source string | id string | question string | options list | answer string | reasoning string |
|---|---|---|---|---|---|
AQUA-RAT | AQUA-RAT-38097 | \$7,382.94 3.2% 01.09.08 \$19.6879
\$7,402.63 3.2% 01.10.08 \$19.7404
\$7,422.37 3.2% 01.11.08 \$19.7930
\$7,442.17 3.2% 01.12.08 \$19.8458
The following is multiple choice question (with options) to answer.
After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article? | [
"1218",
"2777",
"1200",
"2688"
] | C | CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer: C |
AQUA-RAT | AQUA-RAT-38098 | ## A committee of 2 people is to be selected out of
##### This topic has expert replies
Legendary Member
Posts: 1892
Joined: 14 Oct 2017
Followed by:3 members
### A committee of 2 people is to be selected out of
by VJesus12 » Thu Mar 15, 2018 4:23 am
A committee of 2 people is to be selected out of 3 teachers and 4 ... | [
"65 years",
"88 years",
"18 years",
"55 years"
] | C | 9 * 2 = 18 years
Answer: C |
AQUA-RAT | AQUA-RAT-38099 | So on.
=====
Another thing to note:
(Assume only positive values)
$$a < b$$ and $$c < d \implies ac < bd$$. But that is one directional. It doesn't go the other way that $$ac < bd \not \implies a< b$$ and $$c < d$$
So $$1< a < 2\implies (1 < a^2 < 4$$ and $$\frac 12 < \frac 1a < 1)\implies \frac 12 < a<4$$
That i... | [
"1 < 1/a< 1/b",
"1/a< 1 < 1/b",
"1/a< 1/b< 1",
"1/b< 1 < 1/a"
] | D | 0<a<1<b. Let a=1/2 and b=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-38100 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest be... | [
"2178",
"1087",
"2800",
"2689"
] | C | (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Answer: C |
AQUA-RAT | AQUA-RAT-38101 | # 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... | [
"76%.",
"66%.",
"89%.",
"140%."
] | D | Let C.P. = Rs. x.
Then, S.P. = Rs. (12% of x) = Rs. 6x/5
New S.P. = 2 * 6x/5 = Rs. 12x/5
Profit = 12x/5 - x = Rs. 7x/5
Profit = 7x/5 * 1/x * 100 = 140%.
Answer: D |
AQUA-RAT | AQUA-RAT-38102 | ## Wednesday, August 12, 2015
### The angle between the hour and minute hands of a clock.
Q. The time shown in the clock is 7:35 what is the angle between the hour and minute hands of a clock?
A. Consider the simpler problem if the time is 7:00. As there are 12 hours in a complete revolution of the hour hand, one ho... | [
"42",
"41",
"44",
"45"
] | C | Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Answer is C |
AQUA-RAT | AQUA-RAT-38103 | Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Intern Joined: 12 Mar 2015 Posts: 4 Re: It takes Jack 2 more hours than Tom to type 20 pages. If [#permalink] ### Show Tags 05 Oct 2015, 23:05 Barkatis wrote: It takes Jack 2 more... | [
"41.4",
"34.1",
"13.4",
"12.4"
] | A | Break down the problem into two pieces: typing and editing.
Mary needs 30 hours to type the report--> Mary's typing rate = 1/30 (rate reciprocal of time)(point 1 in theory below);
Mary and Jim can type up a report in 12.5and --> 1/30+1/x=1/12.5=2/25 (where x is the time needed for Jim to type the report alone)(point 23... |
AQUA-RAT | AQUA-RAT-38104 | (A) 18 litres
(B) 27 litres
(C) 36 litres
(D) 40 litres
(E) 47 litres
let total qty be x liters
so milk 9x/100
9 liters is withdrawn so left with 9x/100- (9/100) * 9 which becomes equal to 6x/100
we have
9/100 * ( x-9) = 6x/100
3x-27 = 2x
x= 27 litres
OPTION B
Director
Joined: 25 Jul 2018
Posts: 731
A vessel is full o... | [
"23.89",
"72.9",
"33.62",
"78.3"
] | C | Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]^n * T
For the given problem, T = 50, y = 9 and n = 2.
Hence, quantity of milk finally... |
AQUA-RAT | AQUA-RAT-38105 | ## Solution 4
Slightly expanding, we have that $\frac{(a-b)(a^2+ab+b^2)}{(a-b)(a-b)(a-b)}=\frac{73}{3}$.
Canceling the $(a-b)$, cross multiplying, and simplifying, we obtain that
$0=70a^2-149ab+70b^2$. Dividing everything by $b^2$, we get that
$0=70(\frac{a}{b})^2-149(\frac{a}{b})+70$.
Applying the quadratic formu... | [
"-4",
"-2",
"0",
"2"
] | C | (i) 9a - 11b = 70
(ii) 2a + 22b = -70
Adding (i) and (ii):
11a + 11b = 0
The answer is C. |
AQUA-RAT | AQUA-RAT-38106 | # STRNO - Editorial
Setter: Kritagya Agarwal
Tester: Felipe Mota
Editorialist: Taranpreet Singh
Easy
Number theory
# PROBLEM:
Given two integers X and K, you need to determine whether there exists an integer A with exactly X factors and exactly K of them are prime numbers.
# QUICK EXPLANATION
A valid choice for ... | [
"-4",
"-2",
"-1",
"2"
] | B | There is probably an easier way, but I just used the picking numbers option for this.
I chose x=2
2(1)(2-k) then just plugged in the answer choices for K until one wasn't evenly divisible by 3.
B gives you 8. 8/3 is not an integer.
B is the answer |
AQUA-RAT | AQUA-RAT-38107 | 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 ... | [
"30",
"35",
"40",
"45"
] | C | Let V be her normal speed and let T be her normal time.
D = (4/5)V * (T+10)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (4/5)V * (T+10)
T/5 = 8
T=40
The answer is C. |
AQUA-RAT | AQUA-RAT-38108 | 27&305893372041&12,5,5,7,5,8\\ 28&801042337577&12,5,5,7,7,8\\ 29&2097687354880&12,5,7,7,7,8\\ 30&5493183075966&12,7,7,7,7,8\\ 31&14383060457018&12,7,7,7,7,10\\ 32&37658422859324&14,7,7,7,7,10\\ 33&98594676094434&14,7,7,9,7,10\\ 34&258133753770289&14,7,7,9,9,10\\ 35&675827901330148&14,7,9,9,9,10\\ 36&1769404155218244&14... | [
"142",
"231",
"245",
"148"
] | A | A
142
The numbers 42869371 are being repeated in the same sequence. |
AQUA-RAT | AQUA-RAT-38109 | # 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... | [
"18 2/18%",
"18 2/11%",
"18 3/11%",
"18 2/17%"
] | B | 13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: B |
AQUA-RAT | AQUA-RAT-38110 | The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after
6. ### calculus
The population of a certain community is increasing at a rate directly pr... | [
"2(10^5)",
"9(10^5)",
"(2^9)(10^5)",
"(10^9)(10^5)"
] | C | Every 10 minutes, the population is double the previous population.
In 90 minutes, the population doubles 9 times.
The population then is 2^9*10^5.
The answer is C. |
AQUA-RAT | AQUA-RAT-38111 | # If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$.
This seems like a basic proof and I think this is how it goes: $$c \le d, \text{ Given }$$ $$a+c \le a+d$$ $$a+c \lt b+d, \text{ since } a \lt b$$
Is that all I need? I'm thinking this does it all quickly and c... | [
"6",
"2",
"3",
"7"
] | D | (a – b) – (c + d) = 17 and (c – d) – (a + b) = 3
=> (a – c) – (b + d) = 17 and (c – a) – (b + d) = 3
=> (b + d) = (a – c) – 17 and (b + d) = (c – a) – 3
=> (a – c) – 17 = (c – a) – 3 => 2(a – c) = 14 => (a – c) = 7
ANSWER:D |
AQUA-RAT | AQUA-RAT-38112 | recognize that if the event $P(A|A^cB^c)$ is the event that they both miss, and so they must start over again meaning $P(A|A^cB^c)=P(A)$ and therefore
$$P(A)=1 \cdot p_B(1-p_A)+0\cdot (1-p_B)p_A+1\cdot p_Ap_B+P(A)(1-p_B)(1-p_A)$$
solving this equation for $P(A)$ gives
$$P(A)=\frac{p_B}{1-(1-p_A)(1-p_B)}$$
the proba... | [
"8 points",
"10 points",
"14 points",
"40 points"
] | B | Solution
A : B = 100 : 80 and A : C = 100 : 72.
∴ B/C=(B/C x A/C) = (80/100 x 100/72)= 10/9 =100/90= 100 : 90.
∴ B can give C 10 points.
Answer B |
AQUA-RAT | AQUA-RAT-38113 | ### 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... | [
"$1.16",
"$1.17",
"$1.18",
"$1.19"
] | C | Let x be the number of loaves sold in May.
Then 2x/3 loaves were sold in April and 4x/3 loaves were sold in June.
The average price was (2x/3)(117) + 132x + (4x/3)(108) / (2x/3 + x + 4x/3) =
(78 + 132 + 144) / (3) = 354/3 = $1.18
The answer is C. |
AQUA-RAT | AQUA-RAT-38114 | ### 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... | [
"$12.20",
"$12.50",
"$12.55",
"$12.70"
] | A | Correct Answer: A
Explanation: The relevant formula for this problem is Average B= (Sum)/(Number of Terms). Another way to look at the formula is Sum = Average x Number of Terms. For the first purchase, the vendor's sum (total cost) was $140, since 14 x 10 = 140. For the second purchase, the vendor's cost was $165, sin... |
AQUA-RAT | AQUA-RAT-38115 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"25",
"83",
"45",
"53"
] | A | Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 54 = 378
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 378 - 780 = 25.
Answer:A |
AQUA-RAT | AQUA-RAT-38116 | # probability question on a customer
A very frustrated customer is trying to find an electronic receipt on their phone so they can return an item. The trouble is that the customer has three email accounts and can't remember which, one, account it was sent to. The customer assumes that there is an equal probability for... | [
"11.1%",
"12.1%",
"10.1%",
"9.1%"
] | B | Correct Answer: B
The company's total revenue from earbuds=10000*$10=$100000
The company's total revenue from phone cases=5300*$12=$63600
The company's total revenue from power banks=450*$50=$22500
The combined total of all sales=$186100
Therefore % of power banks sales=22500/186100*100= 12.1% |
AQUA-RAT | AQUA-RAT-38117 | $38k - (2*38 - 7)l = 34$
$38(k-2l) + 7l = 34$. Let $m=k-2l$
$38m + 7l = 34$.
$(3+ 5*7)m + 7l = 34$
$3m + 7(5m + l) = 34$. Let $n = 5m+l$.
$3m + 7n = 34$
$3m + 2*3n + n = 34$
$3(m + 2n) + n = 34$. Let $a = m+2n$.
$3a + n = 34$.
Let $a=11; n = 1$. So $a=m+2n; 11=m + 2; m = 9$. and $n= 5m + l; 1=5*9 +l; l = -44$.... | [
"276",
"299",
"312",
"322"
] | D | Solution
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer D |
AQUA-RAT | AQUA-RAT-38118 | # Math Help - Calculus Help Please
Initially a population contains 1000 individuals. After t minutes the number N of individuals in the populataion is such that dN/dt = -0.25N.
a) write down the expression for N in terms of t
b) Find the rate at which the population is decreasing when it is half its orginal size.
Thi... | [
"80",
"100",
"150",
"240"
] | B | 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 25 minutes the population increases by 25 x 4 = 100 people.
Answer. B. |
AQUA-RAT | AQUA-RAT-38119 | Maybe the examiner didn't think through your method.
From 10,000 to 99,999 the numbers divisible by 5 end in 0 or 5.
The first (most significant) digit can be any of nine from 1 to 9.
The 2nd digit can be any of 10.
The 3rd digit can be any of 10.
The 4th digit can be any of 10.
The 5th digit can be either of 2.
That... | [
"137",
"143",
"77",
"88"
] | B | Answer:B |
AQUA-RAT | AQUA-RAT-38120 | So, the number of dealings = 52!/(13!)^4.
How many dealings give each of A,B,C,D exactly one Ace (assuming 4 aces in the deck)? Well, there are 4! ways to give each player one ace, then there are
$$\frac{(N-4)!}{(a-1)! (b-1)! (c-1)! (d-1)!}$$ dealings of (N-4) non-aces to the players, giving (a-1) non-aces to Mr. A, e... | [
"1/336",
"1/120",
"1/56",
"1/720"
] | C | P=P(ace in the first draw)*P(ace in the second draw)*P(ace in the third draw)=3/8*2/7*1/6=1/56.
Answer: C. |
AQUA-RAT | AQUA-RAT-38121 | 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... | [
"299",
"277",
"276",
"370"
] | D | Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 150)/26 = 20
x = 370 m.
Answer: D |
AQUA-RAT | AQUA-RAT-38122 | 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... | [
"12",
"18",
"6",
"1"
] | A | Explanation:
More number of days means – more length, more depth and more width. Hence, it’s a direct proportion.
(100*25*30):(75*20*50)::12:x
75000:75000::12:x
x = 12
ANSWER A |
AQUA-RAT | AQUA-RAT-38123 | At most, 90% of the private homes are brick. So that's 9/10 x 3/8 = 27/80.
100% of the apartments are brick. So that's 5/8 = 50/80.
Add those two together and you get 77/80 not 15/16 (=75/80 as the answer suggests)...
Look at it this way.
Say there were 80 houses in total.
The ration tells us that 30 would be priv... | [
"25%",
"15%",
"20%",
"40%"
] | A | Ratio of 2 Bedroom Apartment: 1 Bedroom Apartment = 700 : 2100 -----> 1 : 3
Let total number of Apartments be X
No. of 2 Bedroom Apartment = (1 / 4) * X
percentage of apartments in the building are two-bedroom apartments ---->
(1/4) * 100 ---> 25%
Answer : A |
AQUA-RAT | AQUA-RAT-38124 | # 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... | [
"20%",
"6%",
"40%",
"5%"
] | B | The total CP = Rs. 2700 + Rs. 300
= Rs. 3000 and SP = Rs. 3180
Profit(%)
= (3180- 3000)/3000 * 100
= 6%
Answer: B |
AQUA-RAT | AQUA-RAT-38125 | The $$26$$ blocks consist of three groups: six of them are face-to-face with $$V_1$$, twelve of them are edge-touching-edge-only with $$V_1$$, and the remaining eight are vertex-touching-vertex-only with $$V_1$$.
The value of each $$I_f$$, $$I_e$$, and $$I_v$$ will be obtained using $$E(a,b,c)$$, successively building... | [
"8 cms",
"12 cms",
"14 cms",
"16 cms"
] | B | Volume of new cube = Volume of cube 1 + cube 2 + cube 3 = 63 + 83 + 103, = 216 + 512 + 1000
a3 = 1728,
a = (1728)1/3 = 12
Answer: B |
AQUA-RAT | AQUA-RAT-38126 | 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... | [
"6:5",
"3:4",
"2:5",
"7:9"
] | C | Let, Maala’s age = A and Kala’s age =4A
Then A + 4A = 20
A =5
Maala’s age = 5 years
and Kala’s age = 20 years
Proportion of their ages after 5 is = (5 + 5) : (20 + 5)
= 10 : 25
= 2 : 5
Answer : C |
AQUA-RAT | AQUA-RAT-38127 | mass, weight
Title: Mass versus Weight What are the difference between mass and weight? I keep getting confused in my physics class, and I am in 8th grade. Thank you in advance. Mass is a measure of how much matter (atoms) make up an object. Weight is a force that results from that quantity of matter accelerating in a... | [
"25 pounds",
"46 pounds",
"92 pounds",
"130 pounds"
] | D | Since only water evaporates, then the weight of pulp (non-water) in grapes and raisins is the same. Thus 0.08*{weight of grapes}=0.8*{weight of raisins} --> 0.08x = 0.8*13 --> x = 130.
Answer: D. |
AQUA-RAT | AQUA-RAT-38128 | # Simple and Compound Interest Problem
• January 14th 2011, 01:41 AM
dumluck
Simple and Compound Interest Problem
Hi All,
Q:Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest be... | [
"4 1/2 %.",
"3 1/2 %.",
"2 1/2 %.",
"2 3/4 %."
] | C | Explanation :
Let sum = x. Then, S.I. = x/4
Let rate = R% and time = R years.
[x * R * 4R / 100] = x / 4 ? R^2 = 25/4
R = 5/2 = 2 1/2.
Hence, R = 2 1/2 %.
Answer : C |
AQUA-RAT | AQUA-RAT-38129 | # 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... | [
"26",
"88",
"90",
"42"
] | C | SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 15 = Rs. 90
Answer:C |
AQUA-RAT | AQUA-RAT-38130 | # smallest integer value of $n$ such that $|S_n-S_\infty|<0.001$
If $S_n$ and $S_\infty$ are sums to $n$ terms and sum to infinity of a geometric progression $3,-\frac{3}{2},\frac{3}{4},...$ respectively, find the smallest integer value of $n$ such that $|S_n-S_\infty|<0.001$
My attempt,
$$|S_n-S_\infty|<0.001$$
$$... | [
"23/28",
"14/15",
"15/19",
"21/24"
] | C | 23/28 =0.821
14/15 = 0.933
15/19 = 0.7894
21/24 = 0.875
So, 15/19 = 0.7894 is smallest.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38131 | the acceptance volume is the volume of water that the bladder is designed to hold, which is smaller than the overall tank size. The volume flow, Q = ∫ u(2π r)dr, can be estimated by a numerical quadrature formula such as Simpson’s rule. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-... | [
"90 cm",
"2 dm",
"1 m",
"1.1 cm"
] | B | Explanation:
Let the thickness of the bottom be x cm.
Then , [(330 - 10) × (260 - 10) × (120 - x)] = 8000 × 1000
=> 320 × 250 × (120 - x) = 8000 × 1000
=> (120 - x) = 8000×1000/320=
100
=> x = 20 cm = 2 dm.
Answer: B |
AQUA-RAT | AQUA-RAT-38132 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"16",
"24",
"32",
"48"
] | C | after 8 girls left remaining 8 girls
now boys 16 are twice as many as remaining girls.
initially boys=16 and girls=16.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38133 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"31",
"36.67",
"88",
"13"
] | B | Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 300.
Total score of the batsman in the 30 matches = 1100.
Average score of the batsman = 1100/30 = 36.67.
Answer:B |
AQUA-RAT | AQUA-RAT-38134 | $11 + 6.5 = 17.5 \text{ or } 24 - 6.5 = 17.5$.
Therefore, 17.5 is the number in the middle of $11 \mathmr{and} 24.$
• 4 minutes ago
• 5 minutes ago
• 7 minutes ago
• 8 minutes ago
• 37 seconds ago
• A minute ago
• A minute ago
• 2 minutes ago
• 2 minutes ago
• 3 minutes ago
• 4 minutes ago
• 5 minutes ago
• 7 minutes... | [
"3.1",
"3.4",
"3.6",
"4"
] | C | 3.6
Option 'C' |
AQUA-RAT | AQUA-RAT-38135 | Change the chapter
Question
Jogging on hard surfaces with insufficiently padded shoes produces large forces in the feet and legs. (a) Calculate the magnitude of the force needed to stop the downward motion of a jogger’s leg, if his leg has a mass of 13.0 kg, a speed of 6.00 m/s, and stops in a distance of 1.50 cm. (Be ... | [
"20",
"500",
"50",
"10"
] | B | 100centimeters=1meter
x centimeters=100meters
(20 centimeters per step) x (nos running steps)=10000 centimeters
nos running steps= 10000 centimeters /20 centimeters
500steps
The answer is B |
AQUA-RAT | AQUA-RAT-38136 | rhombus can be found, also knowing its diagonal. How To Find Area Of Rhombus (1) If both diagonals are given (or we can find their length) then area = (Product of diagonals) (2) If we use Heron’s formula then we find area of one triangle made by two sides and a diagonal then twice of this area is area of rhombus. We no... | [
"218",
"265",
"268",
"480"
] | D | 262 – 102 = 242
d1 = 20 d2 = 48
1/2 * 20 * 48
= 480
Answer: D |
AQUA-RAT | AQUA-RAT-38137 | Let us take another mixture problem:
Question 2:
Two types of rice costing $60 per kg and$40 per kg are mixed in a ratio 2: 3. What will be the cost per kg of mixed rice?
Solution:
• Can we apply alligation to this question?
• Can we assume the price of the mixed rice to be $x per kg and make this diagram? • Now do... | [
"17%",
"20%",
"25%",
"30%"
] | A | Sol.
Let the original consumption = 100 kg and new consumption = x kg.
So, 100 x 10 = x × 12 = x = 83 kg.
∴ Reduction in consumption = 17%.
Answer A |
AQUA-RAT | AQUA-RAT-38138 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"0",
"1",
"10",
"19"
] | D | Solution
average of 20 numbers = 0.
∴ Sum of 20 numbers = (0×20) = 0.
it is quite possible that 19 of these number may be positive and if their sum is a, then 20th number is (-a). Answer D |
AQUA-RAT | AQUA-RAT-38139 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"21 years",
"22 years",
"23 years",
"24 years"
] | A | Sum of the ages of 14 students
= (16 * 35) - (14 * 25) = 560 - 350 = 210
Required average = (210/10) = 21 years.
Answer:A |
AQUA-RAT | AQUA-RAT-38140 | 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... | [
"11 days",
"66 days",
"30 days",
"77 days"
] | C | C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C |
AQUA-RAT | AQUA-RAT-38141 | 1. Let total distance=X.
1st distance =30x/100.Speed=20kmph
2nd distance=60x/100 Speed=40kmph
3rd distance=10x/100Speed=10kmph
T1=1/20*30x/100 = 3x/200
T2=1/40*60x/100 =3x/200
T3=1/10*10x/100 =X/100
Applying S=D/T Formula
30x/100+60x/100+10x/100
______________________________
3x/200+ 3x/200+ X/100.
=100x*200/8x*100
=25... | [
"5hr",
"6hr 30min",
"8hr 10min",
"7hr 20min"
] | D | speed of man = 40km/hr
number of rests = (200/25)-1 = 7
time taken for the man = (200/40)+7*(20/60) = 7 hr 20 min
Answer is D |
AQUA-RAT | AQUA-RAT-38142 | # String probability (with conditional prob and combinations)
I'm having trouble with the questions below, all relating to string probability. I'll write the problem and then provide my work for my (incorrect) answer. Please help me figure out what I did wrong.
SET1: Assume a string, allowing repetition, is randomly ... | [
"1/4",
"1/3",
"1/2",
"1/7"
] | C | Explanation :
There are total 2 letters. The probability that S gets the first position is 1/2.
The probability that S is in the second position is 1/1.
Hence, the required probability is:-
=> (1/2) x 1.
=> 1/2
Answer : C |
AQUA-RAT | AQUA-RAT-38143 | -
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\... | [
"N/8",
"7N/8",
"11N/12",
"17N/24"
] | C | The number of people who answered yes to both questions is (1/2)(1/6)N = N/12
The number of people who did not answer yes to both is 1 - N/12 = 11N/12
The answer is C. |
AQUA-RAT | AQUA-RAT-38144 | "Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" ##### Most Helpful Expert Reply GMAT Club Legend Joined: 11 Sep 2015 Posts: 4959 Location: Canada GMAT 1: 770 Q49 V46 When a positive integer n is divided by 5... | [
"0",
"1",
"2",
"3"
] | A | We first expand (2n + 2)2
(2n + 2)2 = 4n 2 + 8 n + 4
Factor 4 out.
= 4(n 2 + 2n + 1)
(2n + 2)2 is divisible by 4 and the remainder is equal to 0. The answer is A. |
AQUA-RAT | AQUA-RAT-38145 | Also: explore what must happen if one of the variables, say x, is zero.
4. Aug 9, 2013
Thanks for the hints , but I used a different method to solve this equation. From eq. 1 I got y=(6x)/(5x-6) .
I substituted that in eq. 2 to get x in terms of z. ( x=(126z)/(126+45z) ) then I substituted that into eq. 3 to get a qu... | [
"3",
"4",
"5",
"6"
] | C | (1) 5x + 3y + z = 11
If 2x + y + z = 3, then (2) 4x + 2y + 2z = 6
Let's subtract equation (2) for equation (1).
x + y - z = 5
The answer is C. |
AQUA-RAT | AQUA-RAT-38146 | I am also in High School, and it is my understanding that if there is a number squared and then square rooted then it is (by definition) just the original number. Taking your example of -5, plugging it in you would get sqrt (-5)^2 = -5. (-5)^2 is 25 and square rooting it is 5 which is not equal to -5. To avoid this, yo... | [
" 9/4",
" 3/2",
" 4/3",
" 2/3"
] | B | We need to produce an equation from the information given in the problem stem. We are first given that x is multiplied by 2 and then the product is divided by 3. This gives us:
2x/3
Next we are given that the positive square root of the result (which is 2x/3) is equal to x. This gives us
√(2x/3) = x
2x/3 = x^2
2x = 3x^... |
AQUA-RAT | AQUA-RAT-38147 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"74",
"75",
"76",
"77"
] | D | ratio is 4:6:5 , numbers are 4x, 6x, 5x
total scores of each class is (65*4x + 6x * 85 + 77*5x) = 260x+510x+385x = 1155x
total number of students = 15x
average = 1155x/15x = 77
D is the answer |
AQUA-RAT | AQUA-RAT-38148 | |x - a| = b
x is a distance 'b' away from 'a' on either side on the number line.
-4 < x < 8
Mid point of -4 and 8 is 2. Both -4 and 8 are 6 away from 2.
So the absolute value form will be |x - 2| < 6
For more, check: http://www.veritasprep.com/blog/2011/01 ... edore-did/
_________________
Karishma
Veritas Prep GMAT ... | [
" 2 < x < 16",
" 2 <= x < 4",
" 2 < x <= 9",
" 4 < x <= 8"
] | C | Solution:
Let’s isolate x in both inequalities, starting with x + 8 > 10.
x + 8 > 10
x > 2
Next we isolate x in the inequality x – 4 5.
x – 4 <= 5
x <= 9
Bringing these two inequalities together we know:
2 < x <= 9
The answer is C. |
AQUA-RAT | AQUA-RAT-38149 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"0",
"1",
"10",
"19"
] | A | EXPLANATION
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer A |
AQUA-RAT | AQUA-RAT-38150 | homework-and-exercises, special-relativity, inertial-frames, observers
But how much has John aged, according to Mike?
During t1, John was stationary according to Mike and therefore aged t1. During t2 + t2, John was moving at 0.5c, so aged
$$(2\sqrt{\frac{3}{4}} + 2\sqrt{\frac{3}{4}}) * \sqrt{\frac{3}{4}} = 4 * \frac{3... | [
"12",
"15",
"20",
"22"
] | A | Explanation:
Present age is 4x and 3x,
=> 4x + 10 = 26 => x = 4
So Deepak age is = 3(4) = 12
Answer: Option A |
AQUA-RAT | AQUA-RAT-38151 | (ones digit is $$0$$, because it is the difference of two numbers whose ones digit is $$1$$).
Now if $$3n$$ is divisible by $$10$$, for an integer $$n$$, then $$n$$ is divisible by $$10$$. QED.
The following is multiple choice question (with options) to answer.
The number N is 5,3H7, where H represents the ten's digi... | [
"4",
"3",
"5",
"8"
] | B | If the number is divisible by 9, it must also be divisible by 3. Only 3 yields such a number.
Answer: B |
AQUA-RAT | AQUA-RAT-38152 | Re: The letters D, G, I, I , and T can be used to form 5-letter strings as [#permalink]
### Show Tags
16 Apr 2017, 07:45
1
KUDOS
Top Contributor
1
This post was
BOOKMARKED
Bunuel wrote:
The letters D, G, I, I , and T can be used to form 5-letter strings as DIGIT or DGIIT. Using these letters, how many 5-letter string... | [
"5!",
"5! − (3! + 2!)",
"5! − (3! × 2!)",
"5!/(3! + 2!)"
] | A | MANGO - five letters can be arranged in 5! ways
since there is no repetition in MANGO so
5!
Ans. A) 5! |
AQUA-RAT | AQUA-RAT-38153 | You are asked whether |x|=|y| or in other words, is the distance of x from 0 = distance of y from 0 ? You would get a yes if x= y or x=-y. Lets evaluate the choices.
Per statement 1:$$x=-y$$ . Clearly this is one of the conditions we are looking for. Assume 2-3 different values. x=2, y = -2 --> 2 and -2 are both 2 uni... | [
"(-x)+ (-y) is positive integer",
"2x+y is a negative integer",
"x-y is a positive integer",
"2xy/3x is a negative integer"
] | A | Given x, y are less than 0. So both will be negative integers
negative + negative = negative
negative * negative = positive
negative / negative = positive
x-y is false since xSo, option A is true , because if we multiple negative number with negative it becomes positive(x, y are negative numbers)
Answer : A |
AQUA-RAT | AQUA-RAT-38154 | java
public class TestStudents
{
public static void main(String[] args) throws IOException
{
System.out.println("============" + "=================");
System.out.println("Students " + "Personal Details");
System.out.println("============" + "=================");
String name;
int age;
... | [
"30 Years",
"31 Years",
"33 Years",
"34 Years"
] | C | Total age of students is 22X10 = 220 Years
Total age inclusive of teacher = 23X (10+1) = 253
So, Teacher's age is 253-220 = 33 Yrs
There is a shortcut for these type of problems
Teacher's age is 10+(23X1) = 33 Years
C |
AQUA-RAT | AQUA-RAT-38155 | Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.
Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.
Back to the problem:
From F.S 1, ... | [
"3:4",
"8:13",
"5:6",
"13:10"
] | B | The first nine positive multiples of six are {6, 12, 18, 24,30, 36, 42}
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=24 and b=(36+42)/2=39 --> a/b=24/39=8/13.
Answer: B. |
AQUA-RAT | AQUA-RAT-38156 | # 99 Consecutive Positive Integers whose sum is a perfect cube?
What is the least possible value of the smallest of 99 consecutive positive integers whose sum is a perfect cube?
• What have you tried? What do you know about the sum of $99$ consecutive integers? If the first is $n$, what is the sum? – Ross Millikan Au... | [
"99",
"135",
"145",
"171"
] | D | 1) greatest of each will have a difference of 9 and next greatest too will have a difference of 9 and so on..
Therefore all nine terms will have a term MORE by 9..
Sum =90+(9*9)=171
2) if sum is 90, the average= median=90/9=10..The median of next 9 will be 10+9=19..
And sum would be 19*9=171
ANSWER:D |
AQUA-RAT | AQUA-RAT-38157 | (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 ... | [
"1",
"2",
"3",
"4"
] | C | IMO it should be C that is C
reason:
formed an equation... bat = b ball = c
2b+4c=180
1b+6c=190
solving both we get b that is bat = 40 and c that is ball = 25
new equation 195 to be divided in equal
3b+3c=195
3*40 + 3*25 = 195
120+75= 195 |
AQUA-RAT | AQUA-RAT-38158 | At most, 90% of the private homes are brick. So that's 9/10 x 3/8 = 27/80.
100% of the apartments are brick. So that's 5/8 = 50/80.
Add those two together and you get 77/80 not 15/16 (=75/80 as the answer suggests)...
Look at it this way.
Say there were 80 houses in total.
The ration tells us that 30 would be priv... | [
"30",
"35",
"20",
"18"
] | B | {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-18+11 --> {Bike}=53 --> # those who have bike only is {Bike}-{Both}=53-18=35.
Answer: B. |
AQUA-RAT | AQUA-RAT-38159 | ## 5 Feb 2019 Enter the compounding period and stated interest rate into the effective interest rate formula, which is: r = (1 + i/n)^n-1. Where: r = The effective
1 Apr 2019 Based on the method of calculation, interest rates are classified as nominal interest rate, effective interest rate and annual percentage yield ... | [
"8 1/3",
"8 1/6",
"8",
"8 1/2"
] | C | (4200*3*R)/100 = (5000*5*4)/100
R = 8
Answer: C |
AQUA-RAT | AQUA-RAT-38160 | # Physics kinematics SIN question
1. Dec 30, 2011
### ShearonR
1. The problem statement, all variables and given/known data
A car, travelling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car ... | [
"5p.m.",
"6p.m.",
"4p.m.",
"7p.m."
] | A | Suppose the thief overtakes x hours after 2.30p.m.
Distance covered by the thief in x hrs = distance covered by the owner in (x-1/2 hours)
60x = 75(x-1/2)
15x = 75/2
x = 5/2 hrs
Thief is overtaken at 5p.m.
Answer is A |
AQUA-RAT | AQUA-RAT-38161 | 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... | [
"2.31 days",
"4.31 days",
"5.31 days",
"6.31 days"
] | A | 1/3 + 1/10 = 13/30
30/13 = 2.31 days
ANSWER:A |
AQUA-RAT | AQUA-RAT-38162 | # Question on arithmetic (Percentages)
A machine depreciates in value each year at the rate of 10% of its previous value. However every second year there is some maintenance work so that in that particular year, depreciation is only 5% of its previous value. If at the end of fourth year, the value of the machine stand... | [
"2197",
"1267",
"1750",
"2267"
] | C | Explanation:
C.I. = [4000 * (1 + 10/100)2 - 4000]
= (4000 * 11/10 * 11/10 - 4000) = Rs. 840.
Sum = (420 * 100)/(3 * 8) = Rs. 1750
Answer:C |
AQUA-RAT | AQUA-RAT-38163 | # How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?
How would I go about solving this math problem?
if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$?
I got $a/c = 2/5$ but that is not a corr... | [
"16",
"18",
"20",
"24"
] | A | 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
A |
AQUA-RAT | AQUA-RAT-38164 | ### Factoring 2e^2+4e-15 Solution
The variable we want to find is e
We will solve for e using quadratic formula -b +/- sqrt(b^2-4ac)/(2a), graphical method and completion of squares.
${x}_{}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
Where a= 2, b=4, and c=-15
Applying values to the variables of quadratic equation -b, a an... | [
"1/9",
"2/9",
"4/9",
"3/9"
] | B | We just need to find the factor thats all,
e -> quadrupled -> 4e
x-> doubled -> 2x
z-> tripled -> 3Z
Hence, Z^2 = 9Z^2
e is in numerator, and x*z in denominator.
Hence,
Additional factor being introduced = 4/2*9
=4/18 = 2/9 = B |
AQUA-RAT | AQUA-RAT-38165 | Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets
| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com
Originally posted by EgmatQuantExpert on 08 May 2015, 00:28.
Last edited by EgmatQuantExper... | [
"3(5!)",
"4(5!)",
"5(5!)",
"6(6!)"
] | D | GCF is the product of common factors of the numbers involved.
GCF = 6!
a = 8! = 8*7*6!
b will certainly have 5! and cannot have any more common factors with a (as this will increase the GCF)
Looking at the answers only 6 (6!) and 8! will have GCF as 6!
Ans D |
AQUA-RAT | AQUA-RAT-38166 | Option A, your future value will be$10,000 plus any interest acquired over the three years. Let's take a look. Discounting or Present Value Concept Compound Value Concept Vn=Vo*(1+k) ^n. Let’s take a look at a couple of examples. (Also, with future money, there is the additional risk that the … The amount of interest d... | [
"3:5",
"6:5",
"5:4",
"4:3"
] | D | let ratio constant be x.
4x/3x=(p*r*t1/100)/(p*r*t2/100)
t1/t2=4:3.
answer D |
AQUA-RAT | AQUA-RAT-38167 | \text{19 is prime} & \color{gray}{\enclose{circle}{2}}&\color{gray}{\enclose{circle}{3}}&\color{gray}{\cancel{4}}&\color{gray}{\enclose{circle}{5}}&\color{gray}{\cancel{6}}&\color{gray}{\enclose{circle}{7}}&\color{gray}{\cancel{8}}&\color{gray}{\cancel{9}}&\color{gray}{\cancel{10}}&\color{gray}{\enclose{circle}{11}}&\c... | [
"32.2",
"32.22",
"31.22",
"32.27"
] | A | Explanation:
Required prime numbers are 23, 29, 31, 37, 4.
Average will be (23 + 29 + 31 + 37 + 41)/5 = 32.20
Answer: A |
AQUA-RAT | AQUA-RAT-38168 | # Difference between revisions of "1984 AIME Problems/Problem 4"
## Problem
Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. ... | [
"480",
"239",
"270",
"282"
] | A | ANSWER : A |
AQUA-RAT | AQUA-RAT-38169 | ## 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}... | [
"has increased by 20 percent",
"has increased by 12 percent",
"has increased by 8 percent",
"is exactly the same as the old area"
] | C | Let L be the original length and let W be the original width.
The original area was L*W.
The new area is 0.9W*1.2L = (0.9)(1.2)L*W = 1.08*L*W
The answer is C. |
AQUA-RAT | AQUA-RAT-38170 | Difficulty:
65% (hard)
Question Stats:
53% (03:18) correct 47% (03:14) wrong based on 97 sessions
### HideShow timer Statistics
Question of the Week #7
Three pipes P, Q, and R are attached to a tank. P and Q individually can fill the tank in 3 hours and 4 hours respectively, while R can empty the tank in 5 hours.... | [
"2",
"2.5",
"3",
"3.5"
] | C | Solution
part filled by (A+B+C) in 1 hour = (1/5 + 1/6 + 1/30)
‹=› 1/3.
All the three pipes together will fill the tank in 3 hours.
Answer C |
AQUA-RAT | AQUA-RAT-38171 | homework-and-exercises, kinematics
Title: Average Velocity A car travels 100 miles in 2 hours, it then completes the return leg of the journey. How fast must it travel on the return leg to average 100mph over the total journey.
My thoughts on this are that it is impossible as if the total average was 100mph then the... | [
"6.9",
"7.2",
"7.5",
"7.8"
] | C | The time to go 30 miles was 18/9+12/10=2+1.2=3.2 hours.
The average speed for the return trip was 30 miles/4 hours= 7.5 mph.
The answer is C. |
AQUA-RAT | AQUA-RAT-38172 | Overcounting cricketer combinations
Following this, Navneet had a new problem:
I am stuck on another problem:
A team of 11 is to be selected out of 10 batsmen, 5 bowlers, and 2 keepers such that in the team at least 4 bowlers should be included. Find the number of possible ways of selection.
I tried to solve this q... | [
"21",
"22",
"23",
"25"
] | D | Let the average age of the whole team be x years.
11x - (28 + 31) = 9 (x - 1)
=> 11x - 9x = 50
=> 2x = 50
=> x = 25.
So, average age of the team is 25 years.
D |
AQUA-RAT | AQUA-RAT-38173 | Question
# In a school, there are $$1000$$ student, out of which $$430$$ are girls. It is known that out of $$430, 10$$% of the girls study in class $$XII$$. What is the probability that a student chosen randomly studies in class $$XII$$ given that the chosen student is a girl?.
Solution
## Total number of students ... | [
"500",
"450",
"250",
"350"
] | A | Number of students who speak French are 30 + 40 = 70
Of total students, the percentage of students who do not speak French was 86% --> percentage of who do is 14%
70-------14%
x ------- 100%
x = 70*100/14 = 500 = number of all students
Answer is A |
AQUA-RAT | AQUA-RAT-38174 | $38k - (2*38 - 7)l = 34$
$38(k-2l) + 7l = 34$. Let $m=k-2l$
$38m + 7l = 34$.
$(3+ 5*7)m + 7l = 34$
$3m + 7(5m + l) = 34$. Let $n = 5m+l$.
$3m + 7n = 34$
$3m + 2*3n + n = 34$
$3(m + 2n) + n = 34$. Let $a = m+2n$.
$3a + n = 34$.
Let $a=11; n = 1$. So $a=m+2n; 11=m + 2; m = 9$. and $n= 5m + l; 1=5*9 +l; l = -44$.... | [
"101",
"107",
"111",
"112"
] | C | Let the numbers be 37a and 37b.
Then, 37a * 37 b = 4107 => ab = 3
Now, co-primes with product 3 are (1, 3).
So, the required numbers are (37 * 1, 37 * 3) i.e., (1, 111).
Greater number = 111.
ANSWER:C |
AQUA-RAT | AQUA-RAT-38175 | # Proving Congruence Modulo
If $x$ is positive integer, prove that for all integers $a$, $(a+1)(a+2)\cdots(a+x)$ is congruent to $0\!\!\!\mod x$.
Any hints? What are the useful concepts that may help me solve this problem?
-
hint: you multiply $x$ consecutive integers so that one... – Raymond Manzoni Sep 1 '12 at 1... | [
"I only",
"II only",
"III only",
"I and II only"
] | B | X=6q+1
Examine II) put q=0,1,2,3....... we have x=1,7,13,...25 so x must be odd
Examine III) 14/6 has reminder 2 & 49/7 has reminder 1 so not always true
Examine I) X= 7 true but while 2 is prime, it does not give reminder 1
Answer: B |
AQUA-RAT | AQUA-RAT-38176 | java, integer
Title: Return reversed integer - Java The question is from Leetcode.
Given a 32-bit signed integer, reverse digits of an integer.
Example 1:
Input: 123
Output: 321
Example 2:
Input: -123
Output: -321
Example 3:
Input: 120
Output: 21
Note: Assume we are dealing with an environment which could only s... | [
"3",
"4",
"5",
"6"
] | C | we are given that if the integer N has its digits reversed the resulting integer differs from the original by 45. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original b... |
AQUA-RAT | AQUA-RAT-38177 | Sol:
Folks, look at the relative calculation here.
If we consider that all the 120 candidates passed the examination, the average of the entire class must be 39. But it is given that average of the entire class is 35.
So we are getting an extra of 4 in the average i.e. an extra of 4x120=480 in the total sum.
We got... | [
"88",
"104",
"110",
"90"
] | B | total student=198
failed=22
paasd student=198-22=176
from bottom her rank is=176-73+1=104
ANSWER:B |
AQUA-RAT | AQUA-RAT-38178 | Observe that since the items are identical, it does not matter that there are $4$ items in the second box. Your are then asking for the number of sums $a_1+a_2+a_3=3$ where $0\leq a_1\leq 1$, $0\leq a_2\leq 3$, and $0\leq a_3\leq 2$. I will give three answers.
First, an elementary argument: We know that $a_1=0$ or $a_... | [
"20",
"30",
"40",
"50"
] | A | Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138+2x131= 400.
(a + b + c) = square root of 400 = 20
answer :A |
AQUA-RAT | AQUA-RAT-38179 | Kudos [?]: 96083 [0], given: 10706
Re: Find the power of 80 in 40!??? [#permalink]
### Show Tags
19 Oct 2010, 12:42
Expert's post
1
This post was
BOOKMARKED
AtifS wrote:
This is regarding the topic "Factorial" written by Bunuel for GMAT Club's Math Book.
When finding the power of non-prime number in $$n!$$ we first ... | [
"15^60",
"30^40",
"120^80",
"60^60"
] | C | Here 60^80 = 30^80 * 20^80 Only Option C has both .
Smash C |
AQUA-RAT | AQUA-RAT-38180 | Re: How many 4 digit codes can be made, if each code can only contain [#permalink]
### Show Tags
05 Oct 2010, 12:37
utin wrote:
Hi Bunuel,
why can't i write TOO,OTO,OOT AS
(4^3)*3! , taking the T as one entity ans assuming that 3 things can be arranged in 3! ways???
Just one thing: TOO can be arranged in 3!/2! way... | [
"3!",
"3! − (3! + 2!)",
"3! − (2!)",
"3!/(3! + 2!)"
] | A | TIE - three letters can be arranged in 3! ways
since 'there is no repetition'
3!
Ans. A) 3! |
AQUA-RAT | AQUA-RAT-38181 | we need to know definitions... They survived choices in the wrong spot: you still haven ’ t answered the question... Out how to restore/save my reputation the process of trying to answer this I... © 2021 Stack Exchange is a typical Bayes Theorem problem, it ’ s the probability of a student the! Kountz, Ashwini Miryala, ... | [
"100",
"250",
"300",
"400"
] | B | Since 150 students answered yes only for subject M, then the remaining 350 students who answered yes for subject M, also answered yes for subject R. So, 350 students answered yes for both subjects.
If 350 students answered yes for both subjects, then 400-350=50 students answered yes only for subject R.
So, we have that... |
AQUA-RAT | AQUA-RAT-38182 | # 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... | [
"3%",
"16 2/3%",
"25%",
"21 3/7%"
] | D | Profit in 1982 = 15.6 - 10 = 5.6 million $
Profit in 1983 = 18.8 - 12 = 6.8 million $
Percentage increase in profit = (6.8-5.6)/5.6 * 100 %
= 21 3/7%
Answer D |
AQUA-RAT | AQUA-RAT-38183 | ### Show Tags
29 May 2017, 10:14
1
60*3 = 180
+
24*5= 120
120+180 =300
Speed= Distance/Time = 300/8 = 150/4=75/2=37.5
Manager
Joined: 03 Aug 2017
Posts: 103
Re: Jim travels the first 3 hours of his journey at 60 mph speed and the [#permalink]
### Show Tags
09 Dec 2019, 07:43
Bunuel wrote:
Jim travels the first 3 h... | [
"71.11",
"71.12",
"71.1",
"71.17"
] | A | Car travels first 160 km at 64 km/hr
Time taken to travel first 160 km = distancespeed=16064
Car travels next160 km at 80 km/hr
Time taken to travel next 160 km = distancespeed=16080Total distance traveled = 160+160=2×160Total time taken = 16064+16080Average speed = Total distance traveledTotal time taken=2×16016064+16... |
AQUA-RAT | AQUA-RAT-38184 | # If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term. - Mathematics
Sum
If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18,... are the same, find the value of n. Also find that term.
#### Solution
Let the first term, common difference
A... | [
"10",
"30",
"20",
"40"
] | D | Solution:
Let the two numbers be 3x and 4x. Then, (3x+10)/(4x+10) = 4/5.
=> 15x+50 = 16x+40 => x = 10.
.'. Second term = 4*10 =40.
ANSWER IS D |
AQUA-RAT | AQUA-RAT-38185 | # Question involving inequalities
Question: Sam has put sweets in five jars in such a way that no jar is empty and no two jars contain the same number of sweets. Also, any three jars contain more sweets in total than the total of the remaining two jars.
What is the smallest possible number of sweets altogether in the... | [
"12",
"18",
"20",
"24"
] | D | k is the integer that represents kg of pack
ak = 36 --> k = 36/a
bk = 60 --> k = 60/b
36/a = 60/b --> 5a = 3b and then k=12 for min(a+b)
a=36/12=3 , b=60/12=5
Total number of packs = 3+5 = 8
10-8=2 packs more required
2 *12 = 24 kg more sugar required to have 10 packs.
ANSWER: D |
AQUA-RAT | AQUA-RAT-38186 | 5. Hello, James!
Another approach . . .
12 Students are in a class.
Five can go to room A, Four to room B, and Three to room C.
How many ways can this happen?
Assign 5 students to room A.
. . There are: . $_{12}C_5 \:=\:\frac{12!}{5!7!} \:=\:792$ ways.
From the remaining 7 students, assign 4 students to room B.
. .... | [
"26197",
"23578",
"10992",
"14728"
] | C | C
10992
Each girl has seven bags with seven adult cats each.
Also, each adult cat has seven little cats.
Thus each girl has 49 adult cats and 343 little cats.
Hence, seven girls will have
343 adult cats and 2410 little cats.
If we calculate the number of legs now.
Girls = 7 * 2 = 14
Cats + Little cats = 2744 * 4 = 1097... |
AQUA-RAT | AQUA-RAT-38187 | => 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... | [
"Sterling 460",
"Sterling 484",
"Sterling 550",
"Sterling 504"
] | D | Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1260 x 2/5) = Sterling 504.
Answer: Option D |
AQUA-RAT | AQUA-RAT-38188 | # 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... | [
"10% profit",
"10% loss",
"15% profit",
"no profit, no loss"
] | D | 80*1.1+20*0.6/100=1
ANSWER:D |
AQUA-RAT | AQUA-RAT-38189 | 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... | [
"6 days",
"4 days",
"12 days",
"3 days"
] | D | Let x ladies can do the work in 12 days. More ladies, less days (Indirect)
Less work, less days (direct)
Ladies 2x : x Work 1 : ½
2x : x , 1 : ½ : : 12 : y
:. 2x * 1*y = x* ½ *12 or y = 3
Hence the required number of days = 3
ANSWER:D |
AQUA-RAT | AQUA-RAT-38190 | The $i$-th row has $18+2i$ seats, for $i=0,...,20$. The number of seats is thus $$\sum_{i=0}^{20}18+2i=18\times21+\sum_{i=0}^{20}2i=378+2\frac{20\times 21}{2}=378+420=798$$
-
You have a 0-th row... – Thomas Apr 6 '12 at 19:28
I know, and the answer is correct and all, but with the way the question is worded, we have ... | [
"1",
"2",
"9",
"25"
] | C | Total number of passengers = 108
There are 12 rows of seats on the bus.
To find how many seats are there in each row, divide the total number of passengers by the number of rows of seats on the bus.
We get, divide 108 by 12
108 ÷ 12 = 9
Therefore, there are 9 seats in each row
ANSWER IS C |
AQUA-RAT | AQUA-RAT-38191 | EZ as pi
Featured 5 months ago
$\text{males : females } = 6 : 5$
#### Explanation:
When working with averages (means), remember that we can add sums and numbers, but we cannot add averages.
(An exception would be if there were the same number of males and females - in this case we may add the averages and divide by... | [
"(mb + nc)/ (m + b) years",
"(mb + bc)/ (m + n) years",
"(mb + nc)/ (m + n) years",
"(nb + nc)/ (m + n) years"
] | C | (mb + nc) / (m+ n).nswer: C |
AQUA-RAT | AQUA-RAT-38192 | ## 5 Feb 2019 Enter the compounding period and stated interest rate into the effective interest rate formula, which is: r = (1 + i/n)^n-1. Where: r = The effective
1 Apr 2019 Based on the method of calculation, interest rates are classified as nominal interest rate, effective interest rate and annual percentage yield ... | [
"10.28%",
"10.25%",
"10.85%",
"30.25%"
] | B | Let the sum be Rs. 100. Then,
S.I. for first 6 months = (100 * 10 *1) / (100 * 2) = Rs. 5
S.I. for last 6 months = (105 * 10 * 1) / (100 * 2) = Rs. 5.25
So, amount at the end of 1 year = (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%.
Answer: B |
AQUA-RAT | AQUA-RAT-38193 | 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... | [
"90",
"95",
"100",
"105"
] | A | Length = Speed * time
Speed = L/T
S = 3000/120
S = 25 M/Sec
Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 90 Kmph
Answer:A |
AQUA-RAT | AQUA-RAT-38194 | 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... | [
"876 cm",
"800 cm",
"167 cm",
"765 cm"
] | B | Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer:B |
AQUA-RAT | AQUA-RAT-38195 | # 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... | [
"33.33%",
"35%",
"27.75%",
"35.75%"
] | A | SP = CP + g
200 SP = 200 CP + 50 SP
150 SP = 200 CP
150 --- 50 CP
100 --- ? => 33.33%
Answer: A |
AQUA-RAT | AQUA-RAT-38196 | temperature, unit-conversion
Title: Values of coefficient of expansion differ,when temperatures are measured on centigrade scale and on Fahrenheit scale separately In solving above question, it was given that
Change of $5 ℃ = $ change of $9 ℉$
The following is multiple choice question (with options) to answer.
If C... | [
"a) 65/9",
"b) 13",
"c) 25",
"d) 45"
] | B | The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick B which is the only number near half of 25. The other answer choices are too far apart so no need to calculate. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.