 from the code gate
t - 3 from bat
ANSWER:C
Answer: C
Question: The perimeter of an isosceles right triangle is 4 + 4 sq rt 2. What is the length of the hypotenuse of the triangle?
Options:
A)2.82
B)2
C)3
D)4
E)5
Rationale: side of triangle is a then perimeter = a+ a +a.sqrt2 ( right angle and pythagorus) =2a +a .sqrt 2 = 4 + 4 Sqrt2 or,
a. ( 2+ sqrt2) = 4(1 + sqrt2) a= 4.( 1+sqrt2)/2+sqrt2 =4*2.414/3.414 = then hypotenuse = 2.82
A
Answer: A
Question: If the numerator of a fraction is increased by 2 and the denominator is increased by 1, the fraction becomes 5⁄8 and if the numerator of the same fraction is increased by 3 and the denominator is increased by I the fraction becomes 3⁄4. What is the original fraction?
Options:
A)Data inadequate
B)2⁄7
C)4⁄7
D)3⁄7
E)None of these
Rationale: Let the original fraction be x⁄y.
Then x+2y+1=58x+2y+1=58 or, 8x – 5y = – 11........ (i)
Again, x+3y+1=34x+3y+1=34 or, 4x – 3y = –9........ (ii)
Solving, (i) and (ii) we get x = 3 and y = 7
∴ fraction = 3⁄7
Answer D
Answer: D
Question: A city had 400 migrants in the year 2000. Since then, The number of migrants in a countrythe city has doubled every 3 years. If there were 400 migrants in the country in the year 2000, What was the increase in the population of migrants during the period from 2009 to 2012?
Options:
A)1400
B)2300
C)3000
D)3200
E)3800
Rationale: The population will increase in the following order:
2000: 400
2003: 800
2006: 1600
2009: 3200
2012: 6400
Difference between 2009 and 2012 = 3200
Option D
Answer: D
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
Options:
A)1260
B)1279
C)1023
D)1927
E)1298
Rationale: Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: C
Question: Three numbers are in the ratio 1:2:3 and their H.C.F is 62. The numbers are:
Options:
A)62, 124, 186
B)60, 124, 186
C)10, 20, 30
D)62, 24, 186
E)12, 24, 186
Rationale: Let the required numbers be x, 2x and 3x. Then, their H.C.F = x. So, x = 62.
The numbers are 62, 124, 186.
ANSWER:A
Answer: A
Question: The present age of the father is 3years more than 3 times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father?
Options:
A)22years
B)30years
C)33years
D)15years
E)25years
Rationale: Let the son's present age be x years
father's present age = (3x+3)
3x+3+3 = 2(x+3)+10
3x+6 = 2x+16
x = 10
father's present age = 3x+3 = 3*10+3 = 33 years
Answer is C
Answer: C
Question: If a = 105 and a^3 = 21 × 25 × 45 × b, what is the value of b?
Options:
A)35
B)42
C)45
D)49
E)54
Rationale: a=105 = 3* 5 *7
a^3 = 21 × 25 × 45 × b
=> a^3 = (7*3) x (5*5) x ( 3^2 * 5) x b
=> a^3 = 3^3 * 5^3 * 7 x b
=>( 3* 5 *7) ^3 = 3^3 * 5^3 * 7 x b
b = 7^2 = 49
Answer D
Answer: D
Question: Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take a day more. How long does it take to complete the task if they both work together?
Options:
A)5
B)4.5
C)6
D)7
E)8
Rationale: Work done by A & B in a day = x &y respectively.
When A starts:
No. of days when A works = 6No. of days when B works = 4 → 6x + 4y = 1
When B starts:
No. of days when b works = 5 No. of days when A works = 5 → 5x + 5y = 1
Solving the above two equations for xy
x = 1/10 y = 1/10
→ Total work done by AB in a day = 1/10 + 1/10 = 2/10 = 1/5
→ No. of days to complete the work when both work together = 5
Answer: A
Answer: A
Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:
Options:
A)20 liters
B)30 liters
C)40 liters
D)60 liters
E)70 liters
Rationale: Quantity of milk = 60 x	2	litres = 40 litres.
3
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = 40 .
20 + x
Now, 40 =	1
20 + x	2
20 + x = 80
x = 60.
Quantity of water to be added = 60 litres
so the correct answer is option D)
Answer: D
Question: A sock drawer contains seven socks, each one a different solid color. The colors of the socks are yellow, green, blue, indigo, and violet. A person reaches into the drawer, pulls out two socks, and puts a single sock on each foot. If each sock can fit either the left or the right foot, and if it matters whether a particular sock is on the left or the right foot, how many different sock fashion combinations could the person make from the five socks?
Options:
A)12
B)15
C)21
D)36
E)20
Rationale: It's a question of permutation since order matters here ....
It can be deduced to-
5P2 = 5!/3! = 5*4 = 20 .........Answer is - E
Answer: E
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)450
B)490
C)500
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 total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
Options:
A)68,98
B)60,60
C)64,87
D)64,09
E)60,64
Rationale: Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer:B
Answer: B
Question: The product of all the prime numbers less than 25 is closest to which of the following powers of 10?
Options:
A)10^9
B)10^8
C)10^7
D)10^8
E)10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19,23
=2.2 *10^8
D
Answer: D
Question: A computer wholesaler sells 7 different computers and each is priced differently. If the wholesaler chooses three computers for display at a trade show, what is the probability (all things being equal) that the two most expensive computers will be among the three chosen for display?
Options:
A)5/35
B)3/28
C)1/28
D)1/56
E)1/168
Rationale: Since, two of the choices are prefixed, we are free to choose 1 from the rest of the 5 avilable. so 5C1 is the numerator.
Total no of ways we can choose 3 from 7 is 7c3, which is the denominator.
So, the probability: 5c1/7c3= 5/35 ans is A.
Answer: A
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 W in miles per hour for the entire trip?
Options:
A)W=26.7
B)W=30.0
C)W=40.0
D)W=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: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
Options:
A)A.10%
B)B.20%
C)C.25%
D)D.42%
E)E.50%
Rationale: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.D
Answer: D
Question: A father was as old as his son's present at the time of your birth. If the father's age is 36 years now, the son's age 5years back was?
Options:
A)10 years
B)12 years
C)14 years
D)13 years
E)20 years
Rationale: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
D
Answer: D
Question: A man can row 6 kmph in still water. When the river is running at 3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
Options:
A)5.75
B)4.5
C)5.76
D)5.74
E)5.71
Rationale: M = 6
S = 3
DS = 9
US = 3
x/9 + x/3 = 1
x = 2.25
D = 2.25 * 2 = 4.5 Answer: B
Answer: B