divelab/Sys2Bench huggingface dataset:
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 3% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
Options:
A)4 : 11
B)5 : 4
C)2 : 3
D)Data inadequate
E)None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 3% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.03x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.03x
or, 120 = 0.05x
x = 2400
Reqd ratio of population of males and females
2400/9000−2400=2400/6600=4:11
Answer A
Answer: A
Question: Find 3486/189
Options:
A)18.44
B)18.48
C)18.42
D)18.49
E)18.41
Rationale: First we make the denominator 200. i.e., we are introducing an error of 11 which is 11189=11711189=117 th of the denominator.
Now 3486200=17.433486200=17.43
But this answer is less than actual answer. So we have to increase it by 1/17th part of it.
117×17.43≃1117×17.43≃1
So final answer = 17.43 + 1 = 18.43
Actual answer = 18.44
Answer:A
Answer: A
Question: If you write down all the numbers from 1 to 50, then how many times do you write 3 ?
Options:
A)A)11
B)B)15
C)C)20
D)D)21
E)E)22
Rationale: Explanation:
Explanation:
Clearly, from 1 to 50, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 5 + 10 = 15.
Answer:B
Answer: B
Question: Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
Options:
A)15.502%
B)25.7014%
C)12.502%
D)21.7014%
E)none
Rationale: Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/3840)x100 =13.02083%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 13.02083%x (100/60) = 21.7014% and the answer is not there in the options.
The correct answer is (D).
Answer: D
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be
Options:
A)(1.5)^4
B)4(1.5)
C)(1.05)
D)1 + (0.05)^4
E)1 + 4(0.05)
Rationale: f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be
1(1.05)^1
1.05^1
C. (1.05)
Answer: C
Question: x, y, and z are positive integers. The average (arithmetic mean) of x, y, and z is 11. If z is two greater than x, which of the following must be true?
I. x is even
II. y is odd
III. z is odd
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: Given that:
x+y+z = 33 and z=x+2
using both equations
2x(Even) + y = 31 (Odd)
Since the sum is Odd 'y' has to be odd. Hence , only options (B) and (D) to be verified.
To check for 'x'.
x+y+z=33
x+z= 33- Odd
x+z= Even
Even + Even = Even
Odd+Odd = Even
ANSWER:B
Answer: B
Question: If you write down all the numbers from 1 to 100, then how many times do you write 1 ?
Options:
A)A)11
B)B)18
C)C)20
D)D)21
E)E)22
Rationale: Explanation:
Explanation:
Clearly, from 1 to 100, there are ten numbers with 1 as the unit's digit- 1, 11, 21, 31, 41, 51, 61, 71, 81, 91; and ten numbers with 1 as the ten's digit - 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100
So, required number = 10 + 11 = 21.
Answer: D
Answer: D
Question: If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B?
Options:
A)41
B)42
C)43
D)44
E)45
Rationale: A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 44.
The answer is D.
Answer: D
Question: Of the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two?
Options:
A) 90
B) 82
C) 80
D) 45
E) 36
Rationale: Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 800.
Answer:(B)
Answer: B
Question: The measurement of a rectangular box with lid is 25cmx18cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of πcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere)
Options:
A)288
B)48
C)72
D)972
E)964
Rationale: d=18, r=9;
Volume of the largest sphere= 4/3πr3
= 4/3 *π*9*9*9= 972πcm3 ANSWER:D
Answer: D
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
Options:
A)6
B)9
C)4
D)5
E)2
Rationale: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Answer: A
Question: The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 36. Find their present ages.
Options:
A)20,35,45
B)8,20,28
C)16,28,36
D)12,21,27
E)None of these
Rationale: Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 36
20K = 60
K = 3
Therefore, then present ages are 12,21,27.
ANSWER:D
Answer: D
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently ten spaces behind player B, what is the probability that player B will be frozen after player A rolls?
Options:
A)1/12
B)5/36
C)1/6
D)1/3
E)17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 10 (as A is 10 spaces behind B) = 3 ( (4,6), (5,5), (6,4) )
So, the probability = 3/36 =1/12(Option A)
Answer: A
Question: The average mark of the students of a class in a particular exam is 70. If 5 students whose average mark in that exam is 50 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam?
Options:
A)20
B)15
C)10
D)12
E)25
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 70 x.
Total marks of (x - 5) students = 90(x - 5)
70x - (5 * 50) = 90(x - 5)
200 = 20x => x = 10
Answer: C
Answer: C
Question: A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge?
Options:
A)Rs. 105 and Rs. 6
B)Rs. 216 and Rs. 12
C)Rs. 210 and Rs. 12
D)Rs. 210 and Rs. 6
E)None
Rationale: Explanatory Answers
Let half of the full basic fare be Rs. X.
Therefore, full basic fare is Rs. 2X.
Let the reservation charge be Rs. Y per ticket.
Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge)
2X + Y = 216 --- (1)
The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y.
Hence, 3X + 2Y = 327 --- (2)
Solving (1) and (2) we get,
X = 105 and Y = 6
Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6
Answer D
Answer: D
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:
Options:
A)280
B)579
C)500
D)400
E)100
Rationale: C
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500
Answer: C
Question: Find the fourth proportional to 2.9, 4.6 and 7.6?
Options:
A)12.05
B)13.5
C)15.23
D)15.34
E)16
Rationale: Formula = Fourth propotional = (b Ã— c)/a
A = 2.9, B = 4.6 and C = 7.6
(4.6 Ã— 7.6)/2.9 = 12.05
A
Answer: A
Question: Given the equation e = f/4 + g/4^2 + h/4^3, where f, g, and h are each equal to 1 or 0, then e could be any of the values below EXCEPT:
Options:
A)1/16
B)10/32
C)1/8
D)17/64
E)1/64
Rationale: e =f/4 + g/4^2 + h/4^3,
= f/4 + g/16 + h/64,
= (16f + 4g + h ) /64
Depending on whether f, g and h take 0 or 1:
substitute 0 or 1 for the different values of f, g and h.
Answer C
Answer: C
Question: A & B THROW A DICE ALTERNATIVELY TILL ONE OF THEM GETS A '6' AND WINS THE GAME. WHAT WILL BE A PROBABILITY?
Options:
A)4/11
B)5/11
C)6/11
D)7/11
E)8/11
Rationale: Whoever starts first will have a probability of 6/11 and the other has a probability of 5/11. So, if A starts, as has to be logically inferred from the question, pbbl that A wins = 6/11 and that B wins = 5/11.
Pbbl that the starting person wins = (1/6) + (5/6)*(5/6)*(1/6) + (5/6)*(5/6)*(5/6)*(5/6)*(1/6) + ... = G.P. with first term (1/6) and common ratio (5/6)*(5/6) = (1/6)/[1-(5/6)*(5/6)] = 6/11
ANSWER:C
Answer: C
Question: 60% of the registered candidates in an election are from congress and 40% of the registered candidates are from BJP. If 3/4th of the registered Congress candidates and 1/5 of the registered BJP candidates fight election. What is the percentage of people fighting elections?
Options:
A)34%
B)43%
C)53%
D)54%
E)56%
Rationale: Let total people be x
Congress =60/100*x=3x/5
3/4 of 3x/5=9x/20
Bjp=40/100*x=2x/5
1/5 of 2x/5=2x/25
Adding both
9x/20+2x/25=53x/100
Ans=53%
ANSWER:C
Answer: C
Question: If 20 men can build a water fountain 56 metres long in 42 days, what length of a similar water fountain can be built by 35 men in 3 days?
Options:
A)3 m
B)4 m
C)7 m
D)9 m
E)10 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 42: 3 : : 56 : x
Therefore (20 x 42 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/840=7
Hence, the required length is 7 m.
Answer : C
Answer: C
Question: In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 10 and 400, then the least and greatest integer on the card would be
Options:
A)3 and 15
B)3 and 20
C)4 and 13
D)4 and 14
E)5 and 14
Rationale: Given: 10<x(x+1)<400.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>10 --> so, the least value is 3. Test for the largest value: if x=20 then
x(x+1)=20*21=420>400
Answer: B.
Answer: B
Question: If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red socks in your sock drawer, what is the minimum number of socks that you need to pull out in the dark to be sure you had a matching pair?
Options:
A)5
B)7
C)8
D)9
E)2
Rationale: A
5
At least 5, so that at least one color has two socks!
Answer: A
Question: The difference between a number and its two-fifth is 510. What is 10% of that number ?
Options:
A)33
B)85
C)37
D)27
E)28
Rationale: Explanation:
Let the number be x. Then, .
10 % 0f 850 = 85.
Answer: B) 85
Answer: B
Question: 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 25 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks?
Options:
A)1/4
B)9/14
C)1/2
D)7/8
E)8/7
Rationale: Say total male = 40
Total female =60
Required ratio =( .25/40)/ (.75/60) = 1/2 C is the answer
Answer: C
Question: This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 9 days. In how many days Peter complete the work separately.
Options:
A)26 days
B)27.5 days
C)22.5 days
D)25.35 days
E)24 days
Rationale: Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 9 days which means that the whole job(1) can be completed in X days.
<=> 8/20->9 <=> X=9/(8/20)=22.5Thus the answer is C.
Answer: C
Question: N be a number,the 2,3 and 5 base notations u get last digit is 1.and two out of three the leading digit is 1. N is equal to
Options:
A)31
B)63
C)74
D)91
E)98
Rationale: number shuld be in format of 2k+1,3k+1,5k+1
so take lcm of 2 3 5 we get 30k+1
so it may be 31 or 91
but in case of 31 leading digit of all 3 case is one
31 base2 = 11111
31 base3 = 1011
31 base5 = 111
so ans is 91
ANSWER:D
Answer: D
Question: Vid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Vid have meant to type?
Options:
A)10
B)16
C)21
D)24
E)27
Rationale: Vid intended to type a seven-digit number Should be 21.
there are two possibilities for placing 2 3s .
case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.
-5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)
case 2: two 3s are not together, i.e. they have one or more digits between them .
-5-2-1-1-5- , in this arrangement
if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.
if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.
if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.
if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.
if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.
so total 15 ways.
case 2 + case 1 = 6+ 15 = 21 ways
Answer C
Answer: C
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 12% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Options:
A)70 lbs
B)40 lbs
C)30 lbs
D)50 lbs
E)60 lbs
Rationale: These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 12% profit
A+B = 100 pounds
(.07A + .12B)/(A+B) = .10
.07A + .12B = .1A + .1B
.02B = .03A
2B = 3A
2/3 = A/B
So, for every 6 pounds of A, we have 4 pounds of B.
With 100 pounds total, we have 40 pounds of A and 60 pounds of B.
Option B
Answer: B
Question: Express 22 mps in kmph?
Options:
A)79.2 kmph
B)89.2 kmph
C)79.6 kmph
D)99.2 kmph
E)69.2 kmph
Rationale: 22 * 18/5 = 79.2 kmph
ANSWER:A
Answer: A
Question: A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum V of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?
Options:
A) 5
B) 7
C) 9
D) 10
E) 14
Rationale: Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum V of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.D
Answer: D
Question: What percent of 9.6 kg is 28 gms ?
Options:
A)25
B)66
C)288
D)29
E)17
Rationale: Explanation:
Required percentage = (28/9600 * 100)% = 29/100% = 0.29%
Answer: D) .29%
Answer: D
Question: the cost of manufacturing a popular model car is made up of three items:cost of raw material,labour and overheads- in a year the cost of three items were in the ration of 4:3:2.next year the cost of the raw material rose by 10% ,labour cost increased by 8% but overhead reduced by 5%.then %increase int the price of the car ?
Options:
A)7.67%
B)6%
C)0.54%
D)9.54%
E)8.54%
Rationale: before increase total cost = 4+3+2=9,
after increasing the cost = 9.54
so increase of .54 over 9 , equal to 6%
ANSWER:B
Answer: B
Question: Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
Options:
A)350
B)370
C)390
D)430
E)None
Rationale: Explanation:
Assumed mean = Rs. 350
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 350 + Rs. 40 = Rs. 390
Correct Option: C
Answer: C
Question: If a rectangular billboard has an area of 130 square feet and a perimeter of 46 feet, what is the length of each of the longer sides?
Options:
A)4
B)7
C)8
D)13
E)26
Rationale: This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 130 and a perimeter of 46. We're asked for the length of one of the LONGER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 130, the shorter side will almost certainly be closer to 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 130,
IF...
The shorter side = 10...
The area = 130/10 = 13 = the longer side
Perimeter = 10+10+13+13 = 46
D
Answer: D
Question: A standard Veggiematik machine can chop 35 carrots in 5 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes?
Options:
A)63
B)87
C)90
D)98
E)112
Rationale: Direct Relationship:-
1 standard Veggiematik machine - 35 Carrots - 5 minutes,
1 standard Veggiematik machine - 7 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 7X3X3 =63 Carrots
Answer A
Answer: A
Question: The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $12.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
Options:
A)14
B)15
C)16
D)28
E)29
Rationale: Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: A
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)296 m
B)267 m
C)297 m
D)150 m
E)255 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer:D
Answer: D
Question: In how many ways can 4 men & 3 women can be made from a gang of 7 men & 8 women ?
Options:
A)91
B)94
C)89
D)10
E)19
Rationale: Explanation:
7C4 * 8C3 = 91
A
Answer: A
Question: Patrick has three daughters named Avery, Bridget, & Catherine. He decides he wants to make a 3-letter password using the a combination of the each of their first initials (e.g. ABC, CBA, etc.). How many different permutations can he come up with?
Options:
A)3
B)5
C)6
D)8
E)11
Rationale: Permutation calc is: n P r = n! / (n-r)! 3 P 3 = 3!/(3-3)! = 3x2x1/0!=6/1=6 Correct answer is C (6) ANSWER:C
Answer: C
Question: At exactly what time past 8:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
Options:
A)20 13/21 minutes past 8:00
B)20 13/17 minutes past 7:00
C)21 3/23 minutes past 7:00
D)21 9/11 minutes past 7:00
E)22 4/9 minutes past 7:00
Rationale: A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (8*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer A
Answer: A
Question: What is the 26th digit to the right of the decimal point in the decimal form of 6/11?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: 6/11 = 0.54545454...
The even numbered positions in the decimal expansion are all 4.
The answer is B.
Answer: B
Question: The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget?
Options:
A)1:2
B)2:3
C)3:4
D)4:5
E)5:6
Rationale: 5B = 7C and so B = 7C/5
7A = 3B and so A = 3B/7 = 3C/5
A+B = 3C/5 + 7C/5 = 10C/5
B+C = 7C/5 + C = 12C/5
The ratio of A+B:B+C = 10:12 = 5:6
The answer is E.
Answer: E
Question: If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x?
Options:
A)308
B)154
C)70
D)44
E)21
Rationale: If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that.
LCM of 2,7,11= 154
Hence x must be divisible by 154
Hence B
Answer: B