divelab/Sys2Bench huggingface dataset:
Question: In a certain city, 70 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 80 percent of the registered voters who are Democrats and 30 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
Options:
A)65%
B)52%
C)85%
D)69%
E)75%
Rationale: Say there are total of 100 registered voters in that city. Thus 70 are Democrats and 30 are Republicans.
70*0.80=56 Democrats are expected to vote for Candidate A;
30*0.30=9 Republicans are expected to vote for Candidate A.
Thus total of 56+9=65 registered voters are expected to vote for Candidate A, which is 65% of the total number of registered voters.
Answer: A
Answer: A
Question: Find large number from below question The difference of two numbers is 1380. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
Options:
A)1245
B)1345
C)1455
D)1577
E)1653
Rationale: Let the smaller number be x. Then larger number = (x + 1380).
x + 1380 = 6x + 15
5x = 1365
x = 273
Large number = 273+1380 = 1653
E
Answer: E
Question: If X = the product of seven distinct prime numbers, how many factors does X have besides 1 and itself?
Options:
A)108
B)114
C)120
D)126
E)132
Rationale: Since X has 7 distinct prime factors, X has a total of 2^7 = 128 factors.
Besides 1 and itself, X has 126 factors.
The answer is D.
Answer: D
Question: If k^3 is divisible by 336, what is the least possible value of integer k?
Options:
A)56
B)70
C)84
D)96
E)120
Rationale: k^3 = 336*x = 2^4*3*7*x
The factors of k must at minimum include 2^2*3*7 = 84.
The answer is C.
Answer: C
Question: Set #1 = {A, B, C, D, E}
Set #2 = {K, L, M, N, O}
There are these two sets of letters, and you are going to pick exactly one letter from each set. What is the probability of picking at least one vowel?
Options:
A)13/6
B)13/5
C)13/25
D)2/3
E)5/6
Rationale: So Not a vowel in Set-1 : 3/5
And not a vowel in Ser-2:4/5
Now,
3/5∗4/5=12/25
This is for not a vowel.
Then for at least one vowel will be = 1−12/25=13/25
Answer will be C.
Answer: C
Question: 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
Options:
A)20 days
B)30 days
C)40 days
D)60 days
E)70 days
Rationale: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Answer: C
Question: Which of the following CANNOT be a value of 7/(x–7)?
Options:
A)-1
B)-1/2
C)0
D)2
E)7
Rationale: The question doesn't ask for the value of x here, but for the possible results of the equation.
If 7/(x-7) = 0, then the numerator must be 0. But since the numerator is 7, the fraction can not be equal to 0.
The answer is C.
Answer: C
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
A)15
B)88
C)44
D)54
E)23
Rationale: Let the average after 7th inning = x
Then average after 16th inning = x - 3
16(x-3)+87 = 17x
x = 87 - 48 = 39
ANSWER=B
Answer: B
Question: The length of a rectangular landscape is 4times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/3rd of the total landscape. What is the length of the landscape?
Options:
A)100
B)110
C)120
D)134
E)145
Rationale: Sol. x * 4x = 3 * 1200
x = 30
Length = 4 * 30 = 120
C
Answer: C
Question: If positive integer k is divided by 8, the quotient is m and the remainder is 2, then which of the following must be true?
I. k + m is even
II. k cannot be a prime number
III. k is divisible by 4
Options:
A)None
B)I
C)II
D)III
E)I and II only
Rationale: k = 8m+2 = 2(4m+1)
I. k + m = 2(4m+1) + m => even if only m is even, however m can be odd => not always true
II. k can not be a prime: not always true:
m=0 => k=2 : a prime
III. not true if m is even
Ans: none of the above
Answer: A
Question: If the difference between the compound interest & simple interest of a certain sum of money is
Rs.72 at 12% p.a. per two year. Find the sum(in Rs.)?
Options:
A)200/15
B)200/17
C)220/17
D)240/17
E)260/17
Rationale: 200/17
C.I=A-P
A=p(1+12/100)^2
S.I=p*2*12/100
C.I-S.I=72 given
substitute and solve
p=200/17
ANSWER:B
Answer: B
Question: What number has a 5:1 ratio to the number 8?
Options:
A)22
B)40
C)88
D)52
E)12
Rationale: 5:1 = x: 8
x = 40
Answer: B
Answer: B
Question: Three unbiased coins are tossed. What is the probability of getting 3 heads?
Options:
A)3/4
B)1/4
C)3/8
D)7/8
E)1/8
Rationale: Let, H --> Head , T --> Tail
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting 3 heads
Then E = {HHH}
P(E) = n(E)/n(S) =1/8
Answer: E
Question: Which of the following is equal to 2^k*7^(k-1)?
Options:
A)2*14^(k-1)
B)7*14^(k-1)
C)14^k
D)2*14^k
E)14^(2k-1)
Rationale: 2^k*7^(k-1) = 2*2^(k-1)*7^(k-1) = 2*14^(k-1)
The answer is A.
Answer: A
Question: What distance will be covered by a bus moving at 126 kmph in 10 seconds?
Options:
A)287
B)600
C)350
D)276
E)207
Rationale: 126 kmph = 126 * 5/18
= 35 mps
D = Speed * time = 35 * 10
= 350 m.
Answer:C
Answer: C
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 3 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
Options:
A)A)5
B)B)6
C)C)8
D)D)9
E)E)87
Rationale: Relative speed = 3 + 3 = 6 rounds per hour.
So, they cross each other 6 times in an hour and 3 times in half an hour.
Hence, they cross each other 9 times before 9.30 a.m.
ANSWER:D
Answer: D
Question: A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?
Options:
A)17
B)23
C)75
D)77
E)None of these
Rationale: Let the number of apples= 100
sold 60% = 60 apples...remaining =40
Thrown away 15%= 6 apples
Remaining =40-6=34
sold 50 % of remaining = 34/2=17
Remaining thrown away = 17 apples
Total thrown away =6+17=23
Percentage thrown = 23/100=23%
Answer: B
Answer: B
Question: The value of 1/(1-y) + 1/(1+y) + 2/(1+y^2) + 4/(1+y^4)
Options:
A)8/(1-y^8)
B)4x/(1+y^2)
C)4/(1-y^6)
D)4/(1+y^4)
E)4x/(1-y^4)
Rationale: Highlighted part has mistake as the exponent of y must be 4 in last term
CORRECT QUESTION ISThe value of 1/(1-y) + 1/(1+y) + 2/(1+y^2) + 4/(1+y^4) = ?
Solution is as mentioned below...
one more way that could get the answer in the type of eqn and choices given is to substitute some value for y...
0 would be better as the eq has constant term free of term 'y'..
the Eq gives us 8 as the ans , as also only choice A..
Answer: A
Question: The average of 9 numbers is 7 and the average of 7 other numbers is 11. What is the average of all 16 numbers?
Options:
A)9
B)8 3/4
C)7 7⁄8
D)7 1⁄2
E)7 1⁄4
Rationale: The average of 9 numbers is 7....
The sum of those numbers is (9)(7) = 63.
The average of 7 other numbers is 11....
The sum of those numbers is (7)(11) = 77
The sum of ALL 16 numbers is 63+77 = 140. The average of those numbers is 140/16 = 35/4 = 8 3/4.
Final Answer:
[Reveal]Spoiler:
B
Answer: B
Question: What is the sum of all the multiples of 10 between 0 and 100?
Options:
A)500
B)620
C)550
D)340
E)440
Rationale: The multiples of 10 between 0 and 100 are 10, 20, 30, 40, 50, 60, 70, 80, 90 and 100. If these are all added together, the result is 550.
Final Answer:
C
Answer: C
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
Options:
A)16 2/8%
B)16 5/3%
C)10 2/3%
D)16 2/3%
E)16 1/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer:D
Answer: D
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 5 minutes, what part of the cistern will be emptied?
Options:
A)4/9
B)5/18
C)4/2
D)4/8
E)4/1
Rationale: 2/3 ---- 12
? ----- 5 ==> 5/18
Answer: B
Answer: B
Question: In the manufacture of a certain product, 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale. What percent of the units produced are defective units that are shipped for sale?
Options:
A)0.125%
B)0.28%
C)0.8%
D)1.25%
E)2.0%
Rationale: Percent of defective produced = 7%
Percent of the defective units that are shipped for sale = 4%
Percent of units produced are defective units that are shipped for sale = (4/100)*(7/100)*100%
= (28/10000)*100%
= (28/100)%
= .28 %
Answer B
Answer: B
Question: A grocer purchased 80 kg of rice at Rs. 13.50 per kg and mixed it with 120 kg rice at Rs. 16 per kg. At what rate per kg should he sell the mixture to gain 16%?
Options:
A)Rs. 19
B)Rs. 20.5
C)Rs. 17.4
D)Rs. 21.6
E)Rs. 22.6
Rationale: C.P OF 200 kg of mix = Rs.[ 80*13.50+120*16 ] =Rs.3000
S.P =116% of Rs.3000 = Rs. 116/100*3000 = 3480
Rate of S .P of the mixture = Rs. [ 3480/200] per kg
= Rs. 17.40 per kg
ANSWER:C
Answer: C
Question: Three coins are tossed. What is the probability of getting at most two tails
Options:
A)4/8
B)7/8
C)6/8
D)9/8
E)2/4
Rationale: Since three coins are tossed, sample space = 8
Getting at most two tails=7
p(E) =7/8
ANSWER:B
Answer: B
Question: Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
Options:
A)Rs 870
B)Rs 880
C)Rs 890
D)Rs 900
E)None of these
Rationale: Explanation:
Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)
= 48 : 32 : 64
= 3 : 2 : 4
Kamal's share=4005∗2/9=Rs890
Option C
Answer: C
Question: Divide Rs.32000 in the ratio 3:3?
Options:
A)12000, 20000
B)12000, 200098
C)16000, 16000
D)12000, 20006
E)12000, 20001
Rationale: 3/6 * 32000 = 16000
5/6 * 32000 = 16000
Answer: C
Answer: C
Question: A pool which was 2/3 full to begin with, was filled at a constant rate for 1/3 hours until it was until it was 6/7 full. At this rate, how much time would it take to completely fill this pool if it was empty to begin with?
Options:
A)8 hrs 45 mins.
B)9 hrs.
C)9 hrs 30 mins.
D)1 hrs 45 mins.
E)15 hrs 30 mins
Rationale: The pool was 2/3 full initially.
In 1/3 hrs, it was filled to 6/7 of its capacity.
Therefore, in 1/3 hrs, 6/7 - 2/3 was the amount of volume filled.
So, 1/3 hrs = 6/7 - 2/3 = 4/21
Therefore, for filling the vessel from empty to full, you would require 1/3 * 21/4 = 1 Hrs 45 Mins.
Hence D
Answer: D
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. six years from today, the difference between the age of the boy and the combined ages of the girls will be
Options:
A)1
B)-5
C)3
D)–2
E)–1
Rationale: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 6 years there ages are
7 ....................... 7 ............................ 9
Difference = 9 - (7+7) = 9 - 14 = -5
Answer = B
Answer: B
Question: A can do a job in 15 days and B can do it in 60 days. A and B working together will finish twice the amount of work in ------- days?
Options:
A)22 1/2 days
B)22 1/2 days
C)22 days
D)25 days
E)24 days
Rationale: 1/15+ 1/60= 5/60= 1/12
12/1 = 12*2 =24 days
Answer: E
Answer: E
Question: Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?
Options:
A)65
B)75
C)60
D)70
E)85
Rationale: Average mark = (76+65+82+67+855=375)/5=75
Answer is B.
Answer: B
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5760 interest only for the period. The principal amount borrowed by him was:
Options:
A)s. 2000
B)s. 16,000
C)s. 15,000
D)s. 18,000
E)s. 20,000
Rationale: Principal = Rs. (100 x 5760)/(12X3) = Rs. 16000. Answer: Option B
Answer: B
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
Options:
A)20
B)27
C)72
D)28
E)82
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase
=4 * 10 = 40
The new sum = 230 + 40
= 270 The new average = 270/10 = 27.
Answer:B
Answer: B
Question: Pipes A and B can fill a tank in 5 and 7 hours. Pipe C can empty it in 12 hours. If all pipes are opened together, then the tank will be filled in?
Options:
A)27/7 hr
B)17/19 hr
C)52/11 hr
D)6 hr
E)63/19 hr
Rationale: Net part filled in 1 hour = 1/5 + 1/7 - 1/12 = 7/27
The tank will be full in 27/7 hr
Answer is A
Answer: A
Question: The E train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the E train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
Options:
A)1.8m
B)6m
C)7m
D)9m
E)12m
Rationale: The reason it is failing for you is that you chose incorrect numbers. If the question says E it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Answer: B
Question: A can complete a certain job in 9 days. B is 80% more efficient than A. In how many days can B complete the same job?
Options:
A) 5
B) 6.25
C) 7
D) 7.5
E) 4.8
Rationale: Let, Total Work Unit = 90 Units
A can finish in 9 days = 90 unit work
i.e. A can finish in 1 days = 10 unit work
i.e. B can finish in 1 days = 10+(80/100)*10 = 18 unit work
Days in which B will complete the work alone = 90/18 = 5 days
Answer: Option A
Answer: A
Question: Fence X is twice as long as fence Y, and fence Y is 2 feet shorter than fence Z. If 4 feet were added to each fence, which of the following must be true?
I) X is twice as long as Y.
II) Y is 2 feet shorter than Z.
III) X is longer than Z.
Options:
A)I only
B)II and III
C)III only
D)I and II
E)II only
Rationale: If X= 6
Y= 3
Z= 5
Then, after adding 3 feet to each:
X= 10
Y=7
Z=9
And the answer would be ,B which is wrong.
Answer: B
Question: John’s grade was in the 80th percentile out of 70 grades in her class. In another class of 50 students there were 20 grades higher than John’s. If nobody had John’s grade, then John was what percentile of the two classes combined?
Options:
A)80
B)75
C)72
D)65
E)60
Rationale: Being in 80% percentile out of 70 grades means John was 57th (from the least grade) in the class (as long as nobody had John 's grades), he outscored 56.
In another class his grade would rank him 31 (from the least grade out of 51, 50+ John), 31 had the grades lower than John.
So in combined classes he outscored 56+30=86. There are 120 students 86/120=0.717 =0.72 after rounding.
Answer: C(72%)
Generally being in x% means that x% has the grades less than you.
John in 80% --> he outscored 80% of of 70=56 (Amy is 57th).
Of the 50 grades from another class, 20 were higher than John 's, and the rest were lower --> rest is 30, hence John outscored 30.
So out of total 70+50=180, John outscored 56+30=86. Hence he is in 86/120=72%.
72
Answer: C
Answer: C
Question: A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B ?
Options:
A)30 metres
B)50 metres
C)48 metres
D)55 metres
E)20 metres
Rationale: Clearly, A beats B by 10 sec.
Distance covered by B in 10 sec. = ((1000/200) x 10 )m = 50 m.
Therefore A beats B by 50 metres.
Answer is B.
Answer: B
Question: Increasing the original price of an article by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by
Options:
A)40%
B)41%
C)42%
D)43%
E)44%
Rationale: 1.2*1.2*x = 1.44*x
The answer is E.
Answer: E
Question: Ten family members are seated around their circular dinner table. If only arrangements that are considered distinct are those where family members are seated in different locations relative to each other, and Michael and Bobby insist on sitting next to one another, then how many distinct arrangements around the table are possible?
Options:
A)68,640
B)71,640
C)74,640
D)77,640
E)80,640
Rationale: Let's consider Michael and Bobby as one unit.
There are 9! possible arrangements of 9 units.
Around a table, there would be repetitions of each arrangement, so we divide by 9.
Then there are 8! arrangements around a circular table.
For each arrangement, Michael and Bobby can switch places, so we multiply by 2.
The number of arrangements is 8!*2 = 80,640.
The answer is E.
Answer: E
Question: Simple interest at x% for x years will come out to be Rs x on a sum of Rs?
Options:
A)x
B)100/x
C)100/x2
D)100x
E)None of these
Rationale: Explanation:
Formula for Simple Interest:
SI = Principal*Rate*Time
SI= x
Rate= x/100
Time= x
=> x= Principal*(x/100)*x
=>Principal Amount= 100/x
ANSWER B
Answer: B
Question: The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. What is the largest number?
Options:
A)280
B)284
C)292
D)320
E)322
Rationale: HCF of the two numbers = 23
Since HCF will be always a factor of LCM, 23 is a factor of the LCM.
Given that other two factors in the LCM are 13 and 14.
Hence factors of the LCM are 23, 13, 14
So, numbers can be taken as (23 × 13) and (23 × 14)
= 299 and 322
Hence, largest number = 322
E)
Answer: E
Question: If w is a positive integer, then 3^w + 3^(w +1) =
Options:
A)4^a
B)3^a − 1
C)3^(2a) + 1
D)3^a*(a − 1)
E)4(3^w)
Rationale: 3^w + 3^(w +1)
= 3^w + (3^w * 3^1)
= 3^w (1 + 3)
= 3^w(4)
Ans. E) 4(3^w)
Answer: E
Question: If two numbers are in the ratio 2:3. If 23 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?
Options:
A)A)10
B)B)46
C)C)25
D)D)30
E)E)35
Rationale: 2:3
2x + 23 : 3x + 23 = 3 : 4
4[2x + 23] = 3[3x + 23]
8x + 92 = 9x + 69
9x - 8x = 92 - 69
x = 23
Then smallest number is = 2
2x = 46
Correct Option B
Answer: B
Question: After running a series of television advertisements, a leading beverage producer saw its sales increase by 20% to $1 million dollars per month. Prior to the advertising campaign, about how many dollars in sales did the company average per day?
Options:
A)$1.25 million
B)$800,000
C)$750,000
D)$28,000
E)$10,000
Rationale: Let sales in previous month = X
1.2 X=1,000,000
6/5 X= 1,000,000 ..........> X=833,333
sales per day= 833,333/30= less than 30,000 so closest number is 27,000
Answer: D
Answer: D
Question: 2 pipes function simultaneously the reservoir will be filled in 12hrs. One pipe fills reservoir 10hrs faster than other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)10
B)20
C)22
D)24
E)26
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
B
Answer: B
Question: A and B starts a business with Rs.8000 each, and after 7 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
Options:
A)36:25
B)18:25
C)36:10
D)18:14
E)14:11
Rationale: A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 7 months and then withdraws Rs.4000. So, the investment of B for remaining 11 months is Rs.4000 only.
A : B
8000*18 : (8000*7) + (4000*11)
14400 : 100000
A:B = 36:25
Answer: A
Answer: A
Question: Magnabulk Corp sells boxes holding d magnets each. The boxes are shipped in crates, each holding b boxes. What is the price charged per magnet, in cents, if Magnabulk charges n dollars for each crate?
Options:
A)100n/(bd)
B)100bd/n
C)bd/(100n)
D)n/(bd)
E)bd/n
Rationale: crate has = bd magnates
C crate cost = n dollars = 100 m cents
each magnate cost for each crate = 100 n / bd
Ans; A
Answer: A
Question: A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest?
Options:
A)5% p.a.
B)7.5% p.a.
C)10% p.a.
D)12.5% p.a.
E)None of these
Rationale: Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (840 – 800) = S.I. on Rs. 400 for 1 year
40 = (400 * R * 1) / 100
R = 10% p.a.
ANSWER C
Answer: C
Question: The number 523gbc is divisible by 7,8,9. Then what is the value of g*b*c
Options:
A)504
B)532
C)210
D)180
E)280
Rationale: LCM of 7, 8 and 9 is 504, thus 523gbc must be divisible by 504.
523gbc=523000+gbc
523000 divided by 504 gives a remainder of 352.
Hence, 352+gbc=k*504.
k=1 gbc=152 --> g*b*c=10
k=2 gbc=656 --> g*b*c=180
As gbc is three digit number k can not be more than 2.
Two answers? Well only one is listed in answer choices, so D.
Answer: D.
Answer: D
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
Options:
A)36
B)42
C)64
D)69
E)70
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: C
Question: A car salesman earns a base salary of $800 per month plus a commission of $200 for each car he sells. If the car salesman earned $2200 in July, how many cars does he need to sell in August in order to double his July earnings?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: 800+200x=4400
x=18 cars.
The answer is D.
Answer: D
Question: If (1/5)^n * (1/4)^18 = 1/(2*(10)^35), then n =
Options:
A)40
B)45
C)35
D)30
E)25
Rationale: (1/5)^m (1/4)^18 = 1/{2(10)^35}
2(10)^35/4^18 = 5^m
[2(2^35)(5^35)]/[2^36] = 5^m
5^35 = 5^m
n=35
C
Answer: C
Question: The mean daily profit made by a shopkeeper in a month of 30 days was Rs. 350. If the mean profit for the first fifteen days was Rs. 225, then the mean profit for the last 15 days would be
Options:
A)Rs. 200
B)Rs. 350
C)Rs. 475
D)Rs. 425
E)None of these
Rationale: Average would be : 350 = (225 + x)/2
On solving, x = 475.
Answer: C
Answer: C
Question: Balloons and confetti are sold in different colours at a store. Balloons of three different colours and confetti of two different colours are to be bought by Jim Bob Jones from this store. If there are seven colours of balloons available and if there are a total of 350 combinations of different colours of balloons and confetti that can be purchased, how many colours of confetti are available at the store?
Options:
A)4
B)5
C)6
D)8
E)10
Rationale: 350 = Ways of choosing 3 balloon colors * ways of choosing 2 confetti colors
Jim can select 3 colors of balloons in 7C3 = 7*6*5/3*2 = 35 ways
So Ways of choosing 2 confetti colors = 350/35 = 10
If there are n different confetti colors, nC2 = 10 = n(n-1)/2
n = 5 satisfies this equation
Answer (B)
Answer: B
Question: In a100m race A beats B by 25m B beats C by 4 then A beats C by
Options:
A)24 m
B)25m
C)26m
D)27m
E)28m
Rationale: A : B = 100 : 75
B : C = 100 : 96.
A : C =	(A/B	x	B/C)	=	(100/75	x	100/96)	=	100/72	= 100 : 72.
A beats C by (100 - 72) m = 28 m.
ANSWER:E
Answer: E
Question: What is the remainder when 45*49 is divided by 8?
Options:
A) 1
B) 3
C) 4
D) 5
E) 7
Rationale: we can make use of the rule :
Remainder of { (a * b)/n}} = Remainder of (a/n) * Remainder of (b/n)
Here
Remainder of { 45 * 49)/8}} = Remainder of (45/8) * Remainder of (49/8) = 5 * 1 = 7
Answer :D
Answer: D
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)230
B)244
C)245
D)215
E)236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.
Answer: Option D
Answer: D