mathewhe/aqua_rat huggingface dataset:
Question: In the manufacture of a certain product, 8 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
(A) 0.125%
(B) 0.32%
(C) 0.8%
(D) 1.25%
(E) 2.0%
Rationale: Percent of defective produced = 8%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(8/100)*100%
= (32/10000)*100%
= (32/100)%
= .32 %
Answer B
Answer: (B) 0.32%
Question: If a number N is chosen at random from the set of two-digit integers whose digits are both prime numbers, what is the probability Q that N is divisible by 3?
(A) 1/3
(B) ¼
(C) 9/25
(D) 5/16
(E) 0
Rationale: Prime digits are : 2, 3, 5, 7
Total number of 2 digit #s with both digits prime are: 4*4 = 16
out of these numbers divisible by 3 = 33, 27, 57, 72 and 75. I had to find the numbers manually using the 4 numbers above.
=> prob = 5/16.
Ans D. Took me 3:20 mins.
Answer: (D) 5/16
Question: Find the constant k so that : -x2 - (k + 9)x - 8 = -(x - 2)(x - 4)
(A) 11
(B) 12
(C) 15
(D) 14
(E) 19
Rationale: -x2 - (k + 9)x - 8 = -(x - 2)(x - 4) : given
-x2 - (k + 9)x - 8 = -x2 + 6x - 8
-(k + 9) = 6 : two polynomials are equal if their corresponding coefficients are equal.
k = -15 : solve the above for k
correct answer C
Answer: (C) 15
Question: A train running at the speed of 48 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 286
(B) 120
(C) 255
(D) 150
(E) 287
Rationale: Speed=(48 * 5/18) m/sec = (40/3) m/sec Length of the train
= (Speed x Time) = (40/3 * 9) m
= 120 m.
Answer:B
Answer: (B) 120
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 45% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A)  5%
(B)  10%
(C)  15%
(D)  35%
(E)  30%
Rationale: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.
Neither is zero.
Hence 100 = 60 + 50 + 45 - n (Exactly 2 products) - 2*10
100 = 135 - n (Exactly 2 products) => n (Exactly 2 products) = 35.
Answer: D
Answer: (D)  35%
Question: Calculate the time it will take for a train that is 250 meter long to pass a bridge of 150 meter length, if the speed of the train is 35 km/hour ?
(A) 56 seconds
(B) 3515 seconds
(C) 41.15 seconds
(D) 30 seconds
(E) 36 seconds
Rationale: Speed = 35 Km/hr = 35*(5/18) m/sec = 9.72 m/sec
Total distance = 250+150 = 400 meter
Time = Distance/speed
= 400 * (1/9.72) = 41.15 seconds
Answer: C
Answer: (C) 41.15 seconds
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 20 different models of televisions, what is the minimum number of letters that must be used to make the codes?
(A) 5
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥20. The smallest n which fulfills this condition is n = 5.
Answer A
Answer: (A) 5
Question: what is the smallest number by which 3600 be divided to make it a perfect cube ?
(A) 9
(B) 50
(C) 300
(D) 450
(E) 550
Rationale: Solution
3600 = 23 * 52 * 32 * 2.
to make it a perfect cube, it must be divided by 52 * 32 * 2 i.e., 450 .
Answer D
Answer: (D) 450
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.7
(B) 1.4
(C) 1.2
(D) 1.5
(E) 3
Rationale: M = 9
S = x
DS = 9 + x
US = 9 + x
9 + x = (9 - x)2
9 + x = 18 -2x
3x = 9
x = 3
Answer: E
Answer: (E) 3
Question: If p and q are prime numbers, how many divisors does the product p^4 * q^5 have?
(A) 30
(B) 40
(C) 45
(D) 50
(E) 56
Rationale: when a number N=a^x*b^y, where a and b are prime numbers, and x, y are positive integers, the number of divisors of N=(x+1)(y+1)
Therefore, the answer is A. 5*6=30
Answer: (A) 30
Question: Worldwide production of motor vehicles was 3.9 million vehicles in 1946 and 61.3 million in 1987. Of the following, which is closest to the average (arithmetic mean) annual increase, in millions, in worldwide production of motor vehicles during this period?
(A) 0.08
(B) 1.0
(C) 1.1
(D) 10.5
(E) 1.4
Rationale: Change in production of motor vehicles = 61.3 - 3.9 = 57.4 million in 41 years (1987 - 1946)
average increase per year = 57.4/41 = 1.4 million (apporx.)
Answer (E)
Answer: (E) 1.4
Question: Two pipes can fill a tank in 14 and 12 hours, while third pipe will make the tank empty in 20 hours. If all three pipes operate simultaneously. In how many hours the tank will be filled ?
(A) 5.5 Hours
(B) 7.5 Hours
(C) 8.5 Hours
(D) 9.5 Hours
(E) 6.5 Hours
Rationale: In 1 hour it fill 1/14 + 1/12 - 1/20 = 2/19
So fill tank fill up in 19/2= 9.5 Hours
ANSWER:D
Answer: (D) 9.5 Hours
Question: If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 10 minutes?
(A) 40
(B) 100
(C) 150
(D) 240
(E) 300
Rationale: Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 10 minutes the population increases by 10 x 4 = 40 people.
Answer. A.
Answer: (A) 40
Question: The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?
(A) 1.5
(B) 2.4
(C) 3.6
(D) 4.0
(E) 4.6
Rationale: Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]
= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.
Required average = (9.2 / 2) = 4.6.
E
Answer: (E) 4.6
Question: remy bought 2Q steaks for W dollars. Jerome buys R steaks for a 50% discount, how much will the steaks cost him in cents?
(A) 50RW/Q
(B) 50QR/W.
(C) 25RQ/W
(D) 25RW/Q
(E) RW/(4Q)
Rationale: Cost of 1 steaks = W/2Q dollars or 100W/2Q cents
Cost of R steaks at no discount = 100RW/2Q = 50RW/Q
Cost of R steaks at 50% discount = 1/2 * 50RW/Q = 25RW/Q
Hence, answer will be D.
Answer: (D) 25RW/Q
Question: In what ratio P:Q should the Mixture P of milk and water in the ratio of 4:1 be mixed with another Mixture Q of milk and water in the ratio 2:3 so that the resultant mixture contains equal quantities of milk and water?
(A) 1:3
(B) 2:3
(C) 1:4
(D) 3:4
(E) 3:5
Rationale: (4/5)*P +(2/5)*Q = (1/5)*P+(3/5)*Q
3P=Q
P/Q = 1/3
The answer is A.
Answer: (A) 1:3
Question: In how many ways the letters of the word RAIMBON be arranged?
(A) 6468
(B) 9667
(C) 5040
(D) 9865
(E) 4687
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: (C) 5040
Question: For a finite sequence of non zero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6, -5 ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Given sequence: {1, -3, 2, 5, -4, -6}
The questions basically asks: how manypairs of consecutive termsare there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
2*5=10=positive;
5*(-4)=-20=negative;
(-4)*(-6)=24=positive.
So there are 4 pairs of consecutive terms of the sequence for which the product is negative.
Answer: D.
Answer: (D) 4
Question: A student can select one of 6 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
(A) 22
(B) 72
(C) 99
(D) 37
(E) 01
Rationale: 6C1×3C1×4C16C1×3C1×4C1 = 6x3x4=72 ways
Answer:B
Answer: (B) 72
Question: A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per m2 is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.
(A) 6,18,6
(B) 6,18,0
(C) 6,18,7
(D) 6,18,2
(E) 6,18,1
Rationale: Explanation:
Let breadth = x metres, length = 3x metres, height = H metres.
Area of the floor=(Total cost of carpeting)/(Rate) = (270/5)= 54
So, breadth = 6 m and length = = 9 m.
Now, papered area = (1720/10) = 172
Area of 1 door and 2 windows = 8
Total area of 4 walls = (172 + 8) = 180
Answer: A) b=6;l=18;H=6
Answer: (A) 6,18,6
Question: A man taking the census walks up to the apartment of a mathematician and asks him if he has any children and how old they are. The mathematician says "I have three daughters and the product of their ages is 72." The man tells the mathematician that he needs more information, so the mathematician tells him "The sum of their ages is equal to our apartment number." The man still needs more information so the mathematician tells him "My oldest daughter has her own bed and the other two share bunk beds."
How old are his daughters?
(A) 5-2-3
(B) 6-4-4
(C) 9-5-4
(D) 8-3-3
(E) 7-2-2
Rationale: His daughters are 8, 3, and 3. The prime factorization of 72 is 2 * 2 * 2 * 3 * 3, so the possible ages are 2, 3, 4, 6, 8, 9, 12, and 18. Using the prime factorization and these numbers the only combinations of numbers that work for the first clue are:
18, 2 and 2.
9, 4 and 2.
6, 6 and 2.
6, 4 and 3.
8, 3, and 3.
Since he doesn't know the ages after this piece of information the sum of the three numbers must not be unique. The sum of 8, 3, and 3; and 6, 6, and 2 are the same. Now the final clue comes in handy. Since we know that the oldest daughter has her own bed it is likely that she has the bed to herself and is older than the other two so there ages are 8, 3, and 3 rather than 2, 6 and 6.
Answer: (D) 8-3-3
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
(A) 1.04
(B) 2.04
(C) 3.04
(D) 4.04
(E) None of these
Rationale: Explanation:
100 cm is read as 102 cm.
A1 =(100 × 100)cm2 and A2= (102 × 102)cm2
(A2 - A1) = [1022 - 1002]
= (102 + 100) x (102 - 100) = 404 cm2 Answer: D
Answer: (D) 4.04
Question: One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min, then the slower pipe alone will be able to fill the tank in?
(A) 81 min
(B) 108 min
(C) 144 min
(D) 192 min
(E) 120 min
Rationale: Let the slower pipe alone fill the tank in x min.
Then, faster pipe will fill it in x/3 min.
1/x + 3/x = 1/36
4/x = 1/36 => x = 144 min.
ANSWER:C
Answer: (C) 144 min
Question: If Finn was 16 months old one year ago, how old was he, in months, x months ago?
(A) x − 30
(B) x − 12
(C) 28 − x
(D) 24 − x
(E) 30 − x
Rationale: Age Today = 16 months + 12 months (1year) = 28 months
X months ago- Today's Age - X = 28 - X
Ans- C
Answer: (C) 28 − x
Question: On the xy co-ordinate plane, point C is (5,-2) and point D is (-2,2.5). The point on line segment CD that is twice as far from C as from D is:
(A) (1,-1)
(B) (1,1)
(C) (2,0.25)
(D) (3,-0.5)
(E) (3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,-0.5)
Answer: D
Answer: (D) (3,-0.5)
Question: Two bullet train s 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 15.8 sec.
(B) 12.8 sec.
(C) 11.8 sec.
(D) 10.8 sec.
(E) 08.8 sec.
Rationale: D
10.8 sec.
Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = 300x9/250 = 54/5 = 10.8 sec.
Answer: (D) 10.8 sec.
Question: If the number 241 * 523 is completely divisible by 9, then the smallest whole number in place of * will b
(A) 4
(B) 5
(C) 1
(D) 8
(E) 9
Rationale: Sum of digits = (2 + 4 + 1 + x + 5 + 2 + 3) = (17 + x), which must be divisible by 9.
x = 1.
C)
Answer: (C) 1
Question: What is the lowest positive integer that is divisible by each of the odd integers between 17 and 23, inclusive?
(A) 3×17×19×21
(B) 5×17×19×23
(C) 23*21*17*19
(D) 7×15×19×21
(E) 15×17×19×21
Rationale: We should find the LCM of 17, 19, 23 and 21 = 3*7 --> LCM = 3*23*7*17*19 = 23*21*17*19.
Answer: C.
Answer: (C) 23*21*17*19
Question: Umesh directly went from P, to Q which is 9 feet distant. Then he turns to the right and walked 4 feet. After this he turned to the right and walked a distance which is equal from P to Q. Finally he turned to the right and walked 3 feet. How far is he now from P?
(A) 6 feet
(B) 5 feet
(C) 1 feet
(D) 0 feet
(E) 10 feet
Rationale: 1 feet
ANSWER:C
Answer: (C) 1 feet
Question: Income and expenditure of a person are in the ratio 10 : 4. If the income of the person is Rs. 19000, then find his savings?
(A) 79754
(B) 87689
(C) 59875
(D) 11400
(E) 87648
Rationale: Let the income and the expenditure of the person be Rs. 10x and Rs. 4x respectively.
Income, 10x = 19000 => x = 1900
Savings = Income - expenditure = 10x - 4x = 6x = 6(1900)
So, savings = Rs. 11400.
Answer:D
Answer: (D) 11400
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
(A) 340 km
(B) 480 km
(C) 360 km
(D) 450 km
(E) None of these
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Answer: (C) 360 km
Question: There are e members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of e?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 22
Rationale: Combinations of two persons, in which Michael was not selected = 55
number of ways two persons can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11
Thus, e = m + 1(Michael) = 12
option B
Answer: (B) 12
Question: there are 15 cars and 16 trucks? which is greater15 or 16?
(A) 15
(B) 14
(C) 12
(D) 17
(E) 16
Rationale: E
Answer: (E) 16
Question: A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 60 paise per sq. metre
(A) s510
(B) s780
(C) s880
(D) s480
(E) s980
Rationale: area of the plot=110m*65m=7150sq.m
area of plot excluding gravel=105m*60m=6300sq.m
area of gravel =7150sq.m-6300sq.m =850sq.m
cost of building it = 850sq.m*60
= 51000p
in Rs =51000/100=Rs510
ANSWER:A
Answer: (A) s510
Question: Which of the following equivalent to (1/64)^2?
(A) (0.05)^3
(B) (0.06)^3
(C) (0.07)^3
(D) (0.08)^3
(E) (0.09)^3
Rationale: (1/64)^2 = (1/4^3)^2 = (1/4)^6 = (1/16)^3 = (0.06)^3
Answer: Option B
Answer: (B) (0.06)^3
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 4, and 7, if the digits are allowed to repeat within a number?
(A) 10,655
(B) 11,988
(C) 12,433
(D) 13,766
(E) 14,322
Rationale: The number of these 3-digit numbers is 3*3*3 = 27
Each digit 1, 4, and 7 will appear in the ones, tens, and hundreds place 9 times each.
The sum equals 9(111) + 9(444) + 9(777) = 11,988
The answer is B.
Answer: (B) 11,988
Question: If r and y are integers and (15^r + 15^(r+1))/4^y = 15^y what is the value of r?
(A) 2
(B) 3
(C) 4
(D) 5
(E) Cannot be determined
Rationale: \frac{15^r( 1+ 15)}{4^y} = 15^y
(15^r . 4^2 ) / 4^y = 15^y. 4^0
15^r . 4^(2-y) = 15^y. 4^0
Equating the powers, r = y; 2-y = 0; So r = y = 2=A
Answer: (A) 2
Question: Find the odd man out:
5, 8, 20, 42, 124, 246
(A) 20
(B) 99
(C) 77
(D) 26
(E) 81
Rationale: Explanation:
The series is followed on the pattern of 2 alternate sequences with common formula being 2n-2 and 3n-2 respectively.
8 = 2*5-2
22 = 3*8-2
42 = 22*2-2
124 = 42*3-2
246 = 124*2-2
Hence, 20 is the odd no.
ANSWER: A
Answer: (A) 20
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 288
(C) 278
(D) 269
(E) 271
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer:A
Answer: (A) 432
Question: Some pen bought something at loss for Rs 60.He then sold it the price of 81 and his profit was 20% of the loss.At what price did he buy the object
(A) 77.5
(B) 76.5
(C) 75.5
(D) 74.5
(E) 73.5
Rationale: lets Assume loss be Rs x on Rs 60
Cost Price = 60+x
He then sold it the price of 81 and his profit was 20% of the loss
60+x + 20%x = 81
Solving this x will be 17.5
Cost Price = 60 + x = 60 + 17.5 = 77.5
ANSWER:A
Answer: (A) 77.5
Question: In Set T, the average (arithmetic mean) equals the median W. Which of the following must be true?
I. Set T consists of evenly spaced numbers.
II. Set T consists of an odd number of terms.
III. Set T has no mode.
IV. None of the above.
(A) I only
(B) I and II
(C) II and III
(D) I, II, and III
(E) IV only
Rationale: This is a very good 'trap question'.
Consider Set A= { 0,0,0,0 } Mean=Median=Mode=0- Eliminates 1,2 and 3 OR
Consider Set B= {1,2,2,3 } Mean=Median=Mode=2- Eliminates 1,2 and 3
If you think that only in 'consecutive integers' the average is equal to the median W you might fall for 'D'.
Ans: E
Answer: (E) IV only
Question: A rectangular swimming pool is 8 feet by 20 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 540 square feet. What is the width of the deck?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the width =W
Total Area of the pool and deck= (2W+8)(2W+20)
We can Test the answer choices along with unit digit method
A) 2 feet ...........12*24 has unit digit 8..........Eliminate
B) 2.5 feet.........13*25 has unit digit 5..........Eliminate
C) 3 feet............14*26 has unit digit 4...........Hold
D) 4 feet............16*28 has unit digit 8...........Eliminate
E) 5 feet............18*30 has unit digit 0...........Eliminate
Answer: E w=5
Answer: (E) 5
Question: Exactly 3/7 of the people in the room are under the age of 21, and exactly 5/8 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
(A) 24
(B) 35
(C) 39
(D) 60
(E) 65
Rationale: The total number of the people in the room must be a multiple of both 7 and 8 (in order 3/7 and 5/8 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 7 and 8, which is 56.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 56 people in the room.
Therefore there are 3/7*56=24 people in the room under the age of 21.
Answer: A.
Answer: (A) 24
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 0, 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?
(A) 1/6
(B) 1/9
(C) 1/18
(D) 1/24
(E) 1/36
Rationale: There are 6*6 = 36 possibilities.
Bob has 2 chances so the probability is 2/36 = 1/18.
The answer is C.
Answer: (C) 1/18
Question: If in a kindergarten class, there are five children 3 feet 4 inches tall (indicated by notation 3'4"), two children 4'3" tall and thirteen children 2'9" tall, which of the following is the median height of the children?
(A) 2'9"
(B) 2'6"
(C) 3'3"
(D) 3'4"
(E) 4'3
Rationale: Total number of children in class = 20
so median must be between 10th and 11th child when they are arranged in ascending order.
When arranged in ascending order 5th and 6th child will have the height of 3'4"
so required median height = (2'9"+2'9")/2 = 2'6"
Ans:Option A
Answer: (A) 2'9"
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
(A) 2 3/2
(B) 2 2/3
(C) 2.5
(D) 3
(E) 3.5
Rationale: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer: C
Answer: (C) 2.5
Question: Change 1/8 = 8-1 to logarithmic notation.
(A) log(8)8
(B) log7
(C) log(5)8
(D) log 5
(E) None of these
Rationale: Solution:
1/8 = 8-1 = log88
Answer is A
Answer: (A) log(8)8
Question: Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
(A) 54
(B) 72
(C) 105
(D) 108
(E) 118
Rationale: Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.
ANSWER:D
Answer: (D) 108
Question: One lady has 2 children, one of her child is boy, what is the probability of having both are boys
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 3/4
Rationale: n(S)=one of her child is boy out of 2 children=BB,BG=2
n(E)=both are boys=BB=1
so p=n(E)/n(s)=1/2
ANSWER:A
Answer: (A) 1/2
Question: If the product 48^64 × 9x2 is divisible by 12, then what is the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 4864 × 9a2 is divisible by 12
=> 4864 × 9a2 is divisible by 3
and 4864 × 9a2 is divisible by 4
4864 is divisible by 4 because number formed by the last two digits is 64 which is divisible by 4. Hence 4864 × 9a2 will also be divisible by 4
4864 is not divisible by 3 (because 4 + 8 + 6 + 4 = 22 which is not divisible by 3). Hence 9a2 must be divisible by 3 because 48^64 × 9x2 is divisible by 3
=> 9 + x + 2 is divisible by 3
=> 11 + a is divisible by 3
Hence a can be 1 or 4 or 7 such that 11 + a is divisible by 3
So, from the given choices, 1 is the answer.
A
Answer: (A) 1
Question: Sterling Silver is 92.5% pure silver. How many grams of Sterling Silver must be mixed to a 90% Silver alloy to obtain a 500g of a 91% Silver alloy?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: Let x and y be the weights, in grams, of sterling silver and of the 90% alloy to make the 500 grams at 91%. Hence
x + y =500
The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams. The pure silver is given in percentage forms. Hence
92.5% x + 90% y = 91% 500
Substitute y by 500 - x in the last equation to write
92.5% x + 90% (500 - x) = 91% 500
Simplify and solve
92.5 x + 45000 - 90 x = 45500
x = 200 grams.
200 grams of Sterling Silver is needed to make the 91% alloy.
Answer A
Answer: (A) 200
Question: Walking with 4/5 of my usual speed, I miss the bus by 6 minutes. What is my usual time?
(A) 16 min
(B) 26 min
(C) 34 min
(D) 24 min
(E) 12 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:5 1 -------- 6 4 --------- ? è 24
Answer: D
Answer: (D) 24 min