mathewhe/aqua_rat huggingface dataset:
Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then
leaves. A alone can finish the remaining work in
(A) 5 days
(B) 6 days
(C) 7.5 days
(D) 8.5 days
(E) None of these
Rationale: Explanation:
B's 5 days work =
110
∗
5=12Remaining work =1−12=12A can finish work =15
∗
12=7.5days
Answer: C
Answer: (C) 7.5 days
Question: The average of marks obtained by 120 boys was 39. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?
(A) 100
(B) 110
(C) 120
(D) 130
(E) 140
Rationale: Let the number of boys who passed = X.
Then, 39 x X + 15 x (120 - X) = 120 x 39
24X = 4680 - 1800
=> X = 2880/24
X = 120.
Hence, the number of boys passed = 120.
ANSWER:C
Answer: (C) 120
Question: If the numerator of a fraction T is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?
(A) 16 1⁄6%
(B) 25%
(C) 33 1⁄3%
(D) 50%
(E) 66 2⁄3%
Rationale: This question can be dealt with conceptually or by TESTing VALUES.
We're told that the numerator of a fraction T is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction.
Let's TEST 2/1
If we triple the numerator and double the denominator, we end up with....
(2x3)/(1x2) = 6/2 = 3
Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2 = 1/2 of itself = 50%
D
Answer: (D) 50%
Question: At what rate percent on simple interest will Rs.750 amount to Rs.1125 in 5 years?
(A) 2
(B) 10
(C) 4
(D) 5
(E) 6
Rationale: 375 = (750*5*R)/100
R = 10%.Answer: B
Answer: (B) 10
Question: If 45% of a class averages 95% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent).
(A) 83%
(B) 84%
(C) 85%
(D) 86%
(E) 87%
Rationale: This question is a Weighted Average question with a series of dependent variables.
The remaining portion of the class represents 100% - 45% - 50% = 5% of the class
Converting the portions of the class population to decimal weights, we find:
Class Average = 0.45x95 + 0.50x78 + 0.05x60 = 84.75
The class average (rounded) is 85%
Final Answer
C) 85%
Answer: (C) 85%
Question: John's Bank's saving amount is decreased 30% due to loan payment and current balance is Rs.7000. Find the actual balance before deduction?
(A) 8000
(B) 8500
(C) 9000
(D) 9500
(E) 10000
Rationale: CP* (70/100) = 7000
CP= 100 * 100 => CP = 10000
Answer:E
Answer: (E) 10000
Question: An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: n(n+2) to be divisible by 2 either n or n+2 must be a multiples of 2.
In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 4 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 2, or 4. Thus, the overall probability is 2/4 =1/2.
Answer: C.
Answer: (C) 1/2
Question: The sequence a1, a2, a3, ... , an, ... is such that an=an−1+an−2/2 for all n≥3n≥3. If a3=4 and a5=20, what is the value of a6 ?
(A) 12
(B) 16
(C) 20
(D) 24
(E) 28
Rationale: Since given that an=an−1+an−2/2, then:
a5=a4+a3/2 --> 20=a4+4/2 --> a4=36
a6=a5+a4/2 --> a6=20+36/2 --> a5=28
Answer: E.
Answer: (E) 28
Question: The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.
(A) 12, 9
(B) 18, 3
(C) 15.16, 6
(D) 12, 12.37
(E) 12, 15.16
Rationale: CM=3
AREA=PM*CM/2, thus PM=12
By Pythagorean Theorem, we can now find the value of PC.
D is the correct option.
Answer: (D) 12, 12.37
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 34 cm?
(A) 680 sq.cm
(B) 268 sq.cm
(C) 618 sq.cm
(D) 297 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 34
= 680 sq.cm.
Answer:A
Answer: (A) 680 sq.cm
Question: In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk?
(A) 1
(B) 46
(C) 20
(D) 26
(E) 30
Rationale: Explanation :
One bag of husk = 46 cows per day
⇒ 46 × 1 × 46 = 1 × 46 × x
For one cow = 46 days
Answer : B
Answer: (B) 46
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 488. What is the sum of the last 8 of the even integers?
(A) 598
(B) 604
(C) 610
(D) 616
(E) 622
Rationale: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 488
The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =
488 + 8(16) = 488 + 128 = 616
The answer is D.
Answer: (D) 616
Question: A boat travels 40 km downstream in 8 hours and 36 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.
(A) 8 km/hr, 1 km/hr
(B) 5 km/hr, 4 km/hr
(C) 1 km/hr, 6 km/hr
(D) 2 km/hr, 1 km/hr
(E) 4 km/hr, 1 km/hr
Rationale: Downstream speed=40km/8hrs
=5kmph
upstream speed=36km/12hrs
=3kmph
speed of boat=avg of downstream and upstream speeds
speed of boat=(5+3)/2kmph
=4kmph.
current speed=half of the difference of downstream and upstream speeds
currend speed=(5-3)/2kmph
=1kmph
ans is 4km/hr,1km/hr
ANSWER:E
Answer: (E) 4 km/hr, 1 km/hr
Question: During a given week A programer spends 1/4 of his time
preparing flow chart, 3/8 of his time coding and the rest of
the time in debugging the programs. If he works 48 hours
during the week , how many hours did he spend debugging the
program.
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 18 hours
(E) 19 hours
Rationale: 1/4 of time for flow charts =48/4=12 hours
3/8 time for coding =48*3/8=18
so remaining time for debugging =48-12-18=18 hours
ANSWER:D
Answer: (D) 18 hours
Question: Q. How many 6-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5?
(A) 180
(B) 240
(C) 210
(D) 270
(E) 300
Rationale: the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2
i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _
case 1 > 1 _ _ _ _ _ _ here the units digit can be either 2 or 6
when the units digit is 2 i.e 1 _ _ _ _ _ 2
number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60
when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30
case 2 > 2 _ _ _ _ _ _ (here units digit may be 2 or 6)
number of ways this can be done would be 5! / (2!) for 2 =60
and 5! / 2! for 6 ... = 60
adding all of these ... gives the answer 180 ...
the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat
A
Answer: (A) 180
Question: In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 55x/9
(B) 50x/9
(C) 60x/9
(D) 65x/9
(E) 75x/9
Rationale: Sales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5;
Sales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50.
Since the sales of of Japanese tools was x, then 9{total}/50 = x -->9 {total} = 50x
{total} = 50x/9
Answer: B
Answer: (B) 50x/9
Question: 30% of a number is more than 60% of 150 by 120. Find the number?
(A) 770
(B) 712
(C) 720
(D) 740
(E) 700
Rationale: (30/100) * X – (60/100) * 650 = 190
2/7 X = 210
X = 700
Answer:E
Answer: (E) 700
Question: 5,9,17,29,49,__
(A) 79
(B) 80
(C) 81
(D) 82
(E) 83
Rationale: (9+5) +3 = 17
(16+9) +4 = 29
(28+16)+5 = 49
(48+28)+6 = 82
ANSWER:D
Answer: (D) 82
Question: If X and Y are positive integers such that (3X + 7Y) is a multiple of 11, then which of the following will be divisible by 11?
(A) 4X + 6Y
(B) X + Y + 4
(C) 9X + 4Y
(D) 4X - 9Y
(E) 9X - 4Y
Rationale: by hit and trail, we put X = 5 and Y = 1 so that (3X + 7Y)
= ((3*5) + (7*1)) = 22, which is divisible by 11
(4X + 6Y) = 4*5 + 6*1 = 26, which is not divisible by 11
(X + Y + 4) = (5 + 1 + 4) = 10, which is not divisible by 11
(9X + 4Y) = (9*5 + 4*1) = 49 which is not divisible by 11
(4X - 9Y) = (4*5 - 9*1) = 11 which is divisible by 11
(9X - 4Y) = (9*5 - 4*1) = 41 which is not divisible by 11
So the Answer is D
Answer: (D) 4X - 9Y
Question: A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
I. The rate of X is Rs. 20 per kg.
II. The rate of Y is Rs. 13 per kg.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
The ratio, in which X and Y are mixed, is not given.
So, both I and II together cannot give the answer.
answer is (D).
Answer: (D) Both I and II are not sufficient to answer
Question: What percentage of numbers from 1 to 70 have squares that end in the digit 1?
(A) 1
(B) 14
(C) 20
(D) 21
(E) 22
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such numbers = 14.
Required percentage = (14/70 * 100) = 20%
ANSWER:C
Answer: (C) 20
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,056. How much did she invest at 5%?
(A) $500
(B) $400
(C) $700
(D) $900
(E) $950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1056/1000)-1 = 0.053 = 5.3%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.056
(0.05)x +0.06 - (0.06)x = 0.056
-0.01x = -0.004
x= -0.004/-0.01 = 4/10 = 40%
So X = 40% of the 1000 which is 400
ANSWER:B
Answer: (B) $400
Question: There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need
to remove so that only 96% of the apples are green?
(A) 40
(B) 8
(C) 15
(D) 25
(E) 50
Rationale: 98−x/100−x=96100
Or, 9800−100x=9600−96x
Or, 200=4x
Or, x=50
ANSWER:E
Answer: (E) 50
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 288
(B) 660
(C) 500
(D) 267
(E) 298
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.Answer: C
Answer: (C) 500
Question: Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y?
(A) 15.5 sec
(B) 8.4 sec
(C) 33.6 sec
(D) 31.11 sec
(E) 16.8 sec
Rationale: Z--------------------------------------|----------------------------Y
Car A(20mps)------------------------->P<---------------Car B(15mps)
Let 2 cars meet each other at point P in t seconds.
Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t.
From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further.
so, 15t/20 = 10
So t=40/3 sec and total distance = (35*40)/3
Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx.
Answer D
Answer: (D) 31.11 sec
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.
(A) 7/18
(B) 7/19
(C) 7/11
(D) 7/12
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ways.
7/15
Answer: E
Answer: (E) 7/15
Question: A box contains SEVEN bulbs out of which 3 are defective. If TWO bulbs are chosen at random, find the probability that atleast one bulb is good
(A) 5/6
(B) 6/7
(C) 7/8
(D) 8/9
(E) 9/8
Rationale: Required probability ==1-3C2/7C2= 1 - 1/7 = 6/7.Answer:B
Answer: (B) 6/7
Question: The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ?
(A) 2.5
(B) 1.5
(C) 1
(D) 3.5
(E) 4.5
Rationale: Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3
We know that the sum of their ages is 12
so, x+(x+1)+(x+2)+(x+3) = 12
therefore The youngest child is 1.5 years old
Answer: B
Answer: (B) 1.5
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
(A) 187
(B) 190
(C) 192
(D) 195
(E) 213
Rationale: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Answer: (D) 195
Question: If (7)(x^2) has four different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x can have at most 4 prime factors, namely the prime factor 7 plus 3 others.
If x had more than this number of prime factors, then (7)(x^2) would have more than 4 prime factors.
The answer is D.
Answer: (D) 4
Question: How many integers between 324,700 and 436,600 have tens digit 1 and units digit 3?
(A) 327
(B) 645
(C) 987
(D) 1119
(E) 1339
Rationale: The integers are:
324,713
324,813
etc...
436,513
The number of integers is 4366 - 3247 = 1119
The answer is D.
Answer: (D) 1119
Question: If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 15 degrees?
(A) π/3
(B) 3π/2
(C) 2π
(D) 5π/2
(E) 8π
Rationale: Area = 16π
Radius = 4
Circumference = 2 x 4 x π = 8π
Angle forming the arc = 15 degrees. 15/360 = 1/24.
Therefore length of arc = 1/24 * 8π = π/3 - Answer choice A.
Answer: (A) π/3
Question: Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be
(A) Rs.165.50
(B) Rs.1700
(C) Rs. 175.50
(D) Rs. 180
(E) None
Rationale: Solution
Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.
x-143/22.50 = 1 =â€º x - 143 = 22.50 =â€º x=165.50.
Hence, price of the third variety = Rs.165.50 per kg.
Answer A
Answer: (A) Rs.165.50
Question: Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range?
(A) 3
(B) 4
(C) cannot be determined
(D) 6
(E) 8
Rationale: Yes, the correct answer is C
Answer: (C) cannot be determined
Question: If x^3 > y^2 > z, which of the statements could be true?
I. x < y = z
II. x = z < y
III. y < x < z
(A) I only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Given : x^3 > y^2 > z
I. x < y = z is not true i.e. Answers can not be Options A, C or E
II. x = z < y is not true i.e. Answers can not be Options A, C or E
III. y < x < z is true for x=4, y=3, z=5 i.e. Answers can only be Options B
Answer: option B
Answer: (B) III only
Question: A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?
(A) $1520
(B) $1640
(C) $1780
(D) $1850
(E) $1960
Rationale: The total surface area is 2(2*4 +4*5 + 2*5) = 76 square feet
The total cost is 76*$20 = $1520
The answer is A.
Answer: (A) $1520
Question: A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?
(A) 76 ways
(B) 65 ways
(C) 54 ways
(D) 28 ways
(E) 30 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways.
Answer: E
Answer: (E) 30 ways
Question: A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top?
(A) 20th minute
(B) 21th minute
(C) 22th minute
(D) 24th minute
(E) 25th minute
Rationale: in every min person climbs up 12m and slips 8m . hence net displacement becomes 4m.
in 19 minutes person would climb (19*4)=76m
in 20th minute person would climb 12m up.. and it will be on top.
hence in 20th minute. person will reach on pole.
ANSWER:A
Answer: (A) 20th minute
Question: If z is a multiple of 7899, what is the remainder when z^2 is divided by 9?
(A) 0
(B) 2
(C) 3
(D) 6
(E) 7
Rationale: The sum of the digits is 7+8+9+9=33.
Thus 3 is a factor of 7899, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A.
Answer: (A) 0
Question: A bag contains 3 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?
(A) 6/11
(B) 27/55
(C) 31/55
(D) 91/165
(E) 109/165
Rationale: P(no red balls) = 8/11*7/10*6/9 = 56/165
P(at least one red ball) = 1 - 56/165 = 109/165
The answer is E.
Answer: (E) 109/165
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?
(A) 4/7
(B) 3/7
(C) 35/128
(D) 4/28
(E) 28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
7C4 (1/2)^4 (1/2)^r
which is 35/128
Answer is C.
Answer: (C) 35/128
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State?
(A) 7000
(B) 8300
(C) 6000
(D) 5000
(E) 4000
Rationale: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 83 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 83
=> total appeared candidates in State B = 83 x 100 = 8300
=> total appeared candidates in State A = total appeared candidates in State B = 8300
Answer: (B) 8300
Question: What is the Mode of the following data set R- {1,2,7,9,6,6,7,7}
(A) 1
(B) 2
(C) 7
(D) 6
(E) 9
Rationale: Mode of a set is the data point that is repeated the most number of times. In the set given, 7 is repeated.
Answer: C
Answer: (C) 7
Question: 624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: firstly factors of 624 = 1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624
the question says each row will have people no less than 12 and no more than 52,
therefore, we should be interested in the factors between 12 and 52 (inclusive)
12(in each row) * 52(number of columns) =624, similarly
13 * 48
16 * 39
24 * 26
26 * 24
39 * 16
48 * 13
52 * 12
total possibilities = 8
option C
Answer: (C) 8
Question: The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
(A) 37 years
(B) 30 years
(C) 32 years
(D) 44 years
(E) None of these
Rationale: The total age of 10 students with average 25 = 250
The total age of 12 students with average 27 = 324
The total age of 2 new students = 74
Their average =37
Correct Option A
Answer: (A) 37 years
Question: In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 63
Rationale: F:C:W
1:12:30
Sport version:
F:C
3:12
F:W
1:60
OR 3:180
So C:F:W = 12:3:180
C/W = 12/180 = 3 ounces/x ounces
x = 4*180/12 = 60 ounces of water
D
Answer: (D) 60
Question: A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 48pi/x
(B) 75x
(C) 48x
(D) 24x
(E) 20x
Rationale: Let's try the explanation. We have two wheels. One with 14pi and the other one with 42pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (42pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder).
Anyway, we have 14pi*x=42pi*a.
(14pi*x)/(42pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 20x.
Ans :E
Answer: (E) 20x
Question: Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case.
(A) 170
(B) 172
(C) 174
(D) 176
(E) 178
Rationale: The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(31, 5) + 4 = 174.
ANSWER:C
Answer: (C) 174
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.79
(B) 5.77
(C) 5.76
(D) 5.72
(E) 5.71
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76.Answer:C
Answer: (C) 5.76
Question: At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 39 = 19 + 18 + 12 - 4 - 2x
2x = 19 + 18 + 12 - 4 - 39
= 45 - 39
= 6
x = 3
ANSWER:B
Answer: (B) 3
Question: In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
(A) 3/4
(B) 1/4
(C) 1/3
(D) 7/19
(E) 1/7
Rationale: Total number of balls = (8 + 7 + 6) = 21.
Let E	= event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E)=7
P(E)=n(E)/n(S)
=7/21
=1/3
The answer should be C
Answer: (C) 1/3