mathewhe/aqua_rat huggingface dataset:
Question: Of the 800 employees of Company X, 30 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 20 percent ?
(A) 200
(B) 160
(C) 112
(D) 80
(E) 100
Rationale: The # oflong-termemployees is 30%*800=240.
After y of them retire new # oflong-termemployees would become 240-y.
Total # of employees would become 800-y.
We want 240-y to be 20% of 800-y --> 240-y=(800 -y)*20% --> y = 100.
Answer: E.
Answer: (E) 100
Question: A solution of 90 litres contains milk and water in the ratio 7:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
(A) 2
(B) 1.5
(C) 3.5
(D) 2.5
(E) 3
Rationale: Exp. Total new quantity = original sol + water =90+10 =100
New ratio = 3:2, New quantity of milk =3/5*100 = 60 Lit,
New quantity of water = 2/5*100= 40 Lit
Water present initially = (40-10) = 30 Lit
Ratio = 60/30 =7/x There for x = 3.5
Answer: C
Answer: (C) 3.5
Question: A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $70. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)
(A) 70xy
(B) 630xy
(C) xy/9
(D) xy/70
(E) 630/(xy)
Rationale: xy sq ft = $70
1 sq ft = $70/xy
multiplying by 9 on both side
9 sq ft = $630/xy
or 1 sq yard = $630/xy
Hence E.
Answer: (E) 630/(xy)
Question: A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
(A) 620 km/hr
(B) 220 km/hr
(C) 220 km/hr
(D) 120 km/hr
(E) 203 km/hr
Rationale: Explanation:
Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour
Answer: D
Answer: (D) 120 km/hr
Question: An investor deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
(A) $10,200
(B) $10,202
(C) $10,400
(D) $10,404
(E) $10,800
Rationale: The amount in the account after 6 months is 1.02*1.02($10,000) = $10,404.
The answer is D.
Answer: (D) $10,404
Question: Find the odd man out. 30, -5, -45, -90, -145, -195, -255
(A) -145
(B) -195
(C) -30
(D) -90
(E) -5
Rationale: 30
30 - 35 = -5
-5 - 40 = -45
-45 - 45 = -90
-90 - 50 = -140
-140 - 55 = -195
-195 - 60 = -255
Hence, -145 is wrong. -140 should have come in place of -145
Answer is A
Answer: (A) -145
Question: How many positive integers less than 8,000 are there in which the sum of the digits equals 5?
(A) 57
(B) 56
(C) 55
(D) 54
(E) 53
Rationale: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.
Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).
So, for example:
XX|X|X|X = 2111
||XXX|XX = 0032
etc.
There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.
B
Answer: (B) 56
Question: If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?
(A) 16
(B) 1.6
(C) 0.16
(D) 0.016
(E) None of these
Rationale: Explanation :
(204/12.75) = 16
⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10)
⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B
Answer: (B) 1.6
Question: In a deck of cards there are 50 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
(A) 1/4.
(B) 4/17.
(C) 5/29.
(D) 8/31.
(E) 1/3.
Rationale: 4+12 tens/50+12 total cards=16/62=8/31
D
Answer: (D) 8/31.
Question: If x is a whole number, then x²(x² - 1) is always divisible by
(A) 12-x
(B) Multiple of 12
(C) 12
(D) 24
(E) 48
Rationale: Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.
ANSWER:C
Answer: (C) 12
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) 2.3
(B) 2.5
(C) 3.5
(D) 3.6
(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: AB
+BA
___
121
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
(A) 6
(B) 8
(C) 9
(D) 11
(E) 14
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
answer has to be 1 in the units digit..
only 11 fits in..
2) BA=10B+A, and
AB=10A+B..
it is given that BA+AB=121..
or 10B+A +10A+B=121..
11(A+B)=121..
so A+B=11..
ANSWER:D
Answer: (D) 11
Question: Calculate the average mark scored by Adam if he had the following scores in an examination: 86, 75, 72, 63 and 65 marks (out of 100) in French Language, Geography, Art and design, History and Physical Education respectively?
(A) 39.2
(B) 79.2
(C) 72.2
(D) 71.2
(E) 76.2
Rationale: Explanation:
Average mark = 86+75+72+63+65/5=72.2
Answer: Option C
Answer: (C) 72.2
Question: Light glows for every 15 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.
(A) 380 times
(B) 381 times
(C) 382 times
(D) 392 times
(E) 331 times
Rationale: Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/15)=331 times.
ANSWER:E
Answer: (E) 331 times
Question: If both 5^3 and 3^4 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n?
(A) 15
(B) 45
(C) 75
(D) 125
(E) 150
Rationale: (2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and two appearances of 5 (in 10^2).
Thus n must include at least 3^2 * 5 = 45
The answer is B.
Answer: (B) 45
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?
(A) 5320
(B) 5325
(C) 5330
(D) 5334
(E) 5336
Rationale: Divisor = (5 * 46) = 230
= 10 * Quotient = Divisor
=> Quotient = 230/10 = 23
Dividend = (Divisor * Quotient) + Remainder
Dividend = (230 * 23) + 46 = 5336
E)
Answer: (E) 5336
Question: Suppose, the speed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
= seed(s(n)), otherwise,
where s(n) indicates the sum of digits of n.For example, seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many positive integers n, such that n < 500, will have seed (n) = 9?
(A) 39
(B) 72
(C) 81
(D) 108
(E) 55
Rationale: Explanation :
We need to find out numbers less than 500, with sum of digits as 9.
We know that a number will be divisible by 9, if the sum of its digits is divisible by 9.
For eg : 18 has sum of digits 9.
198 has sum of digits 18, which has its sum of digits 9.
So, we need to find numbers less than 500 which are divisible by 9, or are multiples of 9 i.e 500/9 is 55.5555.
Hence, there are 55 numbers which are multiples of 9 less than 500.
Answer : E
Answer: (E) 55
Question: What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0?
(A) -2
(B) 10
(C) -1
(D) 3
(E) 0
Rationale: Let us factorize the denominator and rewrite the expression as (xâˆ’3)/((xâˆ’10)(x+2))> 0
Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.
The values that are relevant to us are x = 3, x = 10 and x = -2.
Let us arrange these values in ascending order: -2, 3 and 10.
The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.
Interval 1: x < -2.
Pick a value in that range and check whether the inequality holds good.
Let us take x = -10. When x = -10, (xâˆ’3)/((xâˆ’10)(x+2))< 0; the inequality DOES NOT hold good in this interval.
Interval 2: -2 < x < 3.
Let us take x = 0. When x = 0, (xâˆ’3)/((xâˆ’10)(x+2)) = (0âˆ’3)/((0âˆ’10)(0+2)) > 0; the inequality holds good in this interval.
The least integer value that x can take if x > -2 is x = -1.
ANSWER : C.
Answer: (C) -1
Question: Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?
(A) 600
(B) 720
(C) 10080
(D) 14320
(E) 14800
Rationale: for such questions , we can treat both as one then total person=7..
these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080
ans C
Answer: (C) 10080
Question: Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio D of men to women?
(A)  5:2
(B)  5:1
(C)  4:3
(D)  4:1
(E)  3:1
Rationale: (A) D=184 x 5 + 170 x 2 = 1260.A
Answer: (A)  5:2
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 73 marks. The maximum marks are?
(A) 450
(B) 300
(C) 500
(D) 600
(E) 175
Rationale: Let the maximum marks be x
Then, 33% of x = 125+73
33x/100 = 198
x = 600
Answer is D
Answer: (D) 600
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. five years from today, the difference between the age of the boy and the combined ages of the girls will be
(A) 1
(B) 2
(C) -4
(D) –2
(E) –1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 5 years there ages are
6 ....................... 6 ............................ 8
Difference = 8 - (6+6) = 8 - 12 = -4
Answer = C
Answer: (C) -4
Question: Two trains are traveling towards the same direction. First train is moving at speed of 100 km/hour and second train 200 km/hour.When will the head of first train start overtaking the second train.
(A) 2 hour
(B) 1 hour
(C) 2.5 hour
(D) 3.5 hour
(E) 4 hour
Rationale: Difference between the speed of two trains 750 – 500 = 250 km. In 60 minutes, the second train reduces the gap from the first train by 100 km. So, to reduce the gap of 250 km, the train will take 180 minutes or 2.5 hours.
Answer: C.
Answer: (C) 2.5 hour
Question: If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?
(A) 100
(B) 272
(C) 287
(D) 189
(E) 289
Rationale: 4/3 π * 10 * 10 * 10 = 8 * 4/3 πr3
r = 5
4π * 5 * 5 = 100π
Answer:A
Answer: (A) 100
Question: Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was five times as old as Sam. How old is Jim now?
(A) 42
(B) 46
(C) 50
(D) 54
(E) 58
Rationale: J = 2F = 2(S+9) = 2S+18
J-6 = 5*(S-6)
(2S+18)-6 = 5S-30
S = 14 and so J = 46
The answer is B.
Answer: (B) 46
Question: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
(A) 11
(B) 24
(C) 55
(D) 66
(E) 71
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/20) + (d/30)]
= (2d)/[5d/60) => 24 kmph.
Answer: B
Answer: (B) 24
Question: 12 : 8 seconds :: ? : 4 minutes
(A) 10
(B) 15
(C) 6
(D) 8
(E) 7
Rationale: 12*4=8*x
x=6
ANSWER:C
Answer: (C) 6
Question: ) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color?
(A) 1
(B) 3
(C) 8
(D) 5
(E) 7
Rationale: If the cube is cut in to 27 smaller cubes, then number of separations made = n = 3 (since 3×3×3=27). Number of smaller cubes with no color = (n–2)3 = (3–2)3 = 13 = 1
Answer:A
Answer: (A) 1
Question: A train 700 m long can cross an electric pole in 40 sec and then find the speed of the train?
(A) 987
(B) 271
(C) 72
(D) 27
(E) 63
Rationale: Length = Speed * time
Speed = L/T
S = 700/40
S = 17.5 M/Sec
Speed= 17.5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 63 Kmph
Answer:E
Answer: (E) 63
Question: Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: On dividing 964807 by 15 we get the remainder 7, so 7 should be subtracted
A
Answer: (A) 7
Question: In 1995 a certain store had 1,800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $60 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?
(A) $0
(B) $4,000
(C) $8,000
(D) $32,000
(E) $40,000
Rationale: The keyword here isGross Profit:
Gross Profit = (Selling Price - Original Price)*(# of Items Sold)
So lets figure out what the Gross Profit for 1995:
GP1995 = (50-30)*(1000) = 20000
And the Gross Profit for 1996:
GP1996 = (60-30)*(800) = 24000
So the difference would be:
24000-20000 = 4000
ANSWER: B. 4000
Answer: (B) $4,000
Question: What is the exact probability that, when rolling six fair dice, at least one of the dice shows a 6?
(A) 1
(B) 31031/46656
(C) 5/6
(D) 35625/46656
(E) 1/6
Rationale: For each dice, the probability of not rolling a 6 is 5/6. The total probability of not rolling a 6 is (5/6)^6. The correct answer is thus 1 - (5/6)^6 = 31031/46656, so the answer is B.
Answer: (B) 31031/46656
Question: A family pays $900 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?
(A) $1,000
(B) $1,200
(C) $1,400
(D) $1,500
(E) $1,700
Rationale: Assuming the medical expenses are $1000 or more, the family pays $900 + $400 = $1300.
The total amount paid by insurance plan for the first $1000 of expenses is $600.
The insurance will pay another $700 when the medical expenses are $1700.
The answer is E.
Answer: (E) $1,700
Question: The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child?
(A) 10
(B) 12
(C) 16
(D) 19
(E) 20
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
x+12= 4+12= 16
C
Answer: (C) 16
Question: 65% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?
(A) (a) 15%
(B) (b) 5%
(C) (c) 10%
(D) (d) 20%
(E) (e) 25%
Rationale: so 35% employees don't have VCD devices.
25% employees don't have MO
20% employees don't have ACs
15% employees don't have WM
Summ of employees that don't have some device = 35%+25%+20%+15% = 95% < 100%
So definitely at least 5% employees have 4 devices.
ans: B
Answer: (B) (b) 5%
Question: Insert the missing number.
2, 6, 12, 20, 30, 42, (....)
(A) 56
(B) 38
(C) 72
(D) 66
(E) 19
Rationale: Explanation:
The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7
So, the next number is 7 x 8 = 56.
Answer: A) 56
Answer: (A) 56
Question: A person traveled 3 equal distances 20km/hr, 30km/hr, 60km/hr then find its avg speed?
(A) 20km/hr
(B) 30km/hr
(C) 22km/hr
(D) 19km/hr
(E) 31km/hr
Rationale: avg speed = 3xyz/(xy+yz+zx)
required answer is = 3*20*30*60/ (600+1800+1200) = 30km/hr
Answer is B
Answer: (B) 30km/hr
Question: How many minutes will be used to cover distance of 520m, if a man running at the speed of 15km/hr?
(A) 125 sec
(B) 124 sec
(C) 114 sec
(D) 115 sec
(E) 117 sec
Rationale: Explanation:
Distance = time × speed
= 125 sec.
Answer: A
Answer: (A) 125 sec
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 6 hours, then the distance covered at 40 kmph is
(A) 220 km
(B) 120km
(C) 100km
(D) 140km
(E) none of these
Rationale: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 6
or, x/40 + (250 - x)/60 = 6
or, (3x + 500 - 2x)//120 = 6
or 500 + x = 720
x=220
ANSWER:A
Answer: (A) 220 km
Question: A and B can do a piece of work in 30 days and 30 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?
(A) 30days
(B) 35days
(C) 40days
(D) 45days
(E) 50days
Rationale: Explanation:
(A+B)’s 10 days work = 10[1/30+1/30]=10[1+1/30]= 2/3
A complete remaining work in 2/3*30 = 20
Total work = 10+20 = 30days
Answer: Option A
Answer: (A) 30days
Question: A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.
(A) 83.5%
(B) 87.5%
(C) 88.5%
(D) 89.5%
(E) Rs 484
Rationale: Explanation:
In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this.
4/15A=2/5B
A=(2/5∗14/4)B
A=3/2B
A/B=3/2
A:B=3:2
B's Share = 2/5∗1210=484
Option E
Answer: (E) Rs 484
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 99
(C) 77
(D) 66
(E) 32
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec
Answer: A
Answer: (A) 40
Question: What are the last two digits of 36*28*61*83*73*62?
(A) 11
(B) 09
(C) 07
(D) 05
(E) 04
Rationale: 36*28*61*83*73*62=
We have to focus on the last two digits only, so 36*28=08*61=88*83=04
04*73=92 therefore 92*62=04
Hence Answer is E
Answer: (E) 04
Question: The overall age of X and Y is 11 year greater than the overall age of Y and Z. Z is how many decades younger that X?
(A) 11
(B) 15
(C) 12
(D) 17
(E) 19
Rationale: A
11
(X + Y) â€“ (Y + Z) = 11
X â€“ Z = 11
Answer: (A) 11
Question: If x = 2^8 and x^x = 2^k, what is k?
(A) 2^15
(B) 2^14
(C) 2^13
(D) 2^12
(E) 2^11
Rationale: Solution:
We know that x=2^8
which implies x^x = (2^8)^(2^8) = 2^(8 * 2^8) [because (x^y)^z = x^(y*z))]
so 2^(2^3 * 2^8) = 2^(2^(3+8)) [because x^a * x^b = x^(a+b)]
therefore x^x = 2^(2^11)
Given that x^x=2^k
so 2^(2^11) = 2^k
Since the base is same the exponent will also be same
therefore k = 2^11
Answer: E
Answer: (E) 2^11
Question: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 90
(B) 52
(C) 63
(D) 87
(E) 10
Rationale: Explanation:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer:A
Answer: (A) 90
Question: The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches?
(A) 66
(B) 83.5
(C) 84
(D) 95
(E) 76
Rationale: sum of last 4 matches = (10 × 66) – (6 × 54)= 336
Average =
336/4
= 84
ANSWER:C
Answer: (C) 84
Question: Two persons starting from the same place walk at a rate of 8kmph and 15kmph respectively. What time will they take to be 14 km apart, if they walk in the same direction?
(A) 7 hrs
(B) 2 hrs
(C) 5 hrs
(D) 12 hrs
(E) 6 hrs
Rationale: The relative speed of the boys = 15kmph – 8kmph
= 7 kmph
Distance between them is 8.5 km
Time= 14km / 7 kmph =2 hrs
Answer : B
Answer: (B) 2 hrs
Question: 17 times a positive integer is more than its square by 70, then the positive integer is
(A) 13
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: Explanation:
Let the number be x. Then,
17x = x2 + 70
=> x2 - 17x + 70 = 0
=>(x - 7)(x - 10) = 0
=> x = 7 or 10
Answer: B
Answer: (B) 10
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 288
(B) 350
(C) 889
(D) 276
(E) 234
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
Answer:B
Answer: (B) 350
Question: If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is
(A) 3.879
(B) 3.875
(C) 3.872
(D) 3.828
(E) 3.192
Rationale: ANS: log5512 = {\color{Black} \frac{\log 512}{\log 5}} = {\color{Black} \frac{\log 2^{9}}{\log (\frac{10}{2})}} ={\color{Black} \frac{9\log 2}{\log10-\log 2 }} ={\color{Black} \frac{(9\times 0.3010)}{1-0.3010 }} ={\color{Black} \frac{2.709}{0.699 }} ={\color{Black} \frac{2709}{699 }} =3.876
Answer: B) 3.875
Answer: (B) 3.875
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?
(A) 12 min
(B) 16 min
(C) 18 min
(D) 15 min
(E) 19 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 6 - 1 = 5 rounds per hour.
Time taken to complete one round at this speed
= 1/5 hr
= 12 min.
Answer:A
Answer: (A) 12 min
Question: If .005^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?
(A) 0
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 0.005^4= (5*10^-3)^4 = 625*10^-12 = 0.625*10^-9 which would have 9 zeros to the right of the decimal point. The answer is C.
Answer: (C) 9
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(A) 4.6%
(B) 3.6%
(C) 6.4%
(D) 7.8%
(E) 8.9%
Rationale: C
6.4%
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (C) 6.4%
Question: If three distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32?
(A) 1/3
(B) 1/2
(C) 2/7
(D) 10/21
(E) 15/28
Rationale: The positive divisors are 1, 2, 4, 8, 16, 32, 64.
If any of the first five are chosen, the sum will be less than 32.
P(sum is less than 32) = 5/7 * 4/6 * 3/5 = 12/42 = 2/7
The answer is C.
Answer: (C) 2/7
Question: A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?
(A) 29798
(B) 27908
(C) 78902
(D) 25000
(E) 27000
Rationale: 27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x
27 = 1/100 * x => x
= 27000
Answer: E
Answer: (E) 27000