divelab/Sys2Bench huggingface dataset:
Question: If P, x, y, and z are positive integers and (x)×(y)×(z)=P^2, which of the following could be the values of x, y, and z?
Options:
A)3, 16, 25
B)9, 25, 24
C)2, 49, 32
D)2, 9, 16
E)8, 16, 36
Rationale: This is one of those questions where using the given options is fastest way to get the solution. We need to find a set where 3 numbers can be paired into 2 pairs of some numbers because we need a product which is a square number.
C fits the bill. 2*49*32 = 2*7*7*8*4 = 7*7*8*8
Ans C
Answer: C
Question: A train is running between Patna to Howrah.Seven people enter the train somewhere between Patna and Howrah.It is given that nine stops are there between patna and howrah.In how many ways can the tickets be purchased if no restriction is there with respect to the number of tickets at any station?(2 people donot buy the same ticket)
Options:
A)45c7 ways
B)45c6 ways
C)44c7 ways
D)46c7 ways
E)45c8 ways
Rationale: P _ _ _ _ _ _ _ _ _ H
P 1 2 3 4 5 6 7 8 9 H
If those people enter in the 1st station, the no. of ways they can buy tickets: 9 ways
If those people enter in the 2nd station, the no. of ways they can buy tickets: 8 ways
.
.
If those people enter in the 9th station, the no. of ways they can buy tickets: 1 way
Now total no. of ways to buy tickets are: 9+8+7+6+5+4+3+2+1=45
So, the tickets can be purchased by 7 people is 45c7 ways
ANSWER:A
Answer: A
Question: How many positive integers between 5 and 5000(both are inclusive) are there such that they are multiples of 5?
Options:
A)1500
B)1000
C)999
D)1001
E)1005
Rationale: Multiples of 5 = 5,10,15-----,5000
Number of multiples of 5 => 5000-5/5+1= 1000
Answer is B
Answer: B
Question: If x^2 - 9 = 0 and x > 0, which of the following must be equal to 0 ?
Options:
A) x^2 - 9x
B) x^2 - 9x + 20
C) x^2 - 2x + 3
D) x^2 + 2x - 3
E) x^2 - 5x + 6
Rationale: x^2-9 = 0
x= +3 or x = -3
if we substitute x= 3 in the equation x^2 -5x+6 = 9-15+6 = 0
E is also the answer
Answer: E
Question: Fifty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
Options:
A) 60
B) 80
C) 84
D) 120
E) 140
Rationale: 50% of the members have passed the test, thus 50% have not passed the test.
We also know that 30+12=42 members have not passed the test, thus 0.5*Total=42 --> Total=84.
Answer: C.
Answer: C
Question: f n = 3^2 - 2^2, which of the following is NOT a factor of n?
Options:
A)5
B)10
C)4
D)15
E)20
Rationale: 9-4 =5 is prime no. any number not multiply with five is not a factor
C
Answer: C
Question: If 125% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 175% of l is equal to 75% of m, then 20% of m is equal to what percent of 150% of j ?
Options:
A)0.35
B)466
C)35
D)350
E)3500
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
20% of 350, comes out to be 70....
150% of 10 is 15....
(70*100)/15=466.66....
Ans : B
Answer: B
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
Options:
A)32 km
B)25 km
C)28 km
D)24 km
E)None of these
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
ANSWER:E
Answer: E
Question: A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Options:
A)Rs. 8,400 .
B)Rs.10,000
C)Rs. 11,980
D)Rs. 13,600
E)Rs.14,700
Rationale: Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. 35000x (21/50)= Rs. 14,700.
answer :E
Answer: E
Question: Which of the following equations has a root in common with x^2−4x+3=0 ?
Options:
A)x^2-4x-4=0
B)x^2-2x+1=0
C)x^2-x-1=0
D)x^2-10x-1=0
E)x^2+1=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
(x-1)(x-3) = 0
so the two roots are 1 and 3.
Now put 1 and 3 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 1: we get -7; Putting 3 we get -7. Reject this option.
(B) putting 1: we get 0. This is the equation.
We are lucky. No need to check other options.
B is the answer.
Answer: B
Question: 2 cyclist begin training at same time A complete each lap in 4 sec B in 6 minutes how many minutes after start will both cyclist pass at exactly same spot when they begin to cycle
Options:
A)160 seconds
B)260 seconds
C)360 seconds
D)460 seconds
E)560 seconds
Rationale: 6 minutes= 360 sec
lcm of 4, 360 is 360
so they meet after 360 seconds
ANSWER:C
Answer: C
Question: The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?
Options:
A)26
B)17
C)25
D)33
E)50
Rationale: Four consecutive odd numbers: k-2, k, k+2, k+4
Three consecutive even numbers: n-2, n, n+2
k-2+k+k+2+k+4=n-2+n+n+2
4k+4=3n
4(k+1)=3n
k+1=(3/4)n
k=(3/4)n-1
All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range:
We know,
101<n<208
104<=n<=204
Count=(204-104)/4+1=100/4+1=25+1=26
Ans: 26.
Answer: A
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,74,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
Options:
A)0.20833
B)0.14544
C)0.25632
D)0.2139
E)0.63435
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 374000x
\therefore Required percentage = \inline \frac{800x}{374000}\times 100 = 0.21390
D
Answer: D
Question: A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?
Options:
A)20
B)30
C)48
D)60
E)72
Rationale: Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1
Bike speed = s2 = 16
Time traveled in bike = t2
d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)
(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6
Walking distance = s1*t1 = 8*6 = 48
Answer: C
Answer: C
Question: Calculate 24 x 99
Options:
A)2976
B)2467
C)2476
D)4276
E)2376
Rationale: = 24-1 = 23
= (Decrement each digit of the number obtained from 9) Here we got 23. Now
= 9-2 = 7 and 9-3=6. So we have 76
Just write these numbers together.
That is we have 23 and 76.
Hence answer is 2376
Answer is E.
Answer: E
Question: Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 4 more than the average expenditure of all the nine. The total money spent by all of them was
Options:
A)31.5
B)40
C)29.25
D)27
E)None of the above
Rationale: Let the average expenditure of all the ninte be x
Then, 3 × 8 + x + 4 = 9x
⇒ x = 3.5
∴ Total money spent = 9x = 9 × 3.5 = 31.5
Answer A
Answer: A
Question: Last year a certain bond yielded 5 percent of its face value in interest. If that interest was approximately 4 percent of the bonds selling price of $6,500, what is the bonds face value?
Options:
A) $5,200
B) $6,750
C) $7,425
D) $7,500
E) $9,375
Rationale: Interest = 0.05*face value = 0.04*6,500 --> face value = 0.04*6,500/0.05 = 5,200.
Answer: A.
Answer: A
Question: Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?
Options:
A)2000
B)3000
C)4000
D)1000
E)5000
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
Answer:B
Answer: B
Question: A vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder. The next day, the vendor sells 80 percent of the remaining pears and throws away the rest. In total, what percent of his pears does the vendor throw away?
Options:
A)6
B)8
C)10
D)12
E)14
Rationale: Let x be the original number of pears.
On day one, the vendor throws away (0.5)(0.2)x=0.1x.
The remaining pears are (0.5)(0.2)x = 0.1x.
On day two, the vendor throws away (0.2)(0.1)x=0.02x.
The vendor throws away a total of 0.1x + 0.02x = 0.12x.
The vendor throws away 12 percent of the pears.
The answer is D.
Answer: D
Question: If 1+2+3+...+n=n (n+1), then 3 (1+3+5+....+89)=?
Options:
A)6150
B)6200
C)6050
D)6075
E)5075
Rationale: Explanation :
To solve this use the formula of AP,
Sn= (n/2)(a+l) ................(1)
To find n, use
=> Tn= a+(n-1)d
=> 89=1+(n-1)2
=> n=45
Use value of n in (1)
then,
Sn = (45/2)(1+89) = 2025
Ans:- 3(Sn) = 6075
Answer : D
Answer: D
Question: Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?
Options:
A)$22
B)$24
C)$30
D)$36
E)$40
Rationale: B its is.
Let price = X
(x-1)8 = 6X
X= 4
hence total money = 6*4= 24
Answer: B
Question: A survey was sent to 90 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
Options:
A)2%
B)6%
C)14%
D)28%
E)63%
Rationale: case 1: (7/90)=x/100
x=8%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-8)%=6%
Answer is B
Answer: B
Question: Population of a city in 20004 was 1500000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
Options:
A)354354
B)545454
C)465785
D)456573
E)3251625/2
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 3251625/2
E
Answer: E
Question: Four points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points?
Options:
A)3
B)5
C)6
D)15
E)20
Rationale: Number of triangles can be formed out of 6 points= 4C3=4
Number of quadrilaterals can be formed out of 6 points= 4C4=1
4-1=3.
Answer=A
Answer: A
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 18 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
Options:
A)288
B)468
C)877
D)278
E)178
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 18 + 21 = 39
T = 12
D = 39 * 12 = 468
Answer: B
Answer: B
Question: In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
Options:
A)18
B)19
C)17
D)16
E)15
Rationale: Explanation :
Let there were x teams participating in the games, then total number of matches:
=>nC2.
=153
On solving, we get n=−17 and n=18.
It cannot be negative so n=18.
Answer : A
Answer: A
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 6095, what is the length of the plot in metres?
Options:
A)333
B)200
C)230
D)276
E)1999
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 6095
[4L - 40] = 6095 / 26.50 = 230
4L = 270
L = 270/4= 67.5 meters.
Answer: C
Answer: C
Question: John's grade was 80th percentile of the 100 grades for his class. Of the 60 grades from another class, 20 were higher than John's, and the rest were lower. If no other grade was the same as John's grade, then John's grade was what percentile of the grades of the two classes of two classes combined?
Options:
A)72nd
B)75th
C)83rd
D)85th
E)94th
Rationale: 72nd/75th/83rd/85th/94th
Correct option: B
Answer: B
Question: The total of the ages of Mahesh, Suresh, Ramesh is 111years. Ten years ago, the ratio of their ages was 2:3:4. What is the present age of Mahesh?
Options:
A)32years
B)46years
C)42years
D)35years
E)30years
Rationale: Let ages of Mahesh, Suresh, Ramesh 10years ago be 2x,3x,4x
2x+10 + 3x+10 +4x+10 = 111
x = 9
Ramesh present age = 4*9+10 = 46 years
Answer is B
Answer: B
Question: Ajay can walk 6km in 1 hour. In how many hours he can walk 70km?
Options:
A)5hrs
B)11.6hrs
C)15.6hrs
D)20.1hrs
E)30hrs
Rationale: 1 hour he walk 6km
he walk 70km in = 70/6 * 1 = 11.6hours
Answer is B
Answer: B
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 500 inclusive?
Options:
A)190
B)255
C)200
D)205
E)210
Rationale: This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 500, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
50(10) = 500
So we know that there are 50 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 500 = 510
20 + 490 = 510
30 + 480 = 510
Etc.
Since there are 50 total terms, this pattern will create 25 'pairs' of 510.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(25)(510)/(50) =
255
Final Answer:
B
Answer: B
Question: If 65% of a number is greater than 5% of 60 by 23, what is the number?
Options:
A)65
B)40
C)55
D)30
E)60
Rationale: Explanation:
65/100 * x - 5/100 * 60 = 23
65/100 * x - 3 = 23
65/100 * x = 26
x = 26 * 100 / 65
x = 40
Answer: Option B
Answer: B
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Options:
A)Rs.2323
B)Rs.2380
C)Rs.2329
D)Rs.2329
E)Rs.2312
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41
= Rs.2380.
Answer: B
Answer: B
Question: 135 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Options:
A)12 liters
B)32 liters
C)41 liters
D)54 liters
E)34 liters
Rationale: Milk = 3/5 * 135 = 81 liters
Water = 54 liters
81 : (54+P) = 3:4
162 + 3P = 324 => P = 54
54 liters of water are to be added for the ratio become 3:4.
Answer:D
Answer: D
Question: Out of a classroom of 5 boys and 6 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
Options:
A)2/11
B)2/33
C)4/33
D)8/165
E)19/165
Rationale: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 6C3=20.
P(only girls are chosen)=20/165=4/33
The answer is C.
Answer: C
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8010/-. Find out the amount that he borrowed.
Options:
A)s. 5266
B)s. 5269
C)s. 5228
D)s. 5201
E)s. 52192
Rationale: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8010 = P + (54P/100)
8010 = (100P + 54P)/100
8010 = 154P/100
P = (8010 * 100)/154 = Rs. 5201.298
ANSWER: D
Answer: D
Question: Find the value of x when the sum of 20x,(2x+15),(3x-12)and (12x+5) is 674?
Options:
A)15
B)12
C)18
D)20
E)22
Rationale: sum = 20x+(2x+15)+(3x-12)+(12x+5) = 37x+8
37x+8 = 674
x = 666/37 = 18
Answer is C
Answer: C
Question: If u > 1 and v = 2^(u −1), then 4^u =
Options:
A)16v^2
B)4v^2
C)v^2
D)v^2/4
E)v^2/16
Rationale: If u > 1 and v = 2^(u −1), then 4^u
Given u>1, so let's assume u=2
v=2^(u-1) = 2^(2-1) = 2, so v=2
hence, 4^u = 4^2 = 16
only 1 ans. choice can satisfy this:
A) 16v^2 --> clearly > 16
B) 4v^2 --> 4*2^2 = 16(we can stop after this as there can be only 1 right answer)
C) v^2 --> clearly < 16
D) v^2/4 --> clearly < 16
E) v^2/16 --> clearly < 16
Ans. B) 4v^2
Answer: B
Question: What is the sum of the squares of the first 20 natural numbers (1 to 20)?
Options:
A)2870
B)2000
C)5650
D)6650
E)7650
Rationale: n(n+1)(2n+1)/6
20(21)(21)/6
=2870
ANSWER:A
Answer: A
Question: A deer is standing 60 meters in from the west end of a tunnel. The deer sees a train approaching from the west at a constant speed ten times the speed the deer can run. The deer reacts by running toward the train and clears the exit when the train is 33 meters from the tunnel. If the deer ran in the opposite direction it would barely escape out the eastern entrance just as the train came out of the eastern entrance. How long is the tunnel in meters?
Options:
A)127
B)132
C)137
D)142
E)147
Rationale: Let x be the length of the tunnel.
When the deer runs 60 meters west , the train goes 600 meters to a point 33 meters from the west entrance of the tunnel.
When the deer runs east, the deer runs x-60 meters while the train goes x + 600 + 33 meters.
x + 600 + 33 = 10(x-60)
9x = 1233
x = 137 meters
The answer is C.
Answer: C
Question: The value of (10^8-10^2)/(10^5-10^3) is closest to which of the following?
Options:
A)1
B)10
C)10^2
D)10^3
E)10^4
Rationale: Because the question asks for what value isclosestthe question invites approximation.
Let's look at the numerator:
10^8 - 10^2
10^8 is HUGE compared to 10^2.
So 10^8 - 10^2 is very close to 10^8 itself. (Just as 100 - 0.0001 is very close to 100 itself).
Likewise, 10^5 is HUGE compared to 10^3.
So 10^5 - 10^3 is very close to 10^5.
So we have:
10^8/10^5
or 10^(8-5) = 10^3.
Choose D.
Answer: D
Question: What is the units digit of (6!*4! + 6!*5!)/12?
Options:
A)0
B)3
C)2
D)1
E)4
Rationale: (6!*4! + 6!*5!)/12
=6!(4! + 5!)/12
=720 ( 24 + 120)/12
=(720 * 144)/12
= 720 * 12
Units digit of the above product will be equal to 0
Answer A
Answer: A
Question: A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options:
A)74
B)25
C)27
D)91
E)11
Rationale: Number of runs scored more to increse the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
Answer: A
Answer: A
Question: The difference between the length and breadth of a rectangle is 24 m. If its perimeter is 210 m, then its area is:
Options:
A)1520 m2
B)2420 m2
C)2480 m2
D)2520 m2
E)2600 m2
Rationale: We have: (l - b) = 25 and 2(l + b) = 210 or (l + b) = 105
Solving the two equations, we get: l = 65 and b = 40
Area = (l x b) = (65 x 40) m2 = 2600 m2
hence E
Answer: E
Question: The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 13 on the fourth day, his average earning for the whole week is ?
Options:
A)Rs . 18.95
B)Rs 16
C)Rs. 21
D)Rs. 25.71
E)None of these
Rationale: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x18 + 4 x 22 -13
= Rs. 147
âˆ´ Average earning = 147 / 7
= Rs. 21
Correct Option: C
Answer: C
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 1000 m?
Options:
A)122.9 m
B)127.5 m.
C)122.2 m
D)222.9 m
E)212.5 m
Rationale: When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800
= 6300/8
= 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 1000 m, the number of meters by which A beats C = (1000 * 212.5)/1000
= 212.5 m.
Answer:E
Answer: E
Question: A grocery shop has a sale of Rs. 6635, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Options:
A)4857
B)4184
C)4012
D)4791
E)5291
Rationale: Let the sale in the sixth month =x
Then
(6635+6927+6855+7230+6562+x)/6 =6500
=>6635+6927+6855+7230+6562+x =6×6500
=> 34209+x=39000
=> x=39000−34209
=4791
ANSWER:D
Answer: D
Question: John bought a shirt on sale for 25% off the original price and another 25 % off the discounted price. If the final price was $17, what was the price before the first discount?
Options:
A)$45.10
B)$30.22
C)$28.44
D)$67.54
E)$65.23
Rationale: let x be the price before the first discount. The price after the first discount is
x - 25%x (price after first discount)
A second discount of 25% of the discounted price after which the final price is 17
(x - 25%x) - 25%(x - 25%x) = 17
Solve for x
x = $30.22
correct answer B
Answer: B
Question: When m is divided by 7, the remainder is 5. When m is divided by 13, the remainder is 6. If 1 < m < 200, what is the greatest possible value of m?
Options:
A)5
B)19
C)61
D)74
E)110
Rationale: Answer is E.
I started with E.110 and it fits the bill . 105 is divisible by 7 and 104 is divisible by 13. so its E.
Modular approach would be the proper way, but this worked at first attempt.
Answer: E
Question: Albert and Bob are painting rooms at constant, but different rates. Albert takes 1 hour longer than Bob to paint n rooms. Working side by side, they can paint a total of 3n/4 rooms in 4/3 hours. How many hours would it take Albert to paint 3n rooms by himself?
Options:
A)7
B)9
C)12
D)D.13
E)15
Rationale: rate of bob to paint n rooms is n/T(bob)
rate of Albert to paint n rooms is n/T(albert).
albert paints the room 1 hour slower than bob, so T (albert) = T(bob) -1
Together they paint the 3n/5 rooms in 4/3 hours. Rate is equal to work over time
Therefore
n/x + n/x-1 = (3n/5)/(4/3) =
n/x + n/x-1 = 9n/20. Fastest way for me is to think how would make the denominator 20. 4*5 = 20 and it fits x and x-1 or you can solve the quadratic
4n/20 + 5n/20 = 9n/20. Therefore you know it takes Albert 5 hours to paint n room, since Albert's rate is n/5.
4*3 = 3n
12 = 3n.
Answer is C
Answer: C
Question: Jar X is 1/3 full of water. Jar Y, which has half the capacity of Jar X, is 1/2 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
Options:
A)5/6
B)5/12
C)7/12
D)7/18
E)11/18
Rationale: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/2*P/2=P/4
Then the total amount in Jar X is P/3+P/4=7P/12
The answer is C.
Answer: C
Question: The ratio of the volumes of two cubes is 729 : 125. What is the ratio of their total surface areas?
Options:
A)81 : 21
B)81 : 22
C)81 : 24
D)81 : 25
E)81 : 29
Rationale: Ratio of the sides = 3√729 : 3√125= 9 : 5
Ratio of surface areas = 9^2 : 5^2 = 81 : 25
Answer: Option D
Answer: D
Question: There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from second group.
Options:
A)2/7
B)6/35
C)8/25
D)14/89
E)3/5
Rationale: Chances of selecting a white ball from group 1: 2/7----------------------Chances of selecting a white ball from group 2: 4/5
Thus combined probability of section of white ball from group 1:
3/5 x 5/7 = 3/7
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (2/25) / (3/7 + 2/25) = 14/89
D
Answer: D
Question: -84x19+100=?
Options:
A)2436
B)2801
C)-1496
D)-2071
E)None of them
Rationale: Given exp.=-84x(20-1)+100
=-(84x20)+84+100
=-1680+184
=-1496
Answer is C
Answer: C