source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-37897 | # Given relatively prime positive integers $a,b>1$, how many positive integers are there which are not non-negative integer combination sum of $a,b$?
Let $a,b>1$ be relatively prime positive integers. I know that $ab-a-b$ is the largest positive integer which can not be written as a sum of non-negative integer combina... | [
"51",
"54",
"162",
"72"
] | C | In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: C. |
AQUA-RAT | AQUA-RAT-37898 | 3,5,-5... The first term in the sequence of #'s shown above is 3. Each even # term is 2 more than the previous term and each odd # term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the
8. ### Math *URGENT
Please give the answers and solutions for each. 1.If the second term ... | [
"−1.5",
"−1",
"0",
"0.2"
] | D | First = 0.8
Second = 2*0.8-1 = 0.6
Second = 2*0.6-1 = 0.2
Answer: option D |
AQUA-RAT | AQUA-RAT-37899 | # Difference between revisions of "2010 AMC 10B Problems/Problem 20"
## Problem
Two circles lie outside regular hexagon $ABCDEF$. The first is tangent to $\overline{AB}$, and the second is tangent to $\overline{DE}$. Both are tangent to lines $BC$ and $FA$. What is the ratio of the area of the second circle to that o... | [
"2∏√3",
"3∏",
"4∏/√3",
"2∏/√3"
] | A | Now AC will be 1 because circle is touching the midpoints of the circle.
Then we get kite ACBO.
We have AC = 1 and CB = 1, now we need to find BO which is radius
from triplets we get 30:60:90 = 1:√3:2
Now CBO is right angled triangle, then we get BO as √3.
r = √3...circumference is 2∏r is 2∏√3.
Answer :option A. |
AQUA-RAT | AQUA-RAT-37900 | Example 2
In a large population of adults, 45% have a post secondary degree.
If people are selected at random from this population,
a) what is the probability that the third person selected is the first one that has a post secondary degree?
b) what is the probability that the first person with a post secondary degree i... | [
"5/55",
"21/55",
"51/55",
"41/55"
] | D | P(at least one graduate) = 1 - P(no graduates)
= 1 - 8C₃/12C₃ = 1 - (8 * 7 * 6)/(10 * 11 *12)
= 41/55
Answer: D |
AQUA-RAT | AQUA-RAT-37901 | ## [1] 22.13
### Changing the Budget
A broader social question is whether the budget is being set at an appropriate level. One way to examine this is to look at how the QALY outcome changes as the budget changes.
1. What is the rate of change of $$f_A(x_A)$$ with respect to $$x_A$$? Of course, this depends on the v... | [
"20",
"10",
"15",
"25"
] | A | 100
125
-----
125 ----- 25
100 ------ ? => 20%
ANSWER A |
AQUA-RAT | AQUA-RAT-37902 | # Analyzing a mixture issue.
I am having a problem with this question:
Coffee A costs $75$ cents per pound and coffee B costs $80$ cents per pound to form a mixture that costs $78$ cents per pound.IF there are $10$ pounds of Mixture how many pounds of Coffee A are used?
According to the text the answer is 4. I don't... | [
"28%",
"30%",
"32%",
"34%"
] | B | 1. 20% of 400=80 pounds of decaffeinated coffee
2. 70% of 100=70 pounds of decaffeinated coffee
3. Wt have 150 pounds of decaffeinated out of 500 pounds, that means 150/500*100%=30%. The correct answer is B. |
AQUA-RAT | AQUA-RAT-37903 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by ... | [
"180 sec",
"190 sec",
"290 sec",
"490 sec"
] | B | Time taken by B run 1000 meters = (1000 * 10)/50
= 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B |
AQUA-RAT | AQUA-RAT-37904 | python, python-3.x, datetime
if sun == 1:
first_sunday = np.busday_offset(start, 0, roll='forward', weekmask='Sun')
last_sunday = np.busday_offset(end, 0, roll='preceding', weekmask='Sun')
sun_count = np.busday_count(first_sunday, last_sunday, weekmask='Sun') + 1
for i in trange(sun_co... | [
"Wednesday",
"Tuesday",
"Sunday",
"Monday"
] | C | The year 2004 is a leap year. So, it has 2 odd days.
Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday
Answer: C |
AQUA-RAT | AQUA-RAT-37905 | $7|61$ gives $61=7\cdot 8 +5$
He would have 5 cows left over. So 61 can't be an answer
5. Hello, swimalot!
A cowboy was asked how many cows were on the ranch.
He replied that he was unsure, but he knew that when he counted them
by twos, threes, fours, fives, or sixes, he always had one left over.
When counted by sev... | [
"1/3",
"1/9",
"2/8",
"6/4"
] | A | 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A |
AQUA-RAT | AQUA-RAT-37906 | # Clock losing time puzzle
The question goes as:
A wall clock and a Table clock are set to correct time today on 10 pm. The wall clock loses 3 minute in 1st hour, 6 minutes in the second hour and 9 minutes in the third hour and so on. The table clock loses 5 minutes in the 1st hour, 10 minutes in the second hour and ... | [
"7:25",
"7:34",
"7:43",
"7:47"
] | B | 7:19 minus 2,880,705 must end with 4, the only answer choice which ends with 4 is B.
Answer : B. |
AQUA-RAT | AQUA-RAT-37907 | # Math Help - word problem.
1. ## word problem.
hi ! im having a difficult time answering this word problem.
"Alvin set out from a certain point and travelled at the rate of 6 kph. After Alvin had gone for two hours, Ben set on to overtake him and went 4km the first hour, 5 km the second hour, 6 km the third hour an... | [
"4 4/5 Km",
"4 1/7 Km",
"3 1/5 Km",
"3 1/7 Km"
] | A | Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 24/6
= 24/2 * 24/60
= 12 * 2/5
= 24/5 = 4 4/5 Km
A) |
AQUA-RAT | AQUA-RAT-37908 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by ... | [
"45 min",
"60 min",
"55 min",
"70 min"
] | B | Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Answer : B |
AQUA-RAT | AQUA-RAT-37909 | take a 5 = 48 ⇒ a r 5-1 = 48 ⇒ a 2 4 = 48 ⇒ a = 3. . To obtain the median, let us arrange the salaries in ascending order: The question asks for a three digit number: call the digits x, y and z. Example 1:Find the arithmetic mean of first five prime numbers. . . Median: Arrange the goals in increasing order We much hav... | [
"3:4",
"6:13",
"5:6",
"13:10"
] | B | The first nine positive multiples of six are {6, 12, 18, 24,30}
The first twelve positive multiples of six are {6, 12, 18, 24, 30,36,42, 48, 54, 60, 66, 72}
Both sets are evenly spaced, thus their median=mean:
a=18 and b=(36+42)/2=39 --> a/b=18/39=6/13.
Answer: B. |
AQUA-RAT | AQUA-RAT-37910 | However, it seems clear that the question is meant to be something along the lines of:
In how many different ways can we pair the boys and the girls to make six couples that will all dance at the same time?
Now, since the order in which we list the pairs doesn't matter, we just care about what girl goes with what boy... | [
" 10",
" 25",
" 60",
" 2520"
] | D | 1st girl can go with 7 guys
2nd girl can go with remaining 6
3rd girl can go with remaining 5 and so on
so the total ways are 7 * 6 * 5 * 4 * 3
D should be the answer |
AQUA-RAT | AQUA-RAT-37911 | -
No, please see what I added for c) – André Nicolas Nov 18 '12 at 3:52
Your answer of $\binom{20}5$ for (a) is correct.
(b) To get the probability that $1$ and $2$ are not in the sample, you must count the $5$-card sets that don’t contain either $1$ or $2$. These are the $5$-card sets chosen from $\{3,4,5,\dots,20\... | [
"1/50",
"1/25",
"1/95",
"1"
] | C | There are 25 primes, 69 composite numbers from 1 to 95. The number
which is neither prime nor composite is 1.
Therefore, required probability = 1/95.
ANSWER:C |
AQUA-RAT | AQUA-RAT-37912 | star
A8 1.784E+01 2.202E+00 7832. 1.900 8.004E+06 1.62 -0.12 0.20 0.10 0.27 2.02 1.74 1.93 1.63 1.47 1.34 1.26 1.23 1.20 0 0
A7 2.226E+01 2.268E+00 8176. 2.000 7.125E+06 1.38 -0.13 0.17 0.08 0.21 1.77 1.51 1.68 1.43 1.30 1.17 1.10 1.07 1.04 ... | [
"6078.58",
"5225.9",
"6258.58",
"6088.58"
] | A | Option 'A' |
AQUA-RAT | AQUA-RAT-37913 | There are 3 crates of apples A, B and C. The ratio of the number of apples in crate A to crate B to crate C is 8 : 5 : 3. David removed 42 apples from crate A and placed them into crate C. as such, there are 2 more apples in crate C than crate B. How many apples are there altogether?
2. HINT: 3k + 42 = 5k + 2
4. Orig... | [
"5",
"10",
"15",
"20"
] | B | Each crate requires 1 apples and totally there are 10 crates so required apples = 10 * 1 = 10
Answer: B |
AQUA-RAT | AQUA-RAT-37914 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"10 a.m",
"07 a.m",
"11 a.m",
"03 a.m"
] | C | Suppose they meet x hrs after 8 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 330
60x + 75(x - 1) = 330 => x = 3
So, they meet at (8 + 3) i.e., 11 a.m.
Answer: C |
AQUA-RAT | AQUA-RAT-37915 | ### Show Tags
06 Feb 2015, 13:28
1
x+y=1600 , X=1600-Y
x+100=3y, 1700=4Y
Y=425
x=1600-y=1600-425=1175
D
Director
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: There are 1600 jelly beans divided between... | [
"Rs.2300",
"Rs.2310",
"Rs.2320",
"Rs.2330"
] | C | Let C gets Rs x. Then We can say B gets Rs (x + 320 ) and D gets Rs ( x + 280) .
x + 320 + x + x + 560 = 6160
3x = 5280
x = 1760 .
C’s share = Rs ( 1760+560 ) = Rs.2320
C |
AQUA-RAT | AQUA-RAT-37916 | have s6 : f (fin.last n.succ) ≤ max (f (fin.last n.succ)) (fin_max n f') := le_max_left (f (fin.last n.succ)) (fin_max n f'),
have s7 : f (fin.last n.succ) ≤ fin_max n.succ f := eq.subst (eq.refl s5) s6,
have s8 : fin_max n f' ≤ max (f (fin.last n.succ)) (fin_max n f') := le_max_right (f (fin.last n.succ)) (fin_max n ... | [
"0.07",
"0.7",
"3.5",
"0.35"
] | D | Given numbers with two decimal place are: 1.75, 5.60 and 7.00. Without decimal places, these numbers are: 175, 560 and 700, whose H.C.F. is 35.
H.C.F. of given numbers = 0.35.
Correct Option : D |
AQUA-RAT | AQUA-RAT-37917 | Advertisement Remove all ads
# Answer the following : The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. - Mathematics and Statistics
Sum
Answer the following :
The mean height of 200 studen... | [
"288",
"151",
"177",
"282"
] | B | :
Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm.
Answer: B |
AQUA-RAT | AQUA-RAT-37918 | 4. A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain. (Assume the crew does not work on any rainy day and rain is the only factor that can deter the crew from working). However, on the 61-st day, after 5 days of rain, he hired 6 more people and finished the pro... | [
"2 1/2",
"3",
"3 1/3",
"4"
] | A | Suppose 1 man can do work in X days..
so 5 men will do in ..
5/X=1/6*1/2 as half job is done
X=60
now 7 more are added then
12/60=1/2*1/d for remaining half job
d=2 1/2 Number of days
A |
AQUA-RAT | AQUA-RAT-37919 | A question on the same concept
The number of television sets sold by Store R last month was approximately what percent less than the number of television sets sold by Store T last month? ( The number of television sets sold by Store R was 20 and number of television sets sold by Store T was 45 as per the attached figu... | [
"520",
"560",
"580",
"620"
] | C | (20/100) * X – (30/100) * 120 = 80
1/5 X = 116
X = 580
Answer:C |
AQUA-RAT | AQUA-RAT-37920 | Puzzle of gold coins in the bag
At the end of Probability class, our professor gave us the following puzzle:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we ca... | [
"20 coins",
"30 coins",
"40 coins",
"60 coins"
] | D | Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 105
⇒ 1.75x = 105 ⇒ x = 60 coins
Answer D |
AQUA-RAT | AQUA-RAT-37921 | # probability of the 3rd pick is a boy
10 students are in a class,
4 of these students are boys and 6 are girls
the teacher wanted to randomly select 3 students to represent the class in an event
what is the probability that the 3rd student is a boy?
Here is what I have tried
the probability of that 1st student i... | [
"8/125.",
"2/5.",
"1/30.",
"1/720."
] | C | probability that only girls will be elected = 4C3/10C3 = 1/30
Answer C. |
AQUA-RAT | AQUA-RAT-37922 | Spoiler:
The middle number is the average of the other two.
$\frac{47+63}{2} \:=\:55,\quad \frac{85+99}{2} \:=\:92,\quad \frac{73+25}{2} \:=\:{\color{red}49}$
3. ## Re: Math puzzles questions?
Originally Posted by amrithaa
1. What number should replace the question mark?
Each row is 8 times the immediate row above.... | [
"2",
"5",
"3",
"19"
] | B | B
5
70 ÷ 14 = 5;
91 ÷ 13 = 7,
120 ÷ 24 = 5; |
AQUA-RAT | AQUA-RAT-37923 | I see from your profile that you’re a programmer. Extreme cases like these are analogous to testing boundary conditions in your code (things like loops that execute 0 times).
Let x to be your gross salary and y = 1600 to be your net salary. Because tax is 20% of gross salary then we have
x = y + tax = 1600 + 0.2x
=> ... | [
"188",
"7500",
"2788",
"1277"
] | B | Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
Answer: B |
AQUA-RAT | AQUA-RAT-37924 | (D)
Manager
Joined: 03 Aug 2017
Posts: 64
Re: If 20 typists can type 48 letters in 20 minutes, then how many letters [#permalink]
### Show Tags
05 Oct 2019, 22:16
Bunuel wrote:
If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
A. 63
B... | [
"1092",
"1300",
"1500",
"1125"
] | A | 1 to 9 = 9 * 1 = 9
10 to 99 = 90 * 2 = 180
100 to 400 = 301 * 3 = 903
=====> 1092
ANSWER A |
AQUA-RAT | AQUA-RAT-37925 | The price then decreased by 12% during 2013
A 12% DECREASE is the same a multiplying the price by 0.88
So, the new price = ($100)(1 + p/100)(0.88) The price of the good at the end of 2013 was 10% higher than the price at the beginning of 2012 If the original price was$100, then the price at the end of 2013 was $110 So,... | [
"20%",
"20.5%",
"20.8%",
"21%"
] | D | 1.1*1.1*x = 1.21*x
The answer is D. |
AQUA-RAT | AQUA-RAT-37926 | Thanks for any help. I am totally confused.
1. 👍 0
2. 👎 0
## Similar Questions
1. ### Probability
jeff has 8 red marbles, 6 blue marbles, and 4 green marbles that are the same size and shape. he puts the marbles into a bag, mixes the marbles, and randomly picks one marble. what is the probability that the marble ... | [
"3/10",
"7/10",
"1",
"4/10"
] | B | Total number of marbles = 7+3 = 10
no. of green marbles = 7
probability of drawn a green marble= 7/10
Answer is B |
AQUA-RAT | AQUA-RAT-37927 | Substitute 0.085 for interest rate, $3000 for the amount deposited and$6000 for the amount after t years in the formula, “A=Pert” as,
$6000=$3000e0.085t
Divide both sides by $3000 as,$6000$3000=$3000e0.085t$3000e0.085t=2 Take natural logarithm on both sides as, ln(e0.085t)=ln2 Now, apply the inverse property of lnex ... | [
"337",
"640",
"297",
"276"
] | B | (P*5*15)/100 - (P*3.5*15)/100 = 144
75P/100 – 52.5P/100 = 144
22.5P = 144 * 100
=> P = Rs.640
Answer:B |
AQUA-RAT | AQUA-RAT-37928 | Since he did not score 45, he lost an average of 4.5 upon the total number of innings, which includes the latest innings as well.
So 45 runs upon x innings will give an average of 4.5
Hence 45/x = 4.5 i.e. x = 10. (Remember, x includes the latest inning as well)
Problem 6:
The average of 8 scores is 87. Of these, t... | [
"12",
"16",
"20",
"24"
] | B | 11x + 60 = 12(x + 4)
x = 12 + 4 = 16
Answer:B |
AQUA-RAT | AQUA-RAT-37929 | Since the number of ways in which $$5$$ books can be arranged is $$5!=120,$$ we have $$120$$ ways.
• thanks for explanation. Can you point out what is wrong in my analysis Sep 17, 2020 at 11:24
• As mentioned in the comments, you calculated the $C$ books to be next to each other, but they do not need to be next to eac... | [
"Rs. 2500",
"Rs. 3000",
"Rs. 3500",
"Rs. 3240"
] | D | The greatest profit is possible only if the cost price of the books are minimum and selling prices are maximum.
Let lowest cost price of the 18 books = 130*18 = Rs. 2,340
Maximum selling price of 18 books = 310 *18 = Rs. 5,580
So, maximum profit = 5580 - 2340 = Rs. 3,240
ANSWER : OPTION D |
AQUA-RAT | AQUA-RAT-37930 | # 6.8 Exponential growth and decay (Page 3/9)
Page 3 / 9
If a quantity grows exponentially, the time it takes for the quantity to double remains constant. In other words, it takes the same amount of time for a population of bacteria to grow from $100$ to $200$ bacteria as it does to grow from $10,000$ to $20,000$ b... | [
"7",
"17",
"27",
"37"
] | B | At 17 hours the one plant will take up 1/4 of the lake (1/2 of 1/2). At 17 hours the two plants would be double the size of the one plant and double 1/4 is one half. |
AQUA-RAT | AQUA-RAT-37931 | For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since $$15 = 6*2 + 3$$.
Hence, the positive integer k is divided by the positive integer n, the remainder is 11, could be written as k = nq + 11. Divide by n: k/n = q + 11/n.
We are also given that k/n = 81.2 = 81 + 0.2. So, the quotient, ... | [
"274",
"270",
"295",
"360"
] | A | Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Smaller number = 274.
ANSWER A |
AQUA-RAT | AQUA-RAT-37932 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"62.5",
"62.0",
"62.6",
"62.1"
] | A | CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A |
AQUA-RAT | AQUA-RAT-37933 | Let one woman complete the job in $$w$$ days and one man in $$m$$ days.
First equation:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is $$\frac{1}{w}$$ job/day, then the rate of 3 women will be $$\frac{3}{w}$$ job/day. As the rate of 1 man is $$\frac{1}{m}$$ job/day... | [
"20",
"10",
"15",
"5"
] | A | Time taken by A to finish the work = XY/(Y-X)
= 10 x 20 / (20-10)
= 200/10
= 20 days
Answer: A |
AQUA-RAT | AQUA-RAT-37934 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"89",
"29.7",
"56",
"79.2"
] | B | Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/40 = y
y = 8.25 Speed = 8.25 m/sec = 8.25 * 18/5 = 29.7 km/hr.
Answer: Option B |
AQUA-RAT | AQUA-RAT-37935 | $(120,34)\simeq S_{5}$
$(120,36)\simeq S_{3}\times(\mathbb{Z}_{5}\rtimes\mathbb{Z}_{4})$
$(144,182)\simeq((\mathbb{Z}_{3}\times\mathbb{Z}_{3})\rtimes\mathbb{Z}_{8})\rtimes\mathbb{Z}_{2}$
$(144,183)\simeq S_{3}\times S_{4}$
$(156,7)\simeq(\mathbb{Z}_{13}\rtimes\mathbb{Z}_{4})\rtimes\mathbb{Z}_{3}$
$(168,43)\simeq((... | [
"40",
"80",
"120",
"200"
] | A | Let the numbers be 3x, 4x and 5x.
Then, their L.C.M = 60x. So, 60x = 2400 or x = 40.
The numbers are (3 * 40), (4 * 40) and (5 * 40).
Hence, required H.C.F = 40.
ANSWER:A |
AQUA-RAT | AQUA-RAT-37936 | -
Hint: There are ten outcomes that give a sum of 12: (4,4,4), (2,2,8), (2,8,2), (8,2,2), (2,4,6), (4,2,6), (6,2,4), (2,6,4), (4,6,2), (6,4,2).
-
This looks like a classic Bayes' rule problem. We want to find the probability of two 2s given that the three numbers sum to 12. We can apply Bayes' rule thusly: $$P(\text... | [
"1/60",
"2/50",
"9/40",
"3/40"
] | C | The probability of success of at least two students will involve the following possibilities.
The first two students are successful, the last two students are successful, the first and third students are successful and all the three students are successful.
Therefore, the required probability = 1/2 x 1/4 x 4/5 + 1/4 x ... |
AQUA-RAT | AQUA-RAT-37937 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"a) $100",
"b) $115",
"c) $125",
"d) $130"
] | C | I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 50... |
AQUA-RAT | AQUA-RAT-37938 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"11",
"12.1",
"13",
"14"
] | B | Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: Option B |
AQUA-RAT | AQUA-RAT-37939 | # Clarification on language of a question on profit and loss.
The question is:
By selling 33 meters of cloth, a shopkeeper gains the cost of 11 meters. Find his gain percentage.
1. 33 1/3%
2. 33 1/2%
3. 33%
4. 34 1/4%
The answer provided by the book says it's the first one.
But if he gains the cost of 11 meters sh... | [
"Rs. 100",
"Rs. 150",
"Rs. 200",
"Rs. 300"
] | C | Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C |
AQUA-RAT | AQUA-RAT-37940 | # Inequality with two absolute values
I'm new here, and I was wondering if any of you could help me out with this little problem that is already getting on my nerves since I've been trying to solve it for hours.
Studying for my next test on inequalities with absolute values, I found this one:
$$|x-3|-|x-4|<x$$ (I pr... | [
" I only",
" II only",
" III only",
" II and III only"
] | A | Answer is D. Let's look at the statements one by one
Stmt I. x^3 < x
if 0<x<1 then x^3< x but if -1<x<0 then x^3>x
So this statement is not always true
Stmt II. x^2 < |x|
Because we know that x is a number less than one but not equal to zero then x^2 will always be less than |x|.
Why? think of positive fractions (and y... |
AQUA-RAT | AQUA-RAT-37941 | A boy and his sister. When you subtract two from the boy’s real age and add two to his sister’s age, his sister
becomes twice his NEW (subtracted) age. If you subtract three from his real age instead and add three to his sister then she becomes thrice his NEW (subtracted) age. What are their real ages?
A little more de... | [
"12",
"14",
"16",
"18"
] | B | Explanation:
Let the son's present age be x years. Then, woman's present age = (x + 18) years
=> (x + 18) + 4 = 2(x + 4)
=> x + 22 = 2x +8
So, x = 14 Answer: B |
AQUA-RAT | AQUA-RAT-37942 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by ... | [
"E982",
"16",
"12",
"121"
] | B | Explanation:
T = 12/45 * 60 = 16
Answer: Option B |
AQUA-RAT | AQUA-RAT-37943 | We are given: .a
5 = 120 .and .a6 = 720
Then: .r .= .a
6/a5 .= .720/120 .= .6
. . The "rule" is multiply-by-six.
Therefore, the preceding term is: .a
4 = 20.
See? .We could have eyeballed the problem . . .
5. Originally Posted by Soroban
. . There is a simpler solution.
I always tell my students that I have a ten... | [
"2.914",
"2.81",
"2.192",
"2.912"
] | D | Explanation:
Formula = Fourth proportional = (b × c)/a
A = 0.5 , B = 1.12 and C = 1.3
(1.12 × 1.3)/0.5
1.456/0.5 = 2.912
Answer: Option D |
AQUA-RAT | AQUA-RAT-37944 | the classroom. What does this mean?. applying Sn formula, we know that d is 3 and 4 respectively. How can you tell if a number is divisible by 3? A. (ZX81 BASIC doesn't do this automatically: both sides of an OR are evaluated, even (c, 5); BigInteger answer15 = GetSumOfNumbersDivisibleByN(c, 15); Console. Thus we do no... | [
"4",
"5",
"8",
"6"
] | D | Obviously,The answer is 6
Option D |
AQUA-RAT | AQUA-RAT-37945 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"a profit of $10",
"a profit of $6.25",
"a loss of $6.25",
"a loss of $10"
] | C | Loss% = (%age Profit or loss / 10)^2 = (20/10)^2 = 4% loss
Total Selling Price = 75*2 = $192
Total Cost Price = 150/(0.96) = $156.25
Loss = 156.25 - 150 = $6.25
Answer: Option C |
AQUA-RAT | AQUA-RAT-37946 | # Find Smallest Positive Integer
#### anemone
##### MHB POTW Director
Staff member
Find the smallest positive integer $n$ such that for every integer $m$ with $0<m<1993$, there exists an integer $k$ for which $$\displaystyle \frac{m}{1993}<\frac{k}{n}<\frac{m+1}{1994}$$.
#### Wilmer
##### In Memoriam
Find the small... | [
"30",
"15",
"12",
"23"
] | A | 5880= 2*2*7*7*5*6, so we need one 5 and one 6 to make it a square of a number. so 5*6= 30
Ans: A |
AQUA-RAT | AQUA-RAT-37947 | The remainder is $\,2 \,P_6(x^2)\,$, which follows for $\,n=6\,$ from the general identity:
\begin{align} P_{2n}(x^2) = \frac{x^{4n}-1}{x^2-1} &= \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}+1}{x+1} \\[5px] &= \, \frac{x^{2n}-1}{x-1} \, \frac{x^{2n}-1+2}{x+1} \\[5px] &= - \, \frac{x^{2n}-1}{x-1} \, \frac{(-x)^{2n}-1}{(-x)-1} ... | [
"74",
"166",
"86",
"92"
] | B | Divisor = (6 * 3) + 22 = 40
5 * Quotient = 40
Quotient = 8.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 8) + 6 = 166.
B) |
AQUA-RAT | AQUA-RAT-37948 | or the length of the line you see in red. After finding your height, substitute your values for base and height into the formula for area of a triangle to find the area. Area of triangle = × Base × Height . Area of a rhombus. Area of Triangle (given base and height) A triangle is a 3-sided polygon. Side of triangle wit... | [
"120",
"110",
"130",
"140"
] | B | The triangle with sides 26 cm, 22 cm and 10 cm is right angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 22 * 10 = 110 cm2
Answer: Option B |
AQUA-RAT | AQUA-RAT-37949 | ### Show Tags
16 Jun 2018, 09:16
agdimple333 wrote:
During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of$25.00 Did the store sell more sweaters than shirts during the sale?
1) The average of the prices of all of the shirts and sweaters that the store sold during the sale wa... | [
"$88",
"$96",
"$100",
"$106"
] | B | 0.8*(1.2*100) = $96
The answer is B. |
AQUA-RAT | AQUA-RAT-37950 | - 6 years, 9 months ago
So, here's my proposed solution.
Solution: It is trivial how to prove the 'if' part. Let us proceed to prove the 'only if' part. Suppose $x,y,z$ are such integers with $xy+1, yz+1, zx+1$ not all squares. Let us also assume that $x,y,z$ is the smallest counterexample, that is, $x+y+z$ is minimu... | [
"33",
"40",
"49",
"61"
] | C | x + y - z = x/5 + x - x/9
= (45 + 9 - 5 )x/45 = 49x/45
49 is not divisible by 45, so for least value, x = 45
C |
AQUA-RAT | AQUA-RAT-37951 | You've got what it takes, but it will take everything you've got
Intern
Joined: 30 Nov 2017
Posts: 42
Re: Working at constant rate, pump X pumped out half of the water in a flo [#permalink]
### Show Tags
15 Feb 2018, 09:56
Suppose X extracts x liters/hour, while Y extracts y liters/hour
In 4 hours, X extracts 4 x l... | [
"17 hr",
"19 hr",
"30 hr",
"14 hr"
] | C | Work done by the tank in 1 hour
= (1/3 - 3 1/3)
= 1/30 Leak will empty the tank in 30 hrs.
Answer:C |
AQUA-RAT | AQUA-RAT-37952 | This simplifies to $$t(9z-x^2)+(2z-y)=0 \tag{1}$$
Now we have two cases:
Case 1: $$9z-x^2\ne0$$:
Then we have
$$t=\frac{2z-y}{9z-x^2}$$
Because of $$x,y,z \in \{0,\ldots,9\}$$ and $$9z-x^2\ne0$$ we have $$|2z-y|\le18$$ and $$|9z-x^2|\ge1.$$ So $$|t|\le18$$, and therefore $$t=11$$.
If we substitute this in $$(1)$$... | [
"0",
"2",
"4",
"6"
] | A | The sum of the digits is 9+4+2=15.
Thus 3 is a factor of 9402, so 3 is a factor of z.
Then 3^3 = 9 is a factor of z^2.
Then the remainder when z^2 is divided by 9 is 0.
The answer is A. |
AQUA-RAT | AQUA-RAT-37953 | So the 1st question you needed to answer was how much distance do they cover together per hour (we just did that), now the next question to answer is how long it takes to cover 810km in total distance at their effective speed.
• it means that if they are covering 135km each our then they would be meet together in 135x... | [
"2:3",
"4:3",
"6:7",
"9:16"
] | B | Explanation:
Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
ANSWER IS B |
AQUA-RAT | AQUA-RAT-37954 | the two rectangles = … Level 5 - Real life composite area questions from photographs. Math Practice Online > free > lessons > Texas > 8th grade > Perimeter and Area of Composite Figures. Match. Solving Practice Area of Composite Figures. The 2 green points in the diagram are the … Edit. Question 4 : Find the area of th... | [
"180 cm",
"190 cm",
"170 cm",
"150 cm"
] | A | Area of the square = s * s = 3(25 * 27)
=> s = 3 * 5 * 3 = 45 cm
Perimeter of the square = 4 * 45 = 180 cm.
Answer: A |
AQUA-RAT | AQUA-RAT-37955 | to solve for the other. Logic To Calculate Percentage Difference Between 2 Numbers. Sale Discount Calculator - Percent Off Mortgage Loan Calculator - Finance Fraction Calculator - Simplify Reduce Engine Motor Horsepower Calculator Earned Value Project Management Present Worth Calculator - Finance Constant Acceleration ... | [
"98%",
"56%",
"96%",
"964%"
] | C | I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C |
AQUA-RAT | AQUA-RAT-37956 | Now since $$x_n\in\mathbb{R}$$ and $$x_n\neq 0\implies x_n^2>0.$$ Now since $$i\ge 0\implies i.x_n^2\ge 0 \implies 2+i-n\ge 0\implies i\ge n-2.$$ Therefore $$i=n-2,n-1$$.
Now when $$i=n-2$$, we have $$(n-2)x_n^2=0.$$ Now since it is given that $$n\ge 3\implies n-2\ge 1>0$$. Therefore $$x_n^2=0\implies x_n=0$$. But $$x... | [
"I only",
"II only",
"none",
"I and II only"
] | C | I. True for all values of n except 1
When n = 1 ; n^2 = 1
II. True for all values of n except 1
When n = 1 ; n - n^2 = 1 - 1 =>0
III True for all values of n
Hence the correct answer will be (C) |
AQUA-RAT | AQUA-RAT-37957 | ### Show Tags
18 Feb 2015, 07:51
1
Using smart numbers:
Jennifer Purchases watches for $5: B=5 Markup of 100%; now selling for$10: x=10
She sells 5 watches: N=5
Her total profit will be (N*x)-(B*N)
(5*10)-(5*5)= 25
T=25
Now using the variables we must look at the answer choices that will solve for the % markup of t... | [
"100T-X",
"100T/NX",
"100TX/N",
"100TX"
] | B | Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/X *100 = 100T/(NX)
Answer : B |
AQUA-RAT | AQUA-RAT-37958 | # Is this a simple answer to the classic problem "A certain city has 10 bus routes..."
A certain city has 10 bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from anyone stop to any other (possibly changing along the way), but if any two rou... | [
"40",
"85",
"60",
"30"
] | B | B/C=1/17
C-B=80.........> B=C-80
(C-80)/C=1/17
Testing answers. Clearly Eliminate ACDE
Put C=85.........> (85-80)/85=5/85=1/17
Answer: B |
AQUA-RAT | AQUA-RAT-37959 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"A Gain of 1.67 times as much",
"A Gain of 1.4 times as much",
"A Gain of 2 times as much",
"A Gain of 1.6 times as much"
] | B | A = 7000; B = 5000; Profit = (3/4)*5000 = 3750
After prices are reversed:
A = 5000; B =7000; Profit = (3/4)*7000 =5250
5250 --> Gain of 1.4 times 3750
Answer: B |
AQUA-RAT | AQUA-RAT-37960 | A: 9
B: 12
C: 16
D: 18
E: 24
This is a copy of the following OG question: five-machines-at-a-certain-factory-operate-at-the-same-constant-rate-219084.html
_________________
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2231
Location: India
Concentration: General Ma... | [
"4",
"6",
"8",
"9"
] | A | the choices give away the answer..
36 machines take 4 hours to fill 8 standard orders..
in next eq we aredoubling the machines from 36 to 72, but thework is not doubling(only 1 1/2 times),= 4*48/72*12/6 = 4
Ans A |
AQUA-RAT | AQUA-RAT-37961 | 4.2 5 customer reviews. And the third angle is three times of the first angle. In a triangle, the second angle is 5° more than the first angle. check your answers against the answer explanation section at the end of each chap-ter. Find the three angles of the triangle. Always let x represent the unknown number. Questi... | [
"L=6/W=18",
"L=18/W=6",
"L=7/W=19",
"L=19/W=7"
] | B | We are looking for three angles.
! 1 - x
! 2 - x + 45
! 3 - 3x
You would not be able to solve this problem unless you knew that the sum of the interior angles
of a triangle is 180°.
! 1 + ! 2 + ! 3 = 180°
x + x + 45 + 3x = 180°
5x + 45 = 180°
5x = 135°
x = 27°
That means the first angle is 27°, the second angle is 27 +... |
AQUA-RAT | AQUA-RAT-37962 | $\frac {0.367}{0.978} = 0.375.$
13. ## Re: Probability with a "known"
Another way to do this is with combinations (since you don't care about the order that you pick the fruit). You will get the same answer either way. With combinations, you can just divide the number of outcomes. So, if we figure out the number of o... | [
"2/3",
"2/5",
"2/7",
"2/9"
] | D | The total number of ways to choose 2 apples is 9C2 = 36
The number of ways that include the spoiled apple is 8C1 = 8
P(the spoiled apple is included) = 8/36 = 2/9
The answer is D. |
AQUA-RAT | AQUA-RAT-37963 | # When will train B catch up with train A?
Printable View
• January 27th 2010, 08:19 PM
bball20
When will train B catch up with train A?
Trains A & B are traveling in the same direction on a parallel tracks. Train A is traveling at 60 mph and train B is traveling at 80 mph. Train A passes a station at 5:15 PM. If tra... | [
"76 sec",
"67 sec",
"98 sec",
"46 sec"
] | D | Speed of train relative to jogger = 46 - 10 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 340 + 120 = 460 m.
Time taken = 460/10 =46 sec.
Answer:D |
AQUA-RAT | AQUA-RAT-37964 | Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?
Total number of pencils Ramesh had = 20
Number o... | [
"113",
"109",
"93",
"97"
] | B | Explanation :
Let the stones with Manish, rahul and Bharti be m,r and b respectively.
Given,
=>5r=7m and 5m=7b.
=>25r=35m and 35m=49b.
=>25r=35m=49b=k.
=>r/49=m/35=b/25.
The least possible integral values for r,m,b will be r=49, m=35 and b=25.
=>Total=49+35+25=109.
Answer : B |
AQUA-RAT | AQUA-RAT-37965 | # In how many ways can 3 distinct teams of 11 players be formed with 33 men?
Problem:
In how many ways can 3 distinct teams of 11 players be formed with 33 men? Note: there are 33 distinct men.
The problem is similar to this one: How many distinct football teams of 11 players can be formed with 33 men?
Fist, I thou... | [
"7",
"8",
"9",
"10"
] | C | For a match u need 2 teams.
Suppose there are totally 'n'teams.
Now we have to choose 2 teams out of 'n' teams.
nC2 = 36;
Solve to get n=9.
n(n-1)/2 = 36
9(9-1)/2 = 36
9(8)/2 = 36
72/2 = 36
So, answer is 9 If 36 matches are totally played.
ANSWER:C |
AQUA-RAT | AQUA-RAT-37966 | => 18x/4=154
x=308/9
TOTAL WAGES PAID WILL BE
(12/11 + 18/7)*309/9
PLEASE TELL ME WHERE I AM WRONG
Lets try -
SW4 wrote:
Elana was working to code protocols for computer processing. She did 11/18 of the job and allowed Andy to finish it. They both work at the same rate and receive the same hourly pay. If the differe... | [
"$1050",
"$2500",
"$3000",
"$3400"
] | A | Let the shares of A,B,C,D are 2x,3x,4x,6x
6x-4x = 700
x = 350
B's share = 3x = $1050
Answer is A |
AQUA-RAT | AQUA-RAT-37967 | your kids. The volume formula for a rectangular box is height x width x length, as seen in the figure below: To calculate the volume of a box or rectangular tank you need three dimensions: width, length, and height. Find the dimensions of the box that minimize the amount of material used. The calculated volume for the ... | [
"24",
"48",
"64",
"80"
] | B | Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 6.
i.e,
x*y*z = 6 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*6 = 48.
Answer is B |
AQUA-RAT | AQUA-RAT-37968 | (1) Kevin spent a total of $18.00 on beer. (2) Kevin bought 3 more cans of beer than bottles of beer. Target question: How many bottles of beer did Kevin buy? Given: Kevin pays$1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that ... | [
"$2.15",
"$2.05",
"$2.45",
"$2.25"
] | B | John spent and gave to his two friends a total of
1.05 + 1.00 + 1.00 = $3.05
Money left
5.10 - 3.05 = $2.05
Answer :B |
AQUA-RAT | AQUA-RAT-37969 | # How to approach this combinatorics problem?
You have $12$ different flavors of ice-cream. You want to buy $5$ balls of ice-cream, but you want at least one to be made of chocolate and also you don't want more than $2$ balls per flavor. In how many ways can you can choose the $5$ balls?
• Does order matter? – vrugte... | [
"60",
"50",
"90",
"45"
] | C | By checking the answer choices:
Since we have an initial ratio of 9:6, the total count should be divisible by 15.
A. 60/15=4, Cake People = 36, Candy People = 24, Since 36-9 is not equal to 24+9 this can not be the answer.
B. Out, Since not divisible by 15.
C. 90/15=6, Cake People = 54, Candy People = 36, Since 54-9 is... |
AQUA-RAT | AQUA-RAT-37970 | # Reset the equation counter
\documentclass{article}
\usepackage{amsmath, amsfonts, chngcntr}
\newcounter{problem}
\newcounter{solution}
\newcommand\Problem{%
\stepcounter{problem}%
\textbf{\theproblem.}~%
\setcounter{solution}{0}%
}
\newcommand\TheSolution{%
\textbf{Solution:}\\%
}
\newcommand\ASolution{%
\stepcou... | [
"5 kmph",
"4 kmph",
"9 kmph",
"8 kmph"
] | B | Speed downstream = d/t = 65/(2 1/2) = 26 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (26 - 18)/2 = 4 kmph
Answer:B |
AQUA-RAT | AQUA-RAT-37971 | Manager
Joined: 07 Jul 2016
Posts: 79
GPA: 4
Re: Two bottles are partially filled with water. The larger bottle current [#permalink]
### Show Tags
04 Aug 2016, 22:33
AbdurRakib wrote:
Two bottles are partially filled with water. The larger bottle currently holds $$\frac{1}{3}$$ of its capacity. The smaller bottle, w... | [
"68",
"72",
"76",
"80"
] | D | 28 liters is 35% of the capacity C.
28 = 0.35C
C = 28/0.35 = 80 liters.
The answer is D. |
AQUA-RAT | AQUA-RAT-37972 | the train is retarding from 60 m/s to 0 m/s, at a retardation of 1 m/s2 , time at which the speed reaches 30 m/s is: $$v = u – at$$ $$=> 30 = 60 – 1xt$$ $$=> t = 30s$$ At 30s, distance covered is: $$S = ut – ½ at^2$$ $$= 60 x 30 – ½ x 1 x (30)2$$ $$= 1800 – (15 x 30)$$ $$= 1800 – 450$$ $$= 1350m$$ (from the initial 90... | [
"30",
"31",
"72",
"25"
] | C | Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/6 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72km/hr.
Answer: Option C |
AQUA-RAT | AQUA-RAT-37973 | Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html
Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html
I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.
Intern
Joined: 17 Nov 2015
Posts: 7
Location: India
Conc... | [
"200",
"300",
"400",
"450"
] | C | a + 18m = 760 (17th term)
a + 15m = 700 (16th term)
You get a = 400 and m = 20
Answer: C |
AQUA-RAT | AQUA-RAT-37974 | $$1\\1+1\\ 1+1+1\quad1+2\\ 1+1+1+1\quad1+1+2\\ 1^5\quad1+1+1+2\quad1+2+2\quad1+1+3\\ 1^6\quad1^4+2\quad1^2+2+2\quad1^3+3\quad1+2+3\\ 1^7\quad1^5+2\quad1^3+2+2\quad1+2^3\quad1^4+3\quad1^2+2+3\quad1^3+4\quad1+2+4\\ 1^8\quad1^6+2\quad1^4+2+2\quad1^2+2+2+2\quad1^5+3\quad1^3+2+3\quad1^2+3+3\quad1+2+2+3\quad1^4+4\quad1+1+2+4... | [
"(2^3-1)(2^3+1)",
"2^6+5",
"2^5-1",
"2^5+1"
] | B | From 7+2+2^2+2^3+2^4+2^5=69,
2^6+5=69
the correct answer is B. |
AQUA-RAT | AQUA-RAT-37975 | # Number of ways in which they can be seated if the $2$ girls are together and the other two are also together but separate from the first two
$5$ boys and $4$ girls sit in a straight line. Find the number of ways in which they can be seated if $2$ girls are together and the other two are also together but separate fr... | [
"25",
"36",
"22",
"42"
] | C | i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
3x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
84 ... |
AQUA-RAT | AQUA-RAT-37976 | # Finding the minimum number of students
There are $p$ committees in a class (where $p \ge 5$), each consisting of $q$ members (where $q \ge 6$).No two committees are allowed to have more than 1 student in common. What is the minimum and maximum number of students possible?
It is easy to see that the maximum number o... | [
"5",
"8",
"70",
"56"
] | C | Out of 8 people, any 4 can be selected for a committee. So 8c4=70 is the answer
C |
AQUA-RAT | AQUA-RAT-37977 | per hour. The time taken to cover the first 60% of the distance is 10 minutes more than the time taken to cover the remaining distance. What is its speed? 4) A car goes 250 km in 4 hours. The total time is 5 seconds, so t = 5. 4. Aptitude Questions and Answers. Learn how teachers can make BrainPOP-style assessments by ... | [
"55 km/hr.",
"25 km/hr.",
"65 km/hr.",
"35 km/hr."
] | D | D
35 km/hr.
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min. = 126/75 hrs.
Let the actual speed be x km/hr.
Then, (5/7)x X 126/75 = 42
--> x = 35 km/hr. |
AQUA-RAT | AQUA-RAT-37978 | reference-request, modelling, voting
For the election $(C, \{v\})$, i.e. with $v$ being the only vote, we have two admissible outcomes: $O_1 = \{p_\mathrm{rep} \mapsto 1, p_\mathrm{dem} \mapsto 0\}$ and $O_2 = \{p_\mathrm{rep} \mapsto 0, p_\mathrm{dem} \mapsto 1\}$. For $(C, \{v, v\})$, we have the same two outcomes. ... | [
"750",
"700",
"800",
"850"
] | B | Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*7 = 280)
100% -----> 700 (100*7 = 700)
Answer: Option B |
AQUA-RAT | AQUA-RAT-37979 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"344",
"218",
"200",
"600"
] | D | Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 3
=> x = 600
Answer: D) Rs 600 |
AQUA-RAT | AQUA-RAT-37980 | ## Digit Problems
1. Use $$3,4,5,6,7,8$$ to make digits between 5,000 & 6,000.
2. 2, 3, 4, 5, 6, 7: 6-digit numbers not divisible by 5
3. 5, 6, 7, 8, 0: Five digit numbers divisible by 4.
4. Make 7-digit numbers using 3, 4, 5, 5, 3, 4, 5, 6, keeping odd digits at odd positions, without using digits more than its frequ... | [
"10080",
"1080",
"10025",
"10050"
] | A | LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER A |
AQUA-RAT | AQUA-RAT-37981 | mass, newtonian-gravity, statics
Title: How do you weigh a box on a scale whose limit is too low? As you will see I know nothing about physics and after being asked to solve a physics problem in a recent interview wanted to ask it of professionals and see what the response would be:
I have a set of domestic scales (a... | [
"21R",
"33R",
"35R",
"31R"
] | D | You can do it in 5 steps.
1,2,4,8,16
Asume stone as S (Left Side) weight of 1kg as T (Right Side)
Move 1T to the same side as S and, Left Side is S+1T, Now weight 2T
Move 2T to the same side as S and, against S+3T, Now weight 4T
Move 4T to the same side as S and, against S+7T, weight 8T
Move 8T to the same side as S an... |
AQUA-RAT | AQUA-RAT-37982 | area of that circle click on the calculate button... It is also known as the longest straight line segment which passes the! Segment which passes through the center of the circle demonstration is to use this calculator, by... 3 = 150687.075 mm if we know circumference as the straight line segment which passes through m... | [
"2",
"1",
"7",
"3"
] | C | 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 168,000 m : C is the circumference
C = 7 meters
correct answer C |
AQUA-RAT | AQUA-RAT-37983 | php, datetime
Title: Get Next Working Date, skip weekends and holidays The object is to be able to pass some dates (start date, holiday) and the number of days you want to skip. We only want to skip working days, not weekends and holidays.
Just let me know what you'd do different than what I have. The code works, but... | [
"24",
"23",
"18",
"21"
] | B | Explanation :
Mentioned month has begins on a Saturday and has 30 days
Sundays = 2nd, 9th, 16th, 23rd, 30th
=> Total Sundays = 5
Second Saturdays = 8th and 22nd
Total Second Saturdays = 2
Total Holidays = Total Sundays + Total Second Saturdays = 5 + 2 = 7
Total days in the month = 30
Total working days = 30 - 7 = 23
An... |
AQUA-RAT | AQUA-RAT-37984 | We know a = $$frac{2}{3}\\$b from the question stem. If each decreased its speed by 10 kmph, the speeds of A and B will be$$$frac{2}{3}\\$b – 10) and$b – 10) respectively.
From statement 2, ($$frac{2}{3}\\$b – 10) = $\frac{1}{2}\\$$b – 10)
$$frac{2}{3}\\$b – $\frac{1}{2}\\$b = 10 – 5 Solving the equation, we get b = ... | [
"5000",
"8000",
"4000",
"3000"
] | B | for 5 tyres running interchangeably 10,000 miles the car runs
for 1 tyre=10000/5=2000
as you all know i suppose the car has 4 tyre
to have equal worn out by 4 tyres we need=2000*4=8000
ANSWER:B |
AQUA-RAT | AQUA-RAT-37985 | leaves at 9:10 from one station and its speed is 90 km/h, what time does it get to the next station? You may speak with a member of our customer support team by calling 1-800-876-1799. Every word problem has an unknown number. When the problem is set up like this, you can usually use the last column to write your equat... | [
"318$",
"380$",
"420$",
"450$"
] | A | 12*1.75 + 0.45*12*55 = 318 hence - A |
AQUA-RAT | AQUA-RAT-37986 | Hence: 5x/100*(t-1/2) + x = 1100 = 4x/100*(t) + x
Solving, xt will get cancelled and you will get:
11000 = 11x
x is 1000
sum of both investments is 2x = 2000 which is Option D
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1326
Location: Viet Nam
Andrew borrows equal sums of money under simple i... | [
"2333",
"2777",
"3000",
"1000"
] | C | (x*5*1)/100 + [(2500 - x)*6*1]/100 = 120
X = 3000
Answer: C |
AQUA-RAT | AQUA-RAT-37987 | time, sun
d represents the day of the year for 2000. For example d=7
would be January 7th, 2000.
If you're willing to lose some precision in exchange for
convenience, you can compute the day of the current year (instead
of counting all the way back to 2000), since the sun's declination
repeats yearly (roughly speaking... | [
"Monday",
"Tuesday",
"Wednesday",
"Friday"
] | B | The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday. answer : B |
AQUA-RAT | AQUA-RAT-37988 | # What's 4 times more likely than 80%?
There's an 80% probability of a certain outcome, we get some new information that means that outcome is 4 times more likely to occur.
What's the new probability as a percentage and how do you work it out?
As I remember it the question was posed like so:
Suppose there's a stude... | [
"6.9",
"69.0",
"0.6845",
"0.624"
] | D | 78%*(4/5)=0.78*0.8=0.624
Answer :D |
AQUA-RAT | AQUA-RAT-37989 | 4. ### MikeML AAC Fanatic!
Oct 2, 2009
5,450
1,066
Psec/1bolt * 5bolts/1rev * 1rev/78.4in *...
The OP specified that the circumference of the wheel is 78.4in. Why do we need to include the radius in the conversion?
Last edited: Sep 8, 2015
5. ### Wendy Moderator
Mar 24, 2008
20,766
2,536
Because I missed that littl... | [
"421 m",
"422 m",
"423 m",
"424 m"
] | B | In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 300 resolutions.
= 300 * 2 * 22/7 * 22.4
= 42200 cm
= 422 m
Answer: B |
AQUA-RAT | AQUA-RAT-37990 | $\displaystyle \Pi_2 := \prod_{p>2} (1 - \frac{1}{(p-1)^2}) = 0.6601618\dots$
(see equation (7) from Supplement 4); note that
$\displaystyle \prod_p (1-\frac{1}{p})^{-2} (1-\frac{\omega(p)}{p}) = 2 \Pi_2$
so from Mertens’ third theorem (Theorem 42 from Notes 1) one has
$\displaystyle \prod_{p < z} (1-\frac{\omega(p... | [
"3",
"7",
"189",
"227"
] | C | In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be C. |
AQUA-RAT | AQUA-RAT-37991 | I shall determine a set of values of $$c$$ such that $$f_c'(x) > 0$$ for all $$x \in [0, 1].$$ (I shall not try to determine all such values of $$c.$$) It was shown above that for all $$c > 0,$$ if either of $$f_c',$$ $$f_{1/c}'$$ is strictly positive on $$[0, 1],$$ then so is the other. Because $$f_1(x) = x,$$ it suff... | [
"1 < 1/e< 1/f",
"1/e< 1 < 1/f",
"1/e< 1/f< 1",
"1/f< 1 < 1/e"
] | D | 0<e<1<f. Let e=1/2 and f=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D |
AQUA-RAT | AQUA-RAT-37992 | ## 28.
The Correct Answer is (D) — Graphs for answer choices A and B imply that the area of this rectangle can be 800$\small&space;ft^{2}$ or greater. These values are not possible with only 40ft of fencing material. Similarly, the graph for answer choice C says that the area can be as large as 400$\small&space;ft^{2}... | [
"95",
"92",
"82",
"88"
] | D | AREA OF FIELD = 680 SQ FEET
LENGTH OF ADJ SIDES 20 FEET AND 680/20 = 34 FEET
REQ LENGTH OF THE FENCING = 20 + 34 + 34 = 88 FEET
ANSWER D |
AQUA-RAT | AQUA-RAT-37993 | ## anonymous 5 years ago 100 people are present in a party. If each of them must do a handshake with all the other people, how many handshakes should be done? Please explain how to get the answer, thanks!
1. anonymous
you need 2 people for an hand shake and u have 100 people so i think that its C(100,2) but i am not ... | [
"30",
"21",
"18",
"15"
] | B | the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 7(7-1)/2 = 7*6/2 = 42/2 = 21
=> the answer is B(21) |
AQUA-RAT | AQUA-RAT-37994 | ### Exercise 20
Mr. Halsey has a choice of three investments: Investment A, Investment B, and Investment C. If the economy booms, then Investment A yields 14% return, Investment B returns 8%, and Investment C 11%. If the economy grows moderately, then Investment A yields 12% return, Investment B returns 11%, and Inves... | [
"$800",
"$900",
"$1000",
"$1100"
] | D | The ratio of capital of A, B and C = 15000 : 21000 : 27000 = 5 : 7 : 9
A's share = (5/7)*1540 = $1100
The answer is D. |
AQUA-RAT | AQUA-RAT-37995 | # Probability based on a percentage
We have a group of 15 people, 7 men and 8 women.
Randomly selecting 5 people, what's the probability to pick 3 men and 2 women? What's the probability to pick at least 1 man?
I tried solving the first question like this: $${7 \choose 3} = \frac{7!}{(7-3)!3!} = 35$$ and $${8 \choos... | [
"5/21",
"5/23",
"5/29",
"5/12"
] | A | Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability
= (5C2 * 6C1)/10C5
= (10 * 6)/252 = 5/21
Answer: A |
AQUA-RAT | AQUA-RAT-37996 | numbers we need to first convert the mixed numbers into improper fractions, multiply the improper fractions and reduce the resultant value to the lowest terms to get the answer. You just need to enter your two fractions, then select the operation you want to perform. Study math with us and make sure that "Mathematics i... | [
"2/9 and 5/18",
"2/9 and 4/18",
"3/9 and 4/18",
"2/9 and 6/18"
] | B | Solution:
We're searching for pairs of numbers which, when multiplied, have the same product. We observe that 4 x 9 = 18 x 2 = 36, so the fractions will be 2/9and4/18
Answer B |
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