mathewhe/aqua_rat huggingface dataset:
Question: If -1 < h < 5, which of the following has the greatest value?
(A) a) 1-h
(B) b) 1+h
(C) c) 1+h^2
(D) d) 1-1/h
(E) e) 1-1/(h^2)
Rationale: easiest way of solving this would be to substitute a value.
lets say h= - 1/2
a) 3/2
b) 1/2
c) 5/4
d) 3
e) - 3
the value you chose is wrong . h cannot be 0.9 as -1<h<0. if you chose -0.9 answer will still be D.
Answer is E.
Answer: (E) e) 1-1/(h^2)
Question: How many words can be formed by using all letters of the word ‘DOHA’ ?
(A) 12
(B) 42
(C) 24
(D) 21
(E) 120
Rationale: Solution
The word DOHA contains 4 different letters.
Required number of words = 4P4 = 4 ! = (4 x 3 x 2 x 1) = 24
Answer C
Answer: (C) 24
Question: Find the odd man out
32, 34, 42, 46, 58, 59, 60, 66
(A) 31
(B) 41
(C) 67
(D) 59
(E) 61
Rationale: as 59 is only odd number.
ANSWER:D
Answer: (D) 59
Question: 40% of a number is added to 60, the result is the same number. Find the number?
(A) 300
(B) 288
(C) 270
(D) 100
(E) 281
Rationale: (40/100) * X + 60 = X
4x+600 = 10x
6x=600
x= 100
Answer : D
Answer: (D) 100
Question: If a2 + b2 + c2 = 560 and ab + bc + ca =8, then a + b + c is
(A) 4
(B) 52
(C) 16
(D) 24
(E) 64
Rationale: by formula ,
(a + b + c)^2= a^2 + b^2 + c^2 + 2(ab + bc + ca),
since, a^2 + b^2 + c^2 = 560 and ab + bc + ca = 8,
(a + b + c)^2 = 560 + 2(8)
= 576
= 24^2
therefore: a + b + c = 24
ANSWER:D
Answer: (D) 24
Question: A can do a piece of work in 40 days; B can do the same in 20 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 24 days
(B) 65 days
(C) 86 days
(D) 40 days
(E) 17 days
Rationale: 10/40 + 10/20 + 10/x = 1
x = 40 days
Answer:D
Answer: (D) 40 days
Question: The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
(A) 4/7
(B) 3/2
(C) 3/5
(D) 9/4
(E) 3/1
Rationale: Let the earnings of P and Q be 9x and 10x respectively.
New ratio = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2
Answer: B
Answer: (B) 3/2
Question: X and Y are both integers. If X/Y = 50.60, then what is the sum of all the possible two digit remainders of X/Y?
(A) 315
(B) 616
(C) 672
(D) 900
(E) 1024
Rationale: Remainder = 0.60 --> 60/100 --> Can be written as (60/4) / (100/4) = 15/25
So remainders can be 15, 30, 45, 60, ..... 90.
We need the sum of only 2 digit remainders --> 15 + 30 + 45 + 60 + 75 + 90 = 315
Answer: A
Answer: (A) 315
Question: 1/2+[(2/11*11/32)+1]-9/16=
(A) 29/16
(B) 19/16
(C) 15/16
(D) 9/13
(E) 0
Rationale: 1/2 - [(2/11*11/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: (E) 0
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 850 in 4 years. The sum is?
(A) s. 738
(B) s. 750
(C) s. 650
(D) s. 730
(E) s. 735
Rationale: S.I. for 1 year = (850 - 825) = Rs. 25
S.I. for 3 years = 25 * 3 = Rs. 75
Principal = (825 - 75) = Rs. 750.
ANSWER:B
Answer: (B) s. 750
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 59?
(A) 3944
(B) 920
(C) 7290
(D) 6928
(E) 4012
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 59 = Rs. 4012.
Answer: Option E
Answer: (E) 4012
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7560 km and comes back to the starting point. The total time taken by him is:
(A) 914.2 hours
(B) 900 hours
(C) 915 hours
(D) 905 hours
(E) 960 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7560/18 + 7560/14 = 420 + 540 = 960 hours
Answer: Option E
Answer: (E) 960 hours
Question: Solve the following quadratic equation by factoring.
U2-5U-14=0
(A) -2,-7
(B) 2,-7
(C) 1,8
(D) 1,-8
(E) 2,6
Rationale: We already have zero on one side of the equation, which we need to proceed with this problem. Therefore, all we need to do is actually factor the quadratic.
(U+2)(U-7) = 0
U=-2 AND U = 7
ANSWER A
Answer: (A) -2,-7
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 58 km/hr
(B) 50 km/hr
(C) 60 km/hr
(D) 98 km/hr
(E) 76
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Answer: (B) 50 km/hr
Question: Moli buys 3 ribbons,7 clips and 1 soap for Rs.120 exactly. At the same place it would cost Rs.164 for 4 ribbons, 10 clips and one soap. How much would it cost for one ribbon, one clip and one soap ?
(A) 36
(B) 34
(C) 38
(D) 32
(E) 31
Rationale: Explanation :
Let us consider, Ribbon is denoted by r
Clips is denoted by c
Soaps is denoted by s
Now according to the question,
=> 3r+7c+s = 120 -------- (1)
=> 4r+10c+s = 164 -------- (2)
(1) - (2)
=> (3r-4r) + (7c - 10c) +(s - s) = 120 - 164
=> -r - 3c = - 44
Multily the equation by -1 , it becomes
=> r + 3c = 44 ------- (3)
Now Perform this operation 2 * (1) - (2)
=> 2r+4c+s=76 ------- (4)
Finaly (4) - (3)
=> r + c + s=32
Hence, the cost of 1 ribbon ,1 clip and 1 saop would be 32 rs.
Answer : D
Answer: (D) 32
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is
(A) 17/29
(B) 17/21
(C) 17/22
(D) 17/20
(E) 17/34
Rationale: Explanation:
n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(Eá´œP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: three friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $650. If one of the friends had a coupon for 35% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) $190
(B) $141
(C) $145
(D) $137
(E) $135
Rationale: 650 * 0,35 = 227
650 - 227 = 423
423 / 3= 141
Answer B
Answer: (B) $141
Question: When John can do a work in 15 days and Marry in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is?
(A) 2/15
(B) 3/25
(C) 8/15
(D) 9/15
(E) None
Rationale: A's 1 day's work =	1	;
15
B's 1 day's work =	1	;
20
(A + B)'s 1 day's work =	(	1	+	1	)	=	7	.
15	20	60
(A + B)'s 4 day's work =	(	7	x 4	)	=	7	.
60	15
Therefore, Remaining work =	(	1 -	7	)	=	8/15
15
C
Answer: (C) 8/15
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 16
(B) 19
(C) 90
(D) 17
(E) 91
Rationale: 200*2 = 400
580
-----
180
1----2
?----180 = 90
Answer: C
Answer: (C) 90
Question: The edges of three metal cubes are 1 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
(A) 3.9
(B) 4.2
(C) 4.5
(D) 4.8
(E) 5.1
Rationale: The total volume is 1^3+3^3+4^3=92
The edge of the new cube is the cube root of 92 which is about 4.5 cm.
The answer is C.
Answer: (C) 4.5
Question: The average of 10 numbers is 23. If each number is increased by 5, what will the new average be?
(A) 36
(B) 28
(C) 72
(D) 29
(E) 22
Rationale: Sum of the 10 numbers = 230
If each number is increased by 5, the total increase =
5 * 10 = 50
The new sum = 230 + 50 = 280 The new average = 280/10
= 28.
Answer:B
Answer: (B) 28
Question: From the given integer n, if n*n*n is odd, then which is true from below options?
(A) n is
(B) n is odd and n*n is even
(C) n*n is even
(D) n is even
(E) n*n is odd
Rationale: n is odd and n*n is even
Option B
Answer: (B) n is odd and n*n is even
Question: In a room there are 9 people. Each person shook hands with every other person. How many hand shakes were there?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: 9C2 = 36
The answer is A.
Answer: (A) 36
Question: In order to complete a reading assignment on time, Terry planned to read 60 pages per day. However, she read only 30 pages per day at first, leaving 480 pages to be read during the last 6 days before the assignment was to be completed. How many days in all did Terry have to complete the assignment on time?
(A) 10
(B) 8
(C) 6
(D) 12
(E) 14
Rationale: D=60*X - according to the plan, assignment to be completed on time reading 60 pages per day for next X days. But, Terry's plans changed so she read as follow:
30 pages for first Y days and 480 pages for last 6 days, we get these equations:
30*Y+480=60*X
X-Y=6 --------->>X planned number of days, Y - actually used reading 30 pages per day and 6 leftover days used to complete a lump 780 pages
From above we find that X=Y+6 and 30Y+480=60Y+360 or 30Y=120 --->>>>> Y=4, hence X=10
Answer : A
Answer: (A) 10
Question: If m is a positive integer and m^2 is divisible by 54, then the largest positive integer that must divide m is?
(A)  3
(B)  6
(C)  18
(D)  12
(E)  16
Rationale: M^2 is divisible by 48 so M^2 must be multiple of 48.
If the value of M is Multiples of 18 then it will satisfy the condition. If we If M is 12 or 24 or 36 then it ans is C but if M = 54 then answer should be 16.
Is the question right? Or am i missing some thing?
C
Answer: (C)  18
Question: Today is Monday. After 37 days, it will be:
(A) Sunday
(B) Saturday
(C) Friday
(D) Thursday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 35 days, it will be Monday.
After 37 days, it will be Wednesday.
Answer :E
Answer: (E) Wednesday
Question: In the storage room of a certain bakery, the ratio of sugar to flour is 5 to 4, and the ratio of flour to baking soda is 10 to 1. If there were 60 more pounds of baking soda in the room, the ratio of flour to baking soda would be 8 to 1. How many pounds of sugar are stored in the room?
(A) 600
(B) 1200
(C) 1500
(D) 1600
(E) 3000
Rationale: Sugar:Flour = 5:4 = 25:20;
Flour:Soda = 10:1 = 20:2;
Thus we have that Sugar:Flour:Soda = 25x:20x:2x.
Also given that 20x/(2x+60) = 8/1 --> x=120 --> Sugar = 25x =3,000
Answer: E.
Answer: (E) 3000
Question: A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 99
(B) 289
(C) 350
(D) 882
(E) 400
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 42 = 50/3
3(x + 300) = 2100 è x = 400m.
Answer: E
Answer: (E) 400
Question: A and B invests Rs.10000 each, A investing for 6 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.24000, find their shares?
(A) 8000, 16000
(B) 1599,2000
(C) 7290,3000
(D) 15000,4000
(E) 72821,5000
Rationale: The ratio of their profits A:B =6:12 = 1 : 2
Share of A = 1 * 24000/3 = 8000
Share of B = 2 * 24000/3 = 16000
Answer : A
Answer: (A) 8000, 16000
Question: If a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is
(A) 4/12
(B) 4/29
(C) 4/22
(D) 4/13
(E) 4/17
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52
= 4/13
Answer:D
Answer: (D) 4/13
Question: A batsman scored 120 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 45(4/11) %
(B) 50 %
(C) 45(5/11) %
(D) 44(5/11) %
(E) None of these
Rationale: Explanation :
Total runs scored = 120
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 120 - 60 = 60
Required % = (60/120) × 100 = 50%
Answer : Option B
Answer: (B) 50 %
Question: The wheel of a car A is having a diameter of 40 inches is rotating at the rate of x inches/minute. The wheel of another car B is having a diameter of 20 inches and is rotating at the rate of y inches/minute. What is the value of x in terms of y if both the rims reach their starting positions at the same time after every rotation?
(A) 4y
(B) 2y
(C) 6y
(D) 3y
(E) 1y
Rationale: t=S1/V1=S2/V2
or 40/x=20/y
or x=40y/20=2y
Answer is B
Answer: (B) 2y
Question: In a game of eight players lasting for 70 minutes, six substitutes alternate with each player. This means that all players, including the substitutes, are on the pitch for the same length of time. For how long?
(A) 43 minutes
(B) 46 minutes
(C) 39 minutes
(D) 40 minutes
(E) 30 minutes
Rationale: D
40 minutes
(70 Ã— 8)Ã· 14.
Total time for eight players = 70 Ã— 8 = 560 minutes.
However, as 14 people are each on the pitch for an equal length of time, they are each on the pitch for 40 minutes (560 Ã· 14);
Answer: (D) 40 minutes
Question: If the Average (mean ) of 3 positive temperatures is x degrees fahrenheit, then the sum of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) 3x
(C) 5x/3
(D) 3x/2
(E) 3x/5
Rationale: Let the 5 numbers be 1,2,3,4(since no restrictions are given). There mean is 2.5 (x).
Now the sum of greatest three would be 2+3+4= 9
so the answer has to be 3x....that is option B
Answer: (B) 3x
Question: The effective annual rate of interest corresponding to a nominal rate of 16% per annum payable half-yearly is?
(A) 16.64%
(B) 16.07%
(C) 16.08%
(D) 16.09%
(E) 16.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 8/100)2] = Rs. 116.64 Effective rate = (116.64 - 100) = 116.64%
ANSWER:A
Answer: (A) 16.64%
Question: A monkey ascends a greased pole 17 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ?
(A) 31st
(B) 22nd
(C) 23rd
(D) 24th
(E) None of these
Rationale: In 2 minutes, he ascends = 1 metre
âˆ´ 15 metres, he ascends in 30 minutes.
âˆ´ He reaches the top in 31st minute.
Answer A
Answer: (A) 31st
Question: A type of extra-large SUV averages 12.2 miles per gallon (mpg) on the highway, but only 7.6 mpg in the city. What is the maximum distance, in miles, that this SUV could be driven on 22 gallons of gasoline?
(A) 190
(B) 284.6
(C) 300
(D) 268
(E) 312
Rationale: so 12.2 * 22 = 268..
IMO option D is correct answer..
Answer: (D) 268
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 5 years respectively. If the difference between their interests is Rs.144, find the each sum?
(A) Rs.578
(B) Rs.125
(C) Rs.640
(D) Rs.220
(E) Rs.300
Rationale: Explanation:
(P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer: C
Answer: (C) Rs.640
Question: If Aaron is now twice as old as Bailey was 20 years ago, and B is Bailey's current age in years, which of the following represents the sum of Aaron and Bailey's ages 4 years from now?
(A) 3B-22
(B) 3B-25
(C) 4B-22
(D) 4B-24
(E) 4B-25
Rationale: B is Bailey's current age.
Let Aaron's current age be A.
given A = 2(B-20).
four years from now Aaron's age will be = 2(B-20) + 4 = 2B-36
four years from now Bailey's age will be = B+4
Sum of ages of Mason and Gunther's after 4 years = 2B-36+B+4 = 3B-22
Ans : A
Answer: (A) 3B-22
Question: A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group?
(A) 657 ways
(B) 600 ways
(C) 345 ways
(D) 876 ways
(E) 415 ways
Rationale: Two men, three women and one child can be selected in ⁴C₂ * ⁶C₃ * ⁵C₁ ways
= (4 * 3)/(2 * 1) * (6 * 5 * 4)/(3 * 2) * 5
= 600 ways.
Answer: B
Answer: (B) 600 ways
Question: Two persons starting from the same place walk at a rate of 0.5kmph and 5.5kmph respectively. What time will they take to be 75km apart, if they walk in the same direction?
(A) 17 hrs
(B) 22 hrs
(C) 25 hrs
(D) 12 hrs
(E) 15 hrs
Rationale: The relative speed of the boys = 5.5kmph â€“ 0.5kmph
= 5 kmph
Distance between them is 75 km
Time= 75km / 5 kmph = 15 hrs
Answer : E.
Answer: (E) 15 hrs
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 388
(B) 277
(C) 500
(D) 2887
(E) 212
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters.Answer: C
Answer: (C) 500
Question: 28,14,15,22.5,24.5,61.25,64.25,?
(A) 224.875
(B) 234.875
(C) 244.875
(D) 254.875
(E) 264.875
Rationale: 28*0.5=14
15*1.5=22.5
24.5*2.5=61.25
64.25*3.5=224.875
ANSWER:A
Answer: (A) 224.875
Question: If 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
(A) 41
(B) 42
(C) 43
(D) 66
(E) 45
Rationale: n(n-1)/2 =12*11/2
=66
ANSWER:D
Answer: (D) 66
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
(A) 1 : 3
(B) 3 : 4
(C) 2 : 5
(D) 3 : 7
(E) 4 : 9
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4.
B
Answer: (B) 3 : 4
Question: Which of the following lines is perpendicular to y = − 2x + 3 and has the same y-intercept as y = 2x − 3?
(A) y = -1/2*x + 3
(B) y = 1/2*x - 3
(C) y = 1/2*x + 3
(D) y = 2x + 3
(E) y = 2x − 3
Rationale: Slope of y = − 2x + 3 is -2.
Product of slope of Perpendicular lines is always -1. Therefor slope of a line perpendicular to the above line is 1/2
1/2*-2 = -1
General equation of a line perpendicular to y = − 2x + 3 is y = 1/2x + k where is the k is the y intercept.
y-intercept of y = 2x − 3 is -3
Therefore equation of the required line is
y = 1/2 x - 3
Answer B
Answer: (B) y = 1/2*x - 3
Question: Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 45. He was allowed to drop his lowest score. After doing so, his average test score improved to 50. What is the lowest test score that was dropped?
(A) 20
(B) 30
(C) 55
(D) 65
(E) 80
Rationale: The arithmetic mean of 4 equally weighted tests was 45. So what we can assume is that we have 4 test scores, each 45.
He dropped his lowest score and the avg went to 50. This means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too. When the lowest score was removed, the other 3 scores got their 5 back. So the lowest score was 3 *5 = 15 less than 45.
So the lowest score = 45 - 15 = 30
Answer (B)
Answer: (B) 30
Question: Joe has a total of $200 in his two pockets. He takes one fourth of the
money in his left pocket and puts it in his right pocket. He then takes
$20 from his left pocket and puts it in his right pocket. If he now has
an equal amount of money in each pocket, then how much money did he
originally have in his left pocket?
(A) $120
(B) $130
(C) $140
(D) $150
(E) $160
Rationale: Joe had $100 in his left and $100 in his right pocket at the end. So, he had $120
in his left pocket (and $80 in his right pocket) before moving $20 from his left to his
right pocket. Thus, he had $160 in his left pocket originally (solve x − x/4 = 120).
correct answer E
Answer: (E) $160
Question: In a 3 x 3 grid, comprising 9 tiles can be painted in red or blue. When tile is rotated by 180 degrees, there is no difference which can be spotted. How many such possibilities are there?
(A) 22
(B) 32
(C) 771
(D) 99
(E) 77
Rationale: This grid even rotated 180 degrees the relative positions of the tiles do not change. So we paint tile number 1's with red or blue (only one color should be used) , 2's with red or blue.....tile 5 red or blue. Then total possibilities are 2525 = 32
Answer:B
Answer: (B) 32
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 32
(B) 50
(C) 99
(D) 77
(E) 51
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.
Answer: B
Answer: (B) 50
Question: A store owner estimates that the average price of type A products will increase by 25% next year and that the price of type B products will increase by 10% next year. This year, the total amount paid for type A products was $4500 and the total price paid for type B products was $8300. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
(A) $14,755
(B) $15,325
(C) $16,000
(D) $16,225
(E) $17,155
Rationale: cost of type A products next year = 1.25 * 4500 = 5625
cost of type B products next year = 1.1 * 8300 = 9130
total 5625 + 9130 = 14755
ANSWER:A
Answer: (A) $14,755
Question: How many pages the book have, if total 294 digits are used to form the page numbers?
(A) 134 pages
(B) 136 pages
(C) 137 pages
(D) 138 pages
(E) 139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 35 pages ... 105 digits
----------------------
Total ...134 pages ...300 digits
ANSWER:A
Answer: (A) 134 pages
Question: Lilly has 10 fish and Rosy has 9 fish. In total, how many fish do they have in all?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: 10+9=19
The answer is D.
Answer: (D) 19
Question: The average (arithmetic mean) of four numbers is 7x + 6. If one of the numbers is x, what is the average of the other three numbers?
(A) 9x + 8
(B) 3x + 3
(C) 5x + 1
(D) 5x + 4
(E) 15x + 12
Rationale: If the average of four numbers is 7x + 3, then the sum of all four numbers if 4 * (7x + 6) = 28x + 24. If one of the numbers is x, then the average of the remaining three numbers would be: (28x + 24 - x)/3 = (27x + 24)/3 = 9x + 8.
Answer is A.
Answer: (A) 9x + 8
Question: If n is an integer and 5^n > 4,000,000, what is the least possible value of n?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: When you separate the 4000000 into factors of 5 and 2 you get - > 10^6 x 2^2 = 5^6 x 2^8
2 to the ^ 8 = 256 so its 256 x 5^6
that means 5^6 x 5^x must be greater
5^x > 256
5^1=5
5^2=25
5^3= 125
5^4= 625 - > so x must be at least 4
5^(6+4)= 5^10
ANSWER:D
Answer: (D) 10
Question: If two sides of a triangle have lengths 6 and 10, which of the following could be the perimeter of the triangle?
I. 10
II. 15
III. 25
(A) I only
(B) II only
(C) II and III only
(D) I, II, and III
(E) none
Rationale: The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
Therefore:
(10-6) < {third side} < (10+6).
4< {third side} < 16.
Perimeter = {third side} + 4 + 16= {third side} + 20.
24 < {perimeter} < 36
Answer: E.
Answer: (E) none
Question: x and y are positive integers. If xy + 2x is odd, then which of the following must be even?
(A) x
(B) y +2
(C) x + y
(D) xy − x
(E) x^2 − y
Rationale: Given that xy + 2x is odd, which means x(y+2) is odd.
Product of two nos. will be odd only if both the nos. are odd.
Hence x is odd, y+2 is also odd.
y+2 is even. Answer will be B.
Answer: (B) y +2