divelab/Sys2Bench huggingface dataset:
Question: Club X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The number of members is 4j+3 = 5k+3.
Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.
31, 35, 39, 43 = 5(8) + 3
The club has 43 members.
43/6 = 6(7) + 1
The answer is A.
Answer: A
Question: An old priest fell on a bottom of the well of a church.
The well is 19 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
Options:
A)15-days
B)14-days
C)11-days
D)19-days
E)10-days
Rationale: A
15-days
In 14-days, he will climb 14-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: A
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
Options:
A)4:3
B)3:4
C)2:4
D)4:2
E)2:5
Rationale: Req ratio = root(16):root of(9)=4:3
ANSWER A
Answer: A
Question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). The temperature required to boil liquid A and liquid B differed by 35 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
Options:
A)a) 17
B)b) 13
C)c) 25
D)d) 45
E)e) 81
Rationale: 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 A which is the only number near half of 35. The other answer choices are too far apart so no need to calculate.
Answer: A
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options:
A)3 hours
B)6 hours
C)4 hours
D)8 hours
E)10 hours
Rationale: Number of pages typed by Ronald in one hour = 32/6 = 16/3
Number of pages typed by Elan in one hour = 40/5 = 8
Number of pages typed by both in one hour = ((16/3) + 8) = 40/3
Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.
ANSWER:D
Answer: D
Question: A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
Options:
A)90
B)2,700
C)4,500
D)2,550
E)324,000
Rationale: Together the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies.
Answer: D.
Answer: D
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
Options:
A)1
B)2
C)3
D)5
E)6
Rationale: C) 3
Answer: C
Question: How much 60% of 50 is greater than 40% of 30?
Options:
A)18
B)99
C)66
D)55
E)71
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Answer: A
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible?
Options:
A)3
B)Z=4
C)Z=5
D)Z=6
E)Z=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E
Answer: E
Question: A 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
Options:
A)20
B)12
C)13
D)14
E)16
Rationale: Amount of salt = 8.0
Assume x gallons of water are added.
8.0 / 80 + x = 8/100
800 = 8x + 640
8x = 160
x = 20
Correct Option: A
Answer: A
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
Options:
A)5418
B)5498
C)5460
D)5179
E)5418
Rationale: 5000 * 104/100 * 105/100
=> 5460
Answer:C
Answer: C
Question: The sum of four consecutive even numbers is 84. What would be the largest number?
Options:
A)33
B)88
C)24
D)123
E)12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 84 => x = 11
Smallest number is: 2(x +1) = 24.
Answer: C
Answer: C
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Options:
A)5:9
B)5:5
C)5:3
D)5:2
E)5:1
Rationale: Let 40% of A = 2/3 B. Then,
40A/100 = 2B/3 => 2A/5 = 2B/3
A/B = (2/3 * 5/2) = 5/3
A:B = 5:3.
Answer:C
Answer: C
Question: Out of seven numbers, average of first six number is 40 and average of last six number is 35. the first number is 55. What is the difference between first and last number?
Options:
A)30
B)37
C)41
D)59
E)None
Rationale: Let the seven numbers be represented by
{a,b,c,d,e,f,g}
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(a + sum(b-f))/6 = 40
(a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
sum(b-f) = 240 - a
sum(b-f) = 240 - 55
sum(b-f) = 185
Now for the average of the last six numbers we have
(sum(b-f) + g)/6 = 35
(sum(b-f) + g) = 210
185 + g = 210
g = 210 - 185
g = 25
The first number is 55 and the last number is 25 so, their difference is 30.
Answer A
Answer: A
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 4 to 5. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
Options:
A)168
B)210
C)280
D)420
E)240
Rationale: A:B:C:D=2x:3x:4x:5x, for some positive number x. Total time 2x+3x+4x+5x=14x.
If 2x = 60 then 14x = 420;
If 3x = 60 then 14x = 280;
If 4x = 60 then 14x = 210;
If 5x = 60 then 14x = 168;
Only answer choices which is not obtained is 240.
Answer: E.
Answer: E
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations W could be chosen from this menu?
Options:
A)10
B)20
C)40
D)80
E)100
Rationale: W=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: C
Question: When we multiply a certain two digit number by the
sum of its digits 405 is achieved. If we multiply the
number written in reverse order of the same digits
by the sum of the digits,we get 486.Find the number?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: Let the number be x y.
When we multiply the number by the sum of its digit
405 is achieved.
(10x+y)(x+y)=405....................1
If we multiply the number written in reverse order by its
sum of digits we get 486.
(10y+x)(x+y)=486......................2
dividing 1 and 2
(10x+y)(x+y)/(10y+x)(x+y) = 405/486.
10x+y / 10y+x = 5/6.
60x+6y = 50y+5x
55x=44y
5x = 4y.
From the above condition we conclude that the above
condition is satisfied by the second option i e b. 45.
ANSWER : B 45
Answer: B
Question: Find the value of (85 + 32/113) × 113
Options:
A)9263
B)9244
C)9636
D)9623
E)9637
Rationale: =(85 + 32/113) × 113
=(9605 + 32)/113× 113
=9637/113× 113
=9637
Answer is E.
Answer: E
Question: For an agricultural experiment, 500 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
Options:
A)35.7%
B)25%
C)32%
D)30.8%
E)60%
Rationale: From the first plot 0.30*500=150;
From the second plot 0.50*200=100;
Total percent = (150+100)/(500+200) = 0.357.
Answer: A.
Answer: A
Question: There are 2 sections A and B in a class, consisting of 40 and 30 students respectively. If the average weight of section A is 50kg and that of section B is 60kg, Find the average of the whole class?
Options:
A)50.78kg
B)49.32kg
C)61.67kg
D)69.15kg
E)54.28kg
Rationale: Total weight of 40+30 students = 40*50 + 30*60 = 2000+1800
Average weight of the class is = 3800/70 = 54.28 kg
Answer is E
Answer: E
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/7.
If a jar cannot contain more than 500 balls, how many yellow balls are in the Jar?
Options:
A)125.
B)124.
C)133.
D)140.
E)149.
Rationale: We need to get some number which is less than 500 and exactly divisible by 8,5 and 7
Lets take LCM of three balls 8,5 and 7 = 280.
The probability of drawing a blue ball is 1/8...For every 8 balls we get 1 BLUE ball then out of 280 balls we get 35 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 280 balls we get 56 REB balls.
The probability of drawing a green ball is 1/7. For every 7 balls we get 1 GREEN ball then out of 280 balls we get 40 GREEN BALLS.
Then out of 280 - ( 35 + 56 + 40 ) = 149 YELLOW balls.
IMO option E is correct.
Answer: E
Question: If x - 5 > 2 and x + 3 < 7, the value of x must be between which of the following pairs of numbers?
Options:
A) -3 and 10
B) -3 and 4
C) 2 and 7
D) 3 and 4
E) 3 and 10
Rationale: Let’s isolate x in each inequality.
x - 5 > 2
x > 3
Next we simplify x +3 < 7.
x +3 < 7
x < 4
We know that x is greater than 3 and less than 4.
The answer is D.
Answer: D
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 88 kg and 93 kg join the group. Find the initial number of members in the group?
Options:
A)23
B)24
C)25
D)26
E)27
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 88 + 93 = 51(n + 2) => 51n - 48n = 79 => n = 26
Therefore there were 26 members in the group initially.
ANSWER:D
Answer: D
Question: If 20 toys cost Rs, 234, what do 35 toys cost?
Options:
A)409.5
B)564.5
C)546.5
D)654.5
E)None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
. = x=(35 X 234)/20=409.50
Answer is A
Answer: A
Question: Nicole cycles at a constant rate of 15 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 30 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
Options:
A)x/3
B)x/2
C)x
D)3x/2
E)2x
Rationale: In x minutes, Jessica travels (x/60)*30 = x/2 miles
The time it takes Nicole to travel x/2 miles is (x/2) / 15 = x/30 hours = 2x minutes
Jessica needs to wait 2x - x = x minutes.
The answer is C.
Answer: C
Question: A bakery currently has 7 pies and 4 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
Options:
A)3/11
B)5/11
C)14/33
D)29/77
E)36/77
Rationale: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 7C3*4C2 = 35*6 = 210
P(exactly 3 pies) = 210/462 = 5/11
The answer is B.
Answer: B
Question: In the rectangular coordinate system, if the line x = 6y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
Options:
A)1/2
B)1/3
C)1/4
D)1/5
E)1/6
Rationale: x = 6y+5, and thus y = x/6 - 5/6
The slope is 1/6.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/6 and thus p = 1/3
The answer is B.
Answer: B
Question: I remember during the school days , the teacher asked the class "can you tell me the sum of the first 50 odd numbers ?".
I ran quickly to the teacher and told her "the answer is 2500". The teacher replied "lucky guess".
She then asked me "can you tell me the sum of first 70 odd numbers ?".
I wait for approx 10 seconds and replied with the correct answer.
How can i answer so quickly and whats the correct answer ?
Options:
A)8715
B)0152
C)3581
D)4900
E)9126
Rationale: D
5625
n^1
70 * 70 = 4900(sum of first 70 odd numbers).
50 * 50 = 2500 (sum of first 50 odd numbers).
Answer: D
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked three times as much as much chestnuts than Peter. Lucy picked 5 kg more than Peter. Together the three of them picked 30 kg of chestnuts. How many kilograms of chestnuts did Mary, Peter, and Lucy pick respectively?
Options:
A)10, 15, and 5
B)15, 10, and 5
C)15, 5, and 10
D)10, 5, and 15
E)5, 10, and 15
Rationale: M = 3P
L = P+5
M + P + L = 30
3P + P + (P+5) = 30
P = 5, M = 15, L = 10
Therefore, Mary, Peter, and Lucy picked 15, 5, and 10 kg, respectively.
The answer is C.
Answer: C
Question: If there are 20 apples and the apples have to be shared equally among 3 babies. What number of apples are to be added?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Given there are 20 apples.If 1 extra apple is added, then it becomes 21 which can be divided equally that is 7 apples to each baby.
Option A is correct.
Answer: A
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least three ingredients? (Also assume that each bin can hold one and only one blend.)
Options:
A) 1
B) 4
C) 7
D) 11
E) 10
Rationale: We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 3 ingredients...
3 ingredient blends:
ABC
ABD
ACD
BCD
Total blends = 4
B
Answer: B
Question: A family consists of grandparents, parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Options:
A)31 5/8 years
B)31 5/7 years
C)31 9/7 years
D)38 5/7 years
E)31 5/4 years
Rationale: Required Average = [(67 * 2) + (35 * 2 ) + (6 * 3)]/(2 + 2 + 3)
= (134 + 70 + 18)/7
= 31 5/7 years.
Answer:B
Answer: B
Question: H.C.F of 3240, 3600 and a third number is 36 and their L.C.M is 24 * 35 * 52 * 72. The third number is?
Options:
A)22 * 35 * 72
B)22 * 35 * 78
C)22 * 35 * 72
D)22 * 35 * 71
E)22 * 35 * 73
Rationale: 3240 = 23 * 34 * 5; 3600 = 24 * 32 * 52
H.C.F = 36 = 22 * 32
Since H.C.F is the product of lowest powers of common factors, so the third number must have (22 * 32 ) as its factor.
Since L.C.M is the product of highest powers of common prime factors, so the third number must have 35 and 72 as its factors.
Third number = 22 * 35 * 72
Answer:A
Answer: A
Question: For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
Options:
A)−5
B)−2
C)2
D)4
E)7
Rationale: if a#b is positive then there are 2 cases
either ab &(3-b) both are negatives or both positives
let both are positives then for (3-b) to be positive b has to less than 3 (3-b>0--->3>b)
from options b can be -5,-2,or 2
but if we take negative value of b then ab will negative & hence a#b which is not possible.
also if we do both negative then (3-b) to be negative b has to be greater than 3 which from options are only 4&7
if we take any value then the term ab will positive leaving a#b negative.which is not possible
Hence b=2
ANSWER:C
Answer: C
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Options:
A)150
B)887
C)167
D)197
E)161
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: A
Question: Select a card from pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?
Options:
A)1/111
B)2/121
C)1/221
D)2/213
E)3/412
Rationale: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.
∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221
C
Answer: C
Question: Twelve coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
Options:
A)2^9
B)2^11
C)3 * 2^8
D)3 * 2^9
E)3 * 2^10
Rationale: Fix the third coin as H. The remaining 11 coins have 2^11 outcomes.
B
Answer: B
Question: The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
Options:
A)4/19
B)1/9
C)2/3
D)1 1/9
E)2 1/9
Rationale: Total bought = 4/19+2/13
left part 4/26--->2/13
so used part 4/19+2/13-2/13=4/19
ANSWER:A
Answer: A
Question: In how many different number of ways 2 boys and 2 girls can sit on a bench?
Options:
A)720
B)730
C)740
D)750
E)24
Rationale: npn = n!
4p4 =4 × 3 × 2 × 1 = 24
E
Answer: E
Question: A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 ays, can do the work alone in
Options:
A)10 days
B)11 days
C)15 days
D)12 days
E)18 days
Rationale: work as x,x/2,x/3
==(1/x+2/x+3/x)
=1/2==>6/x=1/2
==>12
ANSWER D
Answer: D
Question: Two mixtures of A and B have A and B in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of A to B is 5:4?
Options:
A)6:1
B)5:4
C)20:7
D)10:9
E)14:11
Rationale: I got C but with a different, yet slightly longer approach, which I constantly use for proportion problems such as this one. Usually, this approach is very efficient when used with slightly difficult questions, but this problem is quite hard so I had to slightly tweak it. I will show you how I usually use the approach and later show you how to use it with this specific problem.
Example.
1 Liter of Solution A contains 45% alcohol, while 1 Liter of Solution B contains 20% alcohol. In what ratio must the two solutions be used to get a solution with 30% alcohol
Solution:
1.	45/100*[A/(A+B)]+20/100*[B/(A+B)] = 30/100
2.	Multiply 100 to both sides to arrive at 45A/(A+B) + 20B/(A+B) = 30
3.	Multiply (A+B) to both sides to arrive at 45A + 20B = 30A + 30B
4.	Distribute to arrive at 15A = 10B
5.	Thus the ratio is A/B = 10/15 = 2/3
Now using this same approach, we tackle Gopu106’s question. It is important to first think of X in the mixture as the alcohol in the problem above; hence, a mixture of X and Y in the ratio of 3:2 translates to X is 3/5 of the solution. Applying this concept to all three equations, we write:
1.	3/5*[A/(A+B)]+3/7*[B/(A+B)] = 5/9
2.	Now here is the tweak that must be made to continue with this approach. You must find the common denominator for all three numbers and organize the fractions accordingly. By finding the common denominator of 5,7,9 (or 315) we re-write the equations as follows
3.	189/315*[A/(A+B)]+135/315*[B/(A+B)] = 175/315
4.	Multiply 315 to both sides to arrive at 189A/(A+B) + 135B/(A+B) = 175
5.	Multiply (A+B) to both sides to arrive at 189A + 135B = 175A + 175B
6.	Distribute to arrive at 14A = 40B
7.	Thus the ratio is A/B = 40/14 = 20/7 or answer C
Answer: C
Question: Cream costs twice as much as skim milk. A certain brand of milk is 2/5 cream and 3/5 skim milk. What fraction of the cost of this brand is due to the cream?
Options:
A)2/7
B)3/7
C)4/7
D)3/5
E)2/5
Rationale: Let x be the cost of the skim milk in the mixture.
The cost of the cream is (2/3)*x*2 = 4x/3.
The total cost is x+4x/3 = 7x/3 and the fraction due to the cream is (4x/3) / (7x/3) = 4/7
The answer is C.
Answer: C
Question: An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1000 sculptures are not on display, how many pieces of art does the gallery have?
Options:
A)360
B)2250
C)540
D)640
E)720
Rationale: Too many words and redundant info there.
(i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.
(ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.
(iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.
1000 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1000 --> {not on display} = 1500.
According to (i) 2/3*{total} = 1500 --> {total} = 2250.
Answer: B.
Answer: B
Question: A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
Options:
A)10
B)11
C)23
D)43
E)66
Rationale: A
10
4 a 3 |
9 8 4 } ==> a + 8 = b ==> b - a = 8
13 b 7 |
Also, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b)
(9 - b) = 0
b = 9
(b = 9 and a = 1) (a + b) = 10.
Answer: A
Question: Riya covers journey from kavali to nellore by car at average speed of 50 Km/hr. She returns back by scooty with an average speed of 50 Km/hr. Find her average speed during the whole journey?
Options:
A)30Km/hr
B)50Km/hr
C)80Km/hr
D)90Km/hr
E)100km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*50*50/100
= 50 Km/hr
Answer: Option B
Answer: B
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 22.5 years. What is the age of the new member ?
Options:
A)20 years
B)21 years
C)22 years
D)25 years
E)24 years
Rationale: The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 22.5 years.
Let the age of the new member be x.
Then (110+x)/6 = 22.5
=> x = 25 years
Answer D
Answer: D
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 117 grams of water?
Options:
A) 16
B) 104
C) 112
D) 128
E) 142
Rationale: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.
Therefore there are 117*8/9=104 grams of oxygen in 117 grams of water.
Answer: B.
Answer: B
Question: Chunilal invests 65% in machinery 20% in raw material ands till has 1,305 cash with him. Find his total investment.
Options:
A)6,500
B)7,225
C)8,500
D)7,395
E)None of these
Rationale: Let he had originally x.
Then 65% of x + 20 % of x + 1305 = x
0.65x + 0.2x + 1305 = x
⇒ 0.15 x = 1305 ⇒ x = 8700
∴ His total investment = 65% of 8700 + 20% of 8700
= 85% of 700 = 7395
Answer D
Answer: D
Question: The largest 4 digit number exactly divisible by 44 is?
Options:
A)9988
B)9939
C)9944
D)9954
E)9960
Rationale: Largest 4-digit number = 9999
44) 9999 (227
9988
Largest number : 9988
Answer : A
Answer: A
Question: What is the remainder when the number 14^2 * 15^8 is divided by 5?
Options:
A)0
B)1
C)2
D)4
E)5
Rationale: 14^2 has units digit 6
15^8 has units digit 5
Thus 14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
Answer: A