divelab/Sys2Bench huggingface dataset:
Question: Tough and Tricky questions: Combinations.
The product of the digits of the four-digit number h is 60. No two digits of h are identical. How many different numbers are possible values of h?
Options:
A)20
B)22
C)24
D)30
E)36
Rationale: Answer = C = 24
Let number =abcd
Given that a*b*c*d = 60
a,b,c,d can be 1,2,3,10
Number of ways = 4*3*2 = 24
Answer: C
Question: Average age of total 80 students from three classes, V, VI and VII, is 13 years. Average age of 30 students of class V is 11 1/2 years. If average age of another 30 students of class VI is 12 1/2 years, what is the average aage of rest of 20 students of class VIII ?
Options:
A)13 1/2 years
B)14 1/2 years
C)15 years
D)16 years
E)5 years
Rationale: Explanation :
Sum of ages of 80 students = 80 x 13 = 1040
Sum of ages of 30 students of class V = 30 x 11.5 = 345
Sum of ages of 30 students of class VI = 30 x 12.5 = 375
∴ Total age of 20 students of class VII = 1040 - 345 - 375 = 320
∴ Average age = 320/20 = 16 years.
Answer : Option D
Answer: D
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 19 seconds. What is the length of the platform in meters?
Options:
A)220 meters
B)360 meters
C)420 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 19 * 20 = 380 = Length of train
Length of platform = 600 - 380 = 220
Answer: A
Answer: A
Question: If W is the set of all the integers between 35 and 64, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
Options:
A)18
B)19
C)61
D)31
E)11
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 63, the smallest is 36): 63 - 36 = 27
Step 2. Divide by 3: 27 / 3 = 9
Step 3. Add 1: 9 + 1 = 10.
So there are 10 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 64, the smallest is 36): 64 - 36 = 28
Step 2. Divide by 2: 28 / 2 = 14
Step 3. Add 1: 14 + 1 = 15.
So there are 15 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 10 multiples of 3 and the 15 multiples of 2: 10+15=25.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 10+15=25. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 25:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 60 - 30 = 30
Step 2. Divide by 6: 30 / 6 = 5
Step 3. Add 1: 5 + 1 = 6.
So there are 6 multiples of 6 within the range: we counted 6 numbers twice.
Subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3:
= 10+15 - 6
= 25 - 6
= 19
Therefore, the final number of multiples of 2, 3 or 6 is 19.
Hence, this is the correct answer. (B)
Answer: B
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 16-meter platform and caught it after it had traveled 40 meters. How many times did the ball bounce?
Options:
A)2
B)6
C)7
D)8
E)9
Rationale: Division of total distance travelled will be 16+16+8
Ans:2
Answer: A
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is?
Options:
A)3 hr
B)2 hr
C)1 hr
D)4 hr
E)5 hr
Rationale: 600/x - 600/(x + 1/2) = 200
x(2x + 1) = 3 2x2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr.
ANSWER C
Answer: C
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
Options:
A)14
B)16
C)21
D)25
E)27
Rationale: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Answer: C
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 32 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
Options:
A)5
B)4
C)8
D)12
E)32
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 32 + 40 + 10 - (12) - 2x
x = 5
So, answer will be A
Answer: A
Question: Ratio of two numbers x and y is 1:2. If x is increased by 20% and y is increased by 4 then the new ratio becomes 1:5. What is the ratio 2y:x
Options:
A)1:3
B)3:1
C)2:3
D)4:1
E)1:4
Rationale: Let:
x = 1n
y = 2n
1.2n/(2n+4) = 1/5
6n = 2n+4
n = 1
So, x =1; y=2
2y/x = 4/1 = 4:1
Answer = D
Answer: D
Question: Marco rode his dirt bike at 30 miles per hour (mph) for two hours. If he then continued to ride at a different constant rate for another three hours, and at the end of the three hours his average speed for the entire five hour ride was 30mph, what was his average speed over the three hour portion of his ride?
Options:
A)14 mph
B)20 mph
C)70/3 mph
D)80/3 mph
E)30 mph
Rationale: Average speed for first two hours, S1 = 30 mph
Distance travelled in these two hours, D1 = 60 miles
Average speed for the entire 5 hour ride, S = 30 mph
Total Distance traveller in the entire 5 hour ride, D = 30 x 5 = 150 miles.
Hence, distance traveller in the latter 3 hour period, D2 = D - D1 = 150 - 60 = 90
Average speed for the latter 3 hour period S2 = D2/3 = 90/3=30
Hence, the correct answer is E
Answer: E
Question: In a diving competition, each diver has a 30% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)
Options:
A)1/5
B)1/15
C)4/25
D)16/125
E)71/483
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.3 = 30/100 = 2/7
i.e. Probability of Non-Perfect dive = 0.7 = 70/100 = 2/3
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect
Method-1:
i.e. Probability of First two being Imperfect and Third being Perfect dive = (2/3)*(2/3)*(2/7) = 71/483
E
Answer: E
Question: In a certain appliance store, each model of television is uniquely designated by a code made up of a particular ordered pair of letters. If the store has 60 different models of televisions, what is the minimum number of letters that must be used to make the codes?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: If n is the number of distinct letters used to create the two lettered codes, then a total of n∗n=n^2 different codes can be created. We need n2≥60. The smallest n which fulfills this condition is n = 8.
Answer C
Answer: C
Question: A warning notice is to be prepared for a building demolition in which the 'warning' is written in 8 differnent languages, including english, french and german. The authority requires you to put french after english and german after french. In how many different order of languages can you prepare the notice?
Options:
A)4!
B)5!
C)6!
D)7!
E)8!
Rationale: The problem requires you to find the total number of arrangements in which 8 object can be arranged paying attention to the given constraints. The constrain is that English, French and German mus follow the order E>F>G. Since there is only one way to arrange E,F and G, we can consider EFG as one object. Therefore 6 object is to be arranged and we can do this in 6! Ways. So the correct option is C. 6!.
Answer: C
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many E hours does it currently take Anne to clean the house on her own?
Options:
A)6
B)7
C)8
D)12
E)14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in E=3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: D
Question: How many cubes of 10 Cm edge can be put in a cubic box of 1 m edge?
Options:
A)4000
B)2000
C)3000
D)5000
E)1000
Rationale: (110×100×100)/10×10×10 = 1000
Answer is E.
Answer: E
Question: If 45-[28-{37-(15-*)}]= 56, then * is equal to:
Options:
A)-29
B)-19
C)17
D)29
E)39
Rationale: 45-[28-{37-(15-*)}]= 56 => 45-[28-{37-15+*}]=56
45-[28-37+15-*]=56 => 45[43-37-*]=56
45-[6-*]=56 => 45-6+*=56
39+*=56 => *=56-39
= 17
ANSWER:C
Answer: C
Question: If a trader bought 9 balls per rupee and sells at the rate of 8 balls per rupee, what is the percentage profit or loss?
Options:
A)12.5 %
B)11.5 %
C)23.5 %
D)23.5 %x
E)14.5 %
Rationale: Let he total number of oranges bought by the shopkeeper be 12.
If he buys 9 a rupee, his CP = 8
He selling at 8 a rupee, his SP = 9
Profit = SP - CP = 9 - 8 = 1
Profit Percent = 1/8 * 100 = 12.5 %
Answer: A
Answer: A
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 15 days respectively. They worked together for five days and then C completed the remaining work all alone. If $900 was the net sum to be paid for the entire work, what was the average daily wage of B?
Options:
A)$144
B)$90
C)$60
D)$54
E)$48
Rationale: The correct answer is C.
Answer: C
Question: In how many ways can the letters of the word ABEIX be arranged in a row so that the vowels appear in alphabetic order?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: three letters can be arranged in 3! ways.
only one combination AEI is required.
5 letters can be arranged in 5! ways.
thus 5!/ 3! * 1 = 20.
A
Answer: A
Question: A circle has 29 points arranged in a clock wise manner from o to 28. A bug moves clockwise manner from 0 to 28. A bug moves clockwise on the circle according to following rule. If it is at a point i on the circle, it moves clockwise in 1 sec by (1 + r) places, where r is the remainder (possibly 0) when i is divided by 11. If it starts in 23rd position, at what position will it be after 2012 sec.
Options:
A)10th
B)15th
C)20th
D)25th
E)28th
Rationale: After 1st second, it moves 1 + (23/11)r = 1 + 1 = 2, So 25th position
After 2nd second, it moves 1 + 25/11 = 1 + 3 = 4, So 29th position = 0
After 3rd second, it moves 1 + 0/11 = 1 + 0 = 1, So 1st position
After 4th second, it moves 1 + 1 = 3rd position
after 5th, 1 + 3/11 = 4 So 7th
After 6th, 1 + 7/11 = 8 so 15th
After 7th, 1 + 15/11 = 5 so 20th
After 8th, 1 + 20/11 = 10th, So 30th = 1st
So it is on 1st after every 3 + 5n seconds. So it is on 1st position after 2008 seconds (3 + 5 x 401) So on 20th after 2012 position.
ANSWER:C
Answer: C
Question: For how many unique pairs of nonnegative integers {a, b} is the equation a^2 - b^2 = 235 true?
Options:
A)1
B)2
C)5
D)7
E)9
Rationale: Answer B
(a+b)(a-b)=235
2cases For (a+b), (a-b)
235, 1
47, 5
Answer B
Answer: B
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)22
B)27
C)40
D)26
E)11
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%.Answer:C
Answer: C
Question: Three pipes of same capacity can fill a tank in 12 hours. If there are only two pipes of same capacity, the tank can be filled in?
Options:
A)18
B)8
C)12
D)6
E)4
Rationale: The part of the tank filled by three pipes in one hour
= 1/12
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/12 = 1/18.
The tank can be filled in 18 hours.
Answer:A
Answer: A
Question: A certain jeans in a shop was marked down 30% the first week and another 20% the next week. What percent of the regular price was the final cost of the jeans after the two markdowns?
Options:
A)30%
B)36%
C)40%
D)56%
E)60%
Rationale: If the price of the jeans is 100, and it is marked down by 30% and 20% respectively or charged 70% of the price first and 80% of the price of reduced price, the final price is :-
100*70*80/10000= 56
56% is the final price of old price.
D is the answer
Answer: D
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 20, 60, and what number?
Options:
A)25
B)30
C)35
D)40
E)45
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -80 = 25
A
Answer: A
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options:
A)12 days
B)15 days
C)16 days
D)18 days
E)22 days
Rationale: A's 2 day's work = (1/20 × 2) = 1/10	.
(A + B + C)'s 1 day's work = (1/20 + 1/30 + 1/60) = 1/10.
Work done in 3 days = (1/10 + 1/10) = 1/5.
Now,	1/5	work is done in 3 days.
Therefore, Whole work will be done in (3 x 5) = 15 days.
CORRECT ANSWER: "B".
Answer: B
Question: The number of sequences in which 8 players can throw a ball, so that the youngest player may not be the last is ?
Options:
A)43280
B)43280
C)35280
D)32786
E)36124
Rationale: x Not younger
The last ball can be thrown by any of the remaining 8 players. The first 6 players can throw the ball in 7P7 ways.
The required number of ways = 7(7!)
= 35280
Answer:C
Answer: C
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 10 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
Options:
A)$198
B)$216
C)$220
D)$230
E)$240
Rationale: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 10
Employee paid = .9 * 240 = 216 $
Answer B
Answer: B
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, the how old is B?
Options:
A)7
B)9
C)8
D)14
E)10
Rationale: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 37
⇒ 5x = 35
⇒ x = 7.
Hence, B's age = 2x = 14 years.
Answer: D
Answer: D
Question: The mean of 40 observations was 100. It was found later that an observation 50 was wrongly taken as 75 The corrected new mean is
Options:
A)125.8
B)102.8
C)99.375
D)100.52
E)122
Rationale: Explanation:
Correct Sum = (100 * 40 + 50 - 75) = 3975.
Correct mean = = 3975/40 = 99.375
Answer: C
Answer: C
Question: A and B started a partnership business. A's investment was thrice the investment of B and the period of his investment was two times the period of investments of B. If B received Rs 4000 as profit, what is their total profit?
Options:
A)27000
B)25000
C)29000
D)28000
E)26000
Rationale: Suppose B's investment =x.
Then A's investment =3x
Suppose B's period of investment =y
then A's period of investment =2y
A : B =3x×2y:xy=6:1
Total profit ×1/7=4000
=> Total profit =4000×7
=28000
Answer is D.
Answer: D
Question: The area of a rectangular plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot?
Options:
A)18m
B)19m
C)17m
D)16m
E)20m
Rationale: length =115% of breadth.
length×breadth =460 m2
⇒ 115% of breadth×breadth =460 m2
⇒ 115100× breadth×breadth =460 m2
⇒ breadth×breadth =400 m2
⇒ breadth =20 m
Answer is E.
Answer: E
Question: Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x- and y-coordinates of P, Q and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16. How many different triangles with these properties could be constructed?
Options:
A)110
B)1100
C)9900
D)10000
E)12100
Rationale: We know that P,Q, R can only lie on a grid 10x11
Let's start by fixing P' x-coordinate: we have 10 possible places for it
Then we choose x-coordinate for R: since PR || x-axis, R's x-coordinate can not coincide with P's x-coord, so we have only 9 possible choices left.
Then, we fix P's (and R's too) y-coordinate: 11 possible choices.
Finally, after we fixed P and R, Q's x-coordinate must be the same as P's (because P is the right angle and PR || x-axis), so the only choice is for y-coordinate, and we have 10 possible choices left.
So, total number of different triangles: 10*9*11*10=9,900
ANSWER:C
Answer: C
Question: A person's present age is two-fifth of the age of his father. After 8years, he will be one - half of the age of his father. How old is the father at present ?
Options:
A)A)40
B)B)48
C)C)32
D)D)45
E)E)28
Rationale: Let the father's present age be x years
Then the person's present age = 2x/5
(2x/5)+8 = 1/2(x+8)
2(2x+40) = 5 (x+8)
x = 40
Answer is A
Answer: A
Question: Each of eight different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
Options:
A)1/8
B)1/6
C)1/64
D)3/8
E)1/2
Rationale: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 8 is 1/8.
Probability of choosing another right key is 1/8.
since the question is asking for 2 right keys , probability is multiplication of both = 1/8 * 1/8 = 1/64.
Ans C
Answer: C
Question: A person purchased a TV set for Rs. 17000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
Options:
A)16.97%
B)87.97%
C)33.97%
D)17.97%
E)18.97%
Rationale: The total CP = Rs. 17000 + Rs. 6250 = Rs. 23250 and SP
= Rs. 31150
Profit(%) = (31150 - 23250)/23250 * 100
= 33.97%
Answer:C
Answer: C
Question: If each edge of a cube is doubled, then its volume :
Options:
A)Becomes 8 times
B)Becomes 9 times
C)is double
D)Becomes 6 times
E)None
Rationale: Sol.
Let original edge = a. Then, volume = a³
New edge = 2a. So, new volume = (2a)³ = 8a³
∴ Volume becomes 8 times
Answer A
Answer: A
Question: The current birth rate per thousand is 42, where as corresponding death rate is 22 per thousand. The net growth rate in terms of population increase in percent is given by?
Options:
A)2.0%
B)3.2%
C)3.9%
D)4%
E)5.1%
Rationale: Net growth on 1000 = 42-22 = 20
Net growth on 100 = 20*100/1000 = 2.0%
Answer is A
Answer: A
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
Options:
A)40 ml
B)60 ml
C)70 ml
D)80 ml
E)90 ml
Rationale: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Answer: C
Question: Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?
Options:
A)11
B)14.25
C)18.5
D)20
E)Cannot be determined
Rationale: Let the amounts deposited on both accounts be $100.
Then we'd have that 100+100∗0.22+100∗0.22=100(1+r)2100+100∗0.22+100∗0.22=100(1+r)2 --> 144=100(1+r)2144=100(1+r)2 --> (1+r)2=1.44(1+r)2=1.44 --> 1+r=1.21+r=1.2 --> r=0.2
Answer is D
Answer: D
Question: A bag contains 8 red and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4/7
B)2/3
C)5/8
D)1/4
E)5/7
Rationale: Total number of balls = 8+4 = 12
number of white balls = 8
Probability = 8/12 = 2/3
Answer is B
Answer: B
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)2298
B)1000
C)2888
D)2771
E)9911
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer:B
Answer: B
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
Options:
A)6
B)7
C)1
D)8
E)9
Rationale: Let xx be the amount Peter picked. Then Mary and Lucy picked 2x2x and x+2x+2, respectively. So
x+2x+x+2=26x+2x+x+2=26
4x=244x=24
x=6x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
Answer:A
Answer: A
Question: How many three digit numbers W are divisible by 78 or 91?
Options:
A)17
B)19
C)20
D)21
E)22
Rationale: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples W--11+9 -1 =19.
Hence Answer is 19.B
Answer: B
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
Options:
A)22
B)24
C)26
D)23
E)21
Rationale: Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer is C.
Answer: C
Question: When divided by 5, x has a remainder of 4 and y has a remainder of 2. Which of the following could be the remainder when x + y is divided by 10?
Options:
A)6
B)7
C)8
D)9
E)0
Rationale: x = 5k+4 and y = 5j+2
x+y = 5(j+k) + 6
When divided by 10, the remainder is either 6 or 1.
The answer is A.
Answer: A
Question: If a = 0.1039, then the value of âˆš4a2 - 4a + 1 + 3a is:
Options:
A)0.1039
B)0.2078
C)1.1039
D)2.1039
E)3.1039
Rationale: Explanation:
âˆš4a2 - 4a + 1 + 3a = âˆš(1)2 + (2a)2 - 2 x 1 x 2a + 3a
=âˆš(1 - 2a)2 + 3a
= (1 - 2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
ANSWER IS C
Answer: C
Question: The difference between two numbers is 1356. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
Options:
A)240
B)270
C)295
D)360
E)340
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270
ANSWER:B
Answer: B