mathewhe/aqua_rat huggingface dataset:
Question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
(A) 11
(B) 5
(C) 8
(D) 7
(E) 9
Rationale: 39 + 20 = 59/13 = 7 (Remainder)
ANSWER D
Answer: (D) 7
Question: The average of eight numbers is 14. The average of six of these numbers is 16.The average of the remaining two numbers is
(A) 14×8 – 16×6)/9
(B) 14×8 – 16×6)/1
(C) 14×8 – 16×6)/2
(D) 14×8 – 16×6)/5
(E) 14×8 – 16×6)/6
Rationale: Average of eight numbers = 14
Average of six numbers = 16
Average will be = (14×8 – 16×6)/2
\Answer:	C
Answer: (C) 14×8 – 16×6)/2
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 2.8 sec
(C) 7.5 sec
(D) 2.3 sec
(E) 1.5 sec
Rationale: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer:A
Answer: (A) 2.5 sec
Question: A man is trying 2 different pairs of pants &6 different shirts. How many combinations of 1 pair of pants &1 shirt are possible?
(A) 10
(B) 12
(C) 16
(D) 19
(E) 21
Rationale: Use a tree diagram to illustrate the possible selections. In the diagram, use P1 and P2 to represent the pants and S1, S2, S3, S4, S5, and S6 to represent the shirts.
Using the Fundamental Counting Principle, 2 × 6 = 12 outfits are possible.
B
Answer: (B) 12
Question: What is the sum of the greatest common factor and the lowest common multiple of 12 and 36?
(A) 48
(B) 22
(C) 32
(D) 36
(E) 38
Rationale: Prime factorization of 12 = 2 x 2 x 3
Prime factorization of 36 = 2 x 2 x 3 x 3
GCF = 12
LCM = 36
Sum = 48.
Answer A.
Answer: (A) 48
Question: On a certain day, Jared's farm harvested 2526 oranges. If Jared distributes his oranges evenly across 7 different retail shops, how many oranges would remain with him?
(A) 4 oranges
(B) 7 oranges
(C) 1 orange
(D) 2 oranges
(E) 14 oranges
Rationale: This is equivalent to finding the first number that is divisible by 7 that occurs before 2135.
In order to divide the sum in 9 parts, the amount must be divisible by 7
Divisibility rule of 7: The sum of the digits must be divisible by 7
Sum of digits of 2526 = 15 and 7 is divisible by 7.
Hence, we need to remove 1 to this number for it to be divisible by 7
Correct Option: C
Answer: (C) 1 orange
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age six years back was?
(A) 10 years
(B) 12 years
(C) 13 years
(D) 16 years
(E) 18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 6 years back (19 - 6) = 13 years.
C
Answer: (C) 13 years
Question: The compound interest on $ 30,000 at 7% per annum is $4347. The period (in years) is:
(A) 2
(B) 2 1/2
(C) 3
(D) 4
(E) 5
Rationale: Amount = $(30000 + 4347) = $. 34347.
Let the time be n years.
Then, 30000 1 +	7 n	= 34347
100
107 n	=	34347	=	11449	= 107 2
100 30000 10000 100
n = 2 years.
ANSWER A - 2
Answer: (A) 2
Question: If the cost price is 82% of the selling price, then what is the profit percent?
(A) 5%
(B) 22%
(C) 13%
(D) 21%
(E) 19%
Rationale: Let S.P. = $100
C.P. = $82
Profit = $18
Profit% = 18/82 * 100 = 25/6 = 22% approximately
Answer is B
Answer: (B) 22%
Question: Can you find the last number in the number sequence given below?
10 : 10 : 20 : 45 : 110 : 300 : ?
(A) 880
(B) 756
(C) 390
(D) 610
(E) 930
Rationale: E
930
Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer
Answer: (E) 930
Question: Calculate the largest 6 digit number which is exactly divisible by 99?
(A) 999991
(B) 999965
(C) 999912
(D) 999936
(E) 999930
Rationale: Largest 4 digit number is 999999
After doing 999999 ÷ 96 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
ANSWER : D
Answer: (D) 999936
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 11
(B) 18
(C) 13
(D) 17
(E) 12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer:B
Answer: (B) 18
Question: The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :
(A) 4
(B) 8
(C) 12
(D) 16
(E) 18
Rationale: Explanation:
Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.
Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.
or 5x + 20 = 305 or x = 57.
So, required difference = (57 + 8) - 57 = 8 Answer: B
Answer: (B) 8
Question: If $120 invested at a certain rate of simple interest amounts to $160 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
(A) $190
(B) $180
(C) $200
(D) $240
(E) $250
Rationale: 120 amounts to 160 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 160
120 + 120*(r/100)*(3) = 160 => r = 100/9
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
250
Answer is E.
Answer: (E) $250
Question: A certain industrial machine requires 15 quarts (480 ounces) of oil every day, and it is given a mixture of oil A and oil B. Oil A consists of 5% special additives while oil B consists of 9% special additives. If the machine needs exactly 30 ounces of the special additives to ensure smooth operation, then how much of oil A, in ounces, should be in the mixture?
(A) a.	A – 260
(B) b.	B – 280
(C) c. C – 290
(D) d.	D – 330
(E) e.	E – 380
Rationale: 5%*x + 9% *(480-x)=30
13.2 = 4 %*x
x=330
D
Answer: (D) d.	D – 330
Question: The sum of two numbers is 50 and their product is 1050. What will be the sum of their reciprocals?
(A) (11/140)
(B) (1/21)
(C) (35/4)
(D) (75/8)
(E) None
Rationale: Solution
x+y=50 xy=1050 1/x+1/y=x+y/xy 50/1050 = (1/21).
Answer B
Answer: (B) (1/21)
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 35
(B) 43
(C) 62.5
(D) 71
(E) 72.5
Rationale: Let the capacity of bucket be 10 Litres
They said that it requires 25 buckets to fill the tank
Therefore capacity of tank=25*10=250
If the capacity of the bucket is reduced to to 2/5th of original capacity then New capacity of bucket=(2/5)10=4litres
No. of buckets required to fill the tank=250/4 = 62.5
answer:C
Answer: (C) 62.5
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 8 years older than B, the present age of B is
(A) 35
(B) 37
(C) 38
(D) 41
(E) 42
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 8) years.
(x+8+10)=2(x—10)
hence x=38.
Present age of B = 38 years
Answer: Option C
Answer: (C) 38
Question: Ice-ColdIce-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and GRAY. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?
(A) 12
(B) 14
(C) 18
(D) 19
(E) 20
Rationale: IMO: D - 19
There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, GRAY) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.
The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).
#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1
9 + 9 + 1 = 19
answer is D
Answer: (D) 19
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 8 integers, Y consists of 10 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
(A) 6
(B) 16
(C) 22
(D) 30
(E) 174
Rationale: The number of integers that belong to set X ONLY is 8-6=2;
The number of integers that belong to set Y ONLY is 10-6=4;
The number of integers that belong to set X or set Y, but not both is 2+4=6.
Answer: A.
Answer: (A) 6
Question: A bulldog received 1,600 votes in a bulldog competition, giving him 20 percent of the votes. What percent of the remaining votes would he have needed to receive in order to win 28 percent of the total votes?
(A) 10%
(B) 12.5%
(C) 15%
(D) 17.5%
(E) 20%
Rationale: There were 80% of the votes remaining and he needed 8%/80% = 1/10 = 10%
The answer is A.
Answer: (A) 10%
Question: What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 80 ?
(A) 170
(B) 172
(C) 173
(D) 199
(E) 186
Rationale: First of all, discard 173 and 199 since they are odd. Sum of two primes greater than 2 will always be even because both primes will be odd.
Both numbers need to be greater than 80 i.e. their sum needs to be greater than 160. Since two of the given sums, 170 and 172, are quite close to 160, it should be fair to assume that if they can be written as sum of two primes, we will find the primes between 80 to 90.
Between 80 and 90, there are only 2 primes: 83 and 89 (if you don't remember this, you just need to check for 81, 83, 87 and 89)
83+89 = 172 so answer is (B)
Answer: (B) 172
Question: A motor pool has 300 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
(A) 165%
(B) 90%
(C) 65%
(D) 55%
(E) 10%
Rationale: Solution
Percentage of vehicles neither trucks nor diesel = Total Number of trucks - (Diesel Trucks +Non Diesel Trucks +Other Diesel Vehicles)/Total Number of trucks = 300-(75+15+45)/300= 165/300= 55%
Ans D
Answer: (D) 55%
Question: In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
(A) 12
(B) 3
(C) 5
(D) 8
(E) 10
Rationale: Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER A 12
Answer: (A) 12
Question: An employee’s annual salary was increased $5,000. If her new annual salary now equals $25000 what was the percent increase?
(A) 15%
(B) 80%
(C) 20%
(D) 22%
(E) 24%
Rationale: New annual salary = $25000
Salary increase = $5000.
Original salary = $25000 - $5,000.
= $20,000
%Increase = ($15,000/ $75,000 )*100
=80%
Hence B.
Answer: (B) 80%
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √7 ¤ √7 =
(A) 0
(B) 5
(C) 10
(D) 15
(E) 28
Rationale: X = √7 and Y also =√7
Applying the function (√7+√7)^2 - (√7-√7)^2 = (2√7)^2 - 0 = 4 x 7 = 28.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√7 and y = √7 you get the answer 28.
Answer E
Answer: (E) 28
Question: A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
(A) 76 cm2
(B) 30 cm2
(C) 56 cm2
(D) 45 cm2
(E) 19 cm2
Rationale: The circumference of the circle is equal to the permeter of the rectangle.
Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5
= 30 cm2
Answer:B
Answer: (B) 30 cm2
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 387
(B) 320
(C) 375
(D) 372
(E) 322
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 =>
375
Answer: C
Answer: (C) 375
Question: At Deluxe paint store, Fuchsia paint is made by mixing 4 parts of red paint with 2 parts of blue paint. Mauve paint is made by mixing 3 parts of red paint with 6 parts blue paint. How many liters of blue paint must be added to 24 liters of Fuchsia to change it to Mauve paint?
(A) 9
(B) 12
(C) 15
(D) 16
(E) 24
Rationale: in 24 liters, Red = 4/6 * 24 = 16 and Blue = 8
so, 16/(8+x) = 3/6
or, x = 24 (Answer E)
Answer: (E) 24
Question: The average age of an adult class is 40 years. 12 new students with an avg age of 34years join the class. Therefore decreasing the average by 4 years. Find what was the original average age of the class?
(A) 6
(B) 12
(C) 16
(D) 20
(E) 22
Rationale: Let original strength = y
Then , 40y + 12 x 34 = ( y + 12) x 36
â‡’ 40y + 408 = 36y + 432
â‡’ 4y = 48
âˆ´ y = 6
A
Answer: (A) 6
Question: A box contains seven light out of which 3 are defective. If three light are chosen at random, find the probability that all the three light are defective?
(A) 2/35
(B) 3/35
(C) 1/35
(D) 3/37
(E) None of these
Rationale: Out of nine light , five are good and four are defective.
Required probability = 3C3/7C3 = 1/35
C
Answer: (C) 1/35
Question: In the office supply store, Brittany bought 17 pens of three kinds: ball pens, gel pens, and ink pens, which cost $0.05, $0.10 and $0.25 each. The total that Brittany paid was $2.05. If Brittany bought twice as many gel pens as ink pens, how many ball pens did she buy?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 10
Rationale: Denote each pen with the first letter of its kind and build a system of equations:
5B+10G+25I=205
B+G+I=17
G=2I
B+9I=41
B+3I=17
6I=24
I=4
B=5
Answer: B
_____________
Answer: (B) 5
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
(A) 15
(B) 25
(C) 18
(D) 22
(E) 30
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
ANSWER A
Answer: (A) 15
Question: A worker makes a toy in every 2h. If he works for 100h, then how many toys will he make ?
(A) 40
(B) 54
(C) 50
(D) 39
(E) None
Rationale: No. of toys = 100/2 = 50
Answer : C
Answer: (C) 50
Question: The average of five number is 27. if one number is excluded, the average becomes 25. The excluded number is :
(A) 25
(B) 27
(C) 30
(D) 35
(E) None of these
Rationale: Solution
Excluded number = (27 × 5) - (25 × 4) = 135 - 100 = 35. Answer D
Answer: (D) 35
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 10 and 16 is?
(A) 48
(B) 40
(C) 52
(D) 54
(E) 58
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 16 will be divided into 3 parts= 10, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*26*4= 52
C is the answer
Answer: (C) 52
Question: The difference between compound interest and simple interest on a certain amount of money at 5% per annum for 2 years is 17. Find the sum :
(A) 4500
(B) 7500
(C) 5000
(D) 6800
(E) None of these
Rationale: Sol.(d) Let the sum be 100.
Therefore, SI = 100×5×2100=10100×5×2100=10
and CI = 100(1+5100)2−100100(1+5100)2−100
∴ =100×21×2120×20−100=414=100×21×2120×20−100=414
Difference of CI and SI = 41⁄4 - 10 = 1⁄4
If the difference is 1⁄4 , the sum = 100
=> If the difference is 17, the sum
= 400 × 17 = 6800 Answer D
Answer: (D) 6800
Question: Jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 4 percent solution will be required?
(A) 18
(B) 20
(C) 24
(D) 36
(E) 26.25
Rationale: let a=amount of 4% acid and b= amount of 12% acid.
Now, The equation translates to,
0.04a + .12b = .05(a+b)
but a+b= 60
therefore .04a + .12b = .05(60)
=> 4a + 12b = 300
but b=60-a
therefore
4a+ 12(60-a) = 300
=> 16a = 420
hence a = 26.25.
Answer : E
Answer: (E) 26.25
Question: A chemist mixes one liter of pure water with x liters of a 50% salt solution, and the resulting mixture is a 10% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 50%
Concentration of salt in the mixed solution = 10%
The pure solution and the salt solution is mixed in the ratio of --> (50 - 10)/(10 - 0) = 4/1
1/x = 4/1
x = 1/4
Answer: A
Answer: (A) 1/4
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 3:4
(B) 3:5
(C) 15:23
(D) 17:23
(E) None of these
Rationale: Explanation:
P:Q = 85000 : 15000 = 17:3.
ANSWER IS E
Answer: (E) None of these
Question: A recipe requires 2 1/2 (mixed number) cups of flour 2 3/4 (mixed number) cups of sugar and 1 1/3 (mixed number) cups of milk to make one cake. Victor has 15 cups if flour, 16 cups of sugar and 8 cups of milk. What is the greatest number of cakes tom can make using this recipe?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Less work up front: Go through each item and see what the greatest number of cakes you can make with each. The lowest of these will be the right answer.
Flour: 15 cups, we need 2.5 cups each. Just keep going up the line to see how many cakes we can make: That means I can make 2 cakes with 5 cups, so 6 cakes overall with 15 cups. I've already got the answer narrowed to either A or B.
Sugar: 16 cups, we need 2.75 cups each. Same principle. I can make 2 cups with 5.5 cups, so to make 6 cakes I'd need 16.5 cups. I don't have that much sugar, so we're limited to 5 cakes. No need to even do milk because we're already at 5. Sugar will be the limiting factor.
answer is A
Answer: (A) 5
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 85, what is the value of c âˆ’ a?
(A) 25
(B) 80
(C) 90
(D) 140
(E) It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=170 --2
subtracting 1 from 2 we have
c-a=80;
ANSWER:B
Answer: (B) 80
Question: Eighty percent of the lights at Hotel California are on at 8 p.m. a certain evening. However, forty percent of the lights that are supposed to be off are actually on and ten percent of the lights that are supposed to be on are actually off. What percent L of the lights that are on are supposed to be off?
(A) 22(2/9)%
(B) 16(2/3)%
(C) 11(1/9)%
(D) 10%
(E) 5%
Rationale: Is the Answer D.
let me try..
Let the light which are supposed to be OFF = SO
Let the light which are supposed to be ON = SN
Let the light which are ACTUALLY OFF = AO
Let the light which are ACTUALLY ON = AN
Let the total no. of lights be 100,
So ACTUALLY ON lights = 80
And ACTUALLY OFF lights = 20
Also given >> forty percent of the lights that are supposed to off are actually on >>> (40/100)*SO are ACTUALLY ON
it means >>> (60/100)*SO are ACTUALLY OFF
Also given >> ten percent of the lights that are supposed to be on are actually off >>> (10/100)*SN are ACTUALLY OFF
it means >>> (90/100)*SN are ACTUALLY ON
So, Total ACTUALLY ON lights = (40/100)*SO + (90/100)*SN = 80
and Total ACTUALLY OFF lights = (60/100)*SO + (10/100)*SN = 80
From here we get SO = 20
we need to find: What percent of the lights that are on are supposed to be off >>> So light ACTUALLY ON are 80 and light which are ACTUALLY ON, which are supposed to be OFF = (40/100)*SO = 8.
So (8/80)*100 L= 10%.D
Answer: (D) 10%
Question: P is three times as fast as Q and working together, they can complete a work in 24 days. In how many days can Q alone complete the work?
(A) 16
(B) 77
(C) 32
(D) 55
(E) 778
Rationale: P = 3Q
P + Q = 3Q + Q = 4Q
These 4Q people can do the work in 24 days, which means Q can do the work in 96 days.
Hence, P can do the work in 32 days.
Answer:C
Answer: (C) 32
Question: In a room with 9 people, 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if Jane is Paul's friend, Paul is Jane's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
(A) 5/21
(B) 3/7
(C) 4/7
(D) 5/7
(E) 1
Rationale: (6/9)(7/8) + (5/9)(6/8) if you choose one of the 6 with one other friend, then you have a 7/8 chance of not picking their friend 2nd. If you choose one of the 5 with 2 friends, you have a 6/8 chance of not picking one of their friends second. Add them up.
42/72 + 30/72
72/72 = 1
E. 1
Answer: (E) 1
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 326
(B) 372
(C) 375
(D) 381
(E) 312
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
Answer: C
Answer: (C) 375
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 2:5
(B) 1:4
(C) 3:7
(D) 5:3
(E) 2:3
Rationale: Let 40% of A = 2/3 B
then 40A/100 = 2B/3
2A/5 = 2B/3
A/B = 5/3
A:B = 5:3
Answer is D
Answer: (D) 5:3
Question: Jim has arrived late for his golf tee time with his friends. When he arrives at the course, he discovers that his friends have already walked 180 yards ahead on the course and that they are continuing to walk forward at a rate of 1.5 yards per second. A bystander with a golf cart takes pity on Jim and drives him to meet his friends at the rate of 4 yards per second. Once Jim meets his friends, he exits the cart and walks with them at their rate for the next 120 yards. What is Jim’s approximate average speed for his total trip?
(A) 1.8 yards per second
(B) 2.0 yards per second
(C) 2.4 yards per second
(D) 2.7 yards per second
(E) 3.0 yards per second
Rationale: Given Jim's friends has a lead of 180 yards and moving at 1.5 yards/sec speed
Jim on golf cart with speed 4 yards/sec has to meet this friends, assuming he meets them after "t" secs
So the total distance traveled by Jim and his friends should be same so as to meet them=> 180+1.5t=4t
=> 180=2.5t
=>72 secs, so Jim meets his friends after traveling 72 secs at 4 yards/sec speed---First part of his journey (288 yards in 72 secs)
Now, Jim travels 120 yards with speed 1.5 yards/sec in 120/1.5=80 secs---second part of his journey (120 yards in 80 secs)
So avg speed of Jim= total distance traveled/ total time
=> (288+120)/(72+80)=408/152
=>2.7 yards/sec approx
Answer: D
Answer: (D) 2.7 yards per second
Question: What is the minimum value of z for which z^2 + z - 3/8> 0 is not true?
(A)  -5/2
(B)  -3/2
(C)  -1/2
(D)  -3/4
(E)  1/2
Rationale: I think D -3/4 is the best ans...
Answer: (D)  -3/4
Question: A set of 16 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
(A) 32
(B) 37
(C) 40
(D) 44
(E) 50
Rationale: The correct answer is D.
A set of 16 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 26
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 26
The maximum value n15 can have is 26 + n1 (18) = 44
D
Answer: (D) 44
Question: The forth proportional to 2,4,6 is?
(A) 8
(B) 12
(C) 15
(D) 18
(E) 22
Rationale: Let the fourth proportional to 2,4,6 be x
then 2:4::6:x
2x = 4*6
x = 12
Answer is B
Answer: (B) 12
Question: 2, 3, 5, 16, 231, ?
(A) 53789
(B) 53210
(C) 53051
(D) 52109
(E) 53105
Rationale: 2
3
32 - 22 = 5
52 - 32 = 16
162 - 52 = 231
2312 - 162 = 53105
Answer is E
Answer: (E) 53105