divelab/Sys2Bench huggingface dataset:
Question: Mantu starts a month with provisions expected to last for the entire month. After few days, it is discovered that the provisions will, in fact short by 12 days and it is calculated that if the stock of provisions left is immediately tripled, it will be possible to exactly make up for the shortfall. If the stock of provisions left is doubled instead of being tripled, and simultaneously the strength of the Mantu is decreased by 25, then the provisions will fall short by :-
Options:
A)2 days
B)1 days
C)3 days
D)4 days
E)None of these
Rationale: Explanation :
At the moment the shortfall is discovered, let there be n days worth of provision left.
Now, 3n−n=2n extra days worth of provisions lasts for the 12 additional days.
Thus, 3n lasts for 18 days i.e. 18 days are left for the month to end.
But if the provisions are only doubled and the strength becomes (3/4)th then the provisions will last for :-
=>12×(4/3).
=>16 days.
i.e. short fall of 18−16= 2 days.
Answer : A
Answer: A
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?
Options:
A)8 kmph
B)6 kmph
C)7.5 kmph
D)5.5 kmph
E)6.5 kmph
Rationale: Explanation:
Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph
ANSWER IS B
Answer: B
Question: A train passes a station platform in 46 sec and a man standing on the platform in 16 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)227
B)240
C)460
D)450
E)455
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 16 = 240 m.
Let the length of the platform be x m . Then,
(x + 240 )/46= 15=> x = 450 m.
Answer:D
Answer: D
Question: A dealer originally bought 80 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
Options:
A)3q/160
B)3q/2
C)120q
D)q/80
E)120/q
Rationale: The cost of each battery was q/80.
Each battery was sold for 1.5q/80 = 3q/160.
The answer is A.
Answer: A
Question: Two persons A and B can complete a piece of work in 15 days and 30 days respectively. If they work together, what part of the work will be completed in 5 days?
Options:
A)1/8
B)1/3
C)1/6
D)1/2
E)5/3
Rationale: A's one day's work = 1/15
B's one day's work = 1/30
(A + B)'s one day's work = 1/15 + 1/30 = 1/10
The part of the work completed in 5 days = 5 (1/10) = 1/2.
Answer:D
Answer: D
Question: The cost of 4 bags and 12 purses is Rs.2800, what is the cost of 10 bags and 30 purses?
Options:
A)Rs.7000
B)Rs.7500
C)Rs.3800
D)Rs.7900
E)None of these
Rationale: Explanation:
Cost of 4 bags + 12 purses = Rs.2800
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.7000.
Answer: Option A
Answer: A
Question: Find the principle on a certain sum of money at 6% per annum for 2 2/5 years if the amount being Rs.1120?
Options:
A)979
B)1288
C)2778
D)2682
E)1021
Rationale: 1120 = P [1 + (6*12/5)/100]
P= 979
Answer: A
Answer: A
Question: The cost of one photocopy is $0.02. However, a 25% discount is offered on orders of more than 100 photocopies. If Steve and David have to make 80 copies each, how much will each of them save if they submit a single order of 160 copies?
Options:
A)$0.32
B)$0.40
C)$0.45
D)$0.48
E)$0.54
Rationale: If Steve and David submit separate orders, each would be smaller than 100 photocopies, so no discount. Each would pay (80)*($0.02) = $1.60, or together, a cost of $3.20 --- that's the combined "no discount cost".
If they submit things together as one big order, they get a discount off of that $3.20 price ---- 25% or 1/4 of that is $0.80, the discount on the combined sale. They each effective save half that amount, or $0.40. Answer = (B).
Answer: B
Question: If a man crosses a 700 m long street in 5 minutes. What is his speed?
Options:
A)7 km/hr
B)7.1 km/hr
C)7.2 km/hr
D)8 km/hr
E)8.4 km/hr
Rationale: distance = 700 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distance/time=700/300=2.3m/s=2.3×18/5 km/hr=8.4 km/hr
E
Answer: E
Question: Population is 24000. Population increases by 10% every year, then the population after 3 years is?
Options:
A)26630
B)26640
C)36644
D)31944
E)26844
Rationale: population after 1st year = 24000*10/100 = 2400 ===> 24000+2400 = 26400
population after 2nd year = 26400*10/100 = 2640 ===> 26400+2640 = 29040
population after 3rd year = 29040*10/100 = 2904 ===> 29040+2904 = 31944
ANSWER:D
Answer: D
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
Options:
A)276
B)188
C)120
D)982
E)129
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer: C
Answer: C
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
A)7
B)8!
C)9
D)3
E)4
Rationale: Total number of letters
= 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer:B
Answer: B
Question: How many multiples of 3 are there between 15 and 246 ?
Options:
A)128
B)94
C)89
D)76
E)60
Rationale: It should be mentioned whether 15 and 246 are inclusive.
If 15 and 246 are inclusive, then the answer is (246-15)/3+1=78.
If 15 and 246 are NOT inclusive, then the answer is (243-18)/3+1=76.
Since OA is D, then we have NOT inclusive case.
Answer: D
Question: Tom opened a shop investing Rs.3000. Jose joined him 2 months later, investing Rs.4500. They earned a profit of Rs.6300 after completion of one year. What will be Jose's share of profit?
Options:
A)3500
B)2800
C)3251
D)4251
E)3508
Rationale: SoL = ~s- So Anju’s share = [5/9] x 6300 = 3500
A
Answer: A
Question: x, a, z, and b are single digit positive integers. x = 1/5 a. z = 1/5 b. (10a + b) – (10x + z) could NOT equal
Options:
A)36
B)33
C)44
D)64
E)56
Rationale: a=5x , b =5z therefore(5x*10+5z) - (10x +z) = (5-1) (10x+z) =.(10x+Z)
number should be divisible by 4
B
Answer: B
Question: A man took loan from a bank at the rate of 12% p.a. S.I. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was?
Options:
A)3887
B)2768
C)15000
D)76887
E)16711
Rationale: Principal = (100 * 5400) / (12 * 3) = Rs. 15000
Answer: C
Answer: C
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
Options:
A)240
B)88
C)66
D)528
E)22
Rationale: (3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240.Answer:A
Answer: A
Question: What is the sum of this series?
1, 3, 5, 7, 9, ...... 77.
Options:
A)1666
B)1555
C)1777
D)1444
E)1333
Rationale: Number of odd numbers between 1 and 59 is (77+1)/2=38
Therefore Sum of odd numbers 38*38= 1444
ANSWER: D
Answer: D
Question: A box has 10 black and 10 white balls. What is the probability of getting two balls of the same color?
Options:
A)9/18
B)9/19
C)9/12
D)9/11
E)9/13
Rationale: ANSWER:B
Answer: B
Question: The G.C.D. of 1.08, 0.32 and 0.9 is:
Options:
A)0.02
B)0.9
C)0.18
D)0.108
E)None
Rationale: EXPLANATION
Given numbers are 1.08, 0.32 and 0.90. H.C.F. of 108, 32 and 90 is 2,
H.C.F. of given numbers = 0.02.
Answer A
Answer: A
Question: If 225/999=0.225, what is the 81st digit to the right of the decimal point in the decimal equivalent of the fraction?
Options:
A)9
B)8
C)7
D)6
E)5
Rationale: 0.[u]225[/u = 0.225225225.....
Every 3rd digit is 5 and every multiple of 3 will be the digit 5. Since 81 is multiple of 3, the 81st digit is 5.
Answer E
Answer: E
Question: List L: ABC, BCA, CAB
In list L above, there are 2 positive integers, where each of A, B, and C is a different nonzero digit. Which of the following is the sum of all the positive integers that MUST be factors of the sum of the integers in list L?
Options:
A)47
B)114
C)152
D)161
E)488
Rationale: Let's try to sum the 2 given numbers taking their place values into account:
(100A + 10B + C) + (100B + 10C + A) + (100C + 10A + B)
= 100(A + B + C) + 10(A + B + C) + (A + B + C)
= 111*(A + B + C)
We know 111 = 37 * 3 so the sum will certainly have 1, 3, 37 and 111 as factors. 1 + 3 + 37 + 111 = 152
Note: How do we know that (A + B + C) will not give us a factor that we get every time? Try and take a few cases where A, B and C have different characteristics e.g. case 1: they are all odd, case 2: they are all even with no multiple of 3 etc. We want to see if there are cases where (A+B+C) has no common factors with other cases.
Let's say A, B and C are all odd. 1+3+5 = 9. Factors 3 and 3
A, B and C are all even. 2+4+8 = 14. Factors 2 and 7
Other factors will depend on values of A, B and C. Hence there is no other factor which we MUST get.
D
Answer: D
Question: In 1950, Richard was 4 times as old as Robert. In 1955, Richard was 3 times as old as Robert. In which year was Richard 1.3 times as old as Robert?
Options:
A)1960
B)1965
C)1970
D)1975
E)2040
Rationale: In 1950: Ri = 4 Ro -------------- eq1
In 1955: Ri +5 = 3(Ro+5)---------eq2
Thus in 1950, solving eq1 and eq2
Ro= 10 , Ri =40
Now for each year we can calculate:
1960: Ri = 50 , Ro =20
1965: Ri= 55, Ro=25
2040: Ri= 100, Ro = 130
Thus Ans:E
Answer: E
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, x
Options:
A)29
B)31
C)23
D)43
E)53
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 38 + 5 = 43.
Answer: D
Question: How many 4-digit numbers are completely divisible by 7?
Options:
A)1354
B)1286
C)1178
D)1224
E)None
Rationale: Solution: 4- digit numbers divisible by 7 are: 1001, 1008, 1015….. 9996.
This is an A.P. in which a=1001, d=7, l=9996.
Let the number of terms be n.
Then Tn=9996. .'. a+(n-1)d=9996
=> 1001+(n-1)7= 9996
=>(n-1)7=8995
=>(n-1)= 8995/7= 1285
=> n=1286.
.'. number of terms =1286.
Answer B
Answer: B
Question: A certain club has 10 members, including Rarry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Rarry will be either the member chose to be secretary or the member chose to be treasurer?
Options:
A)1/720
B)1/80
C)1/10
D)1/9
E)1/5
Rationale: In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary = 8/9, probability of treasurer 1/8
probability to become a treasurer = (9/10 * 8/9 * 1/8) = 1/10
Since, the problem is saying Rarry secretary OR Treasurer it is addition: 1/10 + 1/10 = 1/5=E
Answer: E
Question: If a and b are positive integers and (2^a)^b = 2^7, what is the value of 2^a*2^b?
Options:
A)16
B)32
C)64
D)256
E)128
Rationale: 2^ab =2^7 therefore ab=7 either a=1 or 7 or b=7 or 1
therefore 2^a* 2^b = 2^(a+b)= 2^8 =256
D
Answer: D
Question: The average temperature of the first three days is 27∘C and that of the next three days is 29∘C. If the average of the whole week is 28.5∘C, the temperature of the last day of the week is :
Options:
A)10.5∘C
B)21∘C
C)31.5∘C
D)42∘C
E)None
Rationale: Explanation:
Let the seventh day temperature be x. Then total temperature for the whole week is
3×27+3×29+1×x=7×28.5
x = 31.5
Correct Option: C
Answer: C
Question: If x and y are integer, which of the following must also be an integer?
I. xy
II. y/x
III. x
Options:
A)I alone
B)II alone
C)III alone
D)I and III
E)None of the above
Rationale: Let's take X = 4and Y = 3
XY which is an integer
Y/X = 3/4 Not an integer.
X alone is 4 which is an integer.
Hence D.
Answer: D
Question: As x increases from 121 to 122, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
Options:
A)I,II only
B)I only
C)II only
D)III only
E)II,III only
Rationale: On Increasing the value of x from 121 to 122
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer:A
Answer: A
Question: 50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?
Options:
A)140 days.
B)140 days.
C)120 days.
D)100 days.
E)110 days.
Rationale: D
100 days.
After 5 days, the following situation prevails.
50 men can complete the work in 60 days.
30 men can complete the work in ? days.
M1 D1 = M2 D2
=> 50 * 60 = 30 * D2
=> D2 = (50 * 60)/30 = 100 days.
Answer: D
Question: The odds in favour of an events are 3:5. The probability of occurrence of the event is
Options:
A)3/8
B)2/7
C)1/3
D)2/5
E)6/7
Rationale: Number of cases favourable to E = 3
Total number of cases = 3+5 = 8
P(E) = 3/8
Answer is A
Answer: A
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
Options:
A)14 min 70 sec
B)14 min 60 sec
C)14 min 47 sec
D)14 min 40 sec
E)13 min 40 sec
Rationale: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec)
= 14 min 40 sec.
Answer: D
Answer: D
Question: There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
Options:
A)0.9
B)0.8
C)0.5
D)0.7
E)0.2
Rationale: Ans: Very interesting question.
As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box
So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls
Probability of choosing any box is 1/ 2.
So probability of taking one red ball = 12×(1)+12(3864)≃0.8
Answer:B
Answer: B
Question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
Options:
A)2.5
B)3
C)5
D)7
E)9
Rationale: D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 sec = 2.5 mins
Answer: A
Answer: A
Question: When positive integer W is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
Options:
A)a. k + 1
B)b. k -11
C)c. 4k + 2
D)d. (k-3)/3 +2
E)e. W/3
Rationale: When positive integer W is divided by 6 the remainder is 3
So, W could equal 3, 9, 15, 21, etc
let's TEST W =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: E
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
Options:
A)9287
B)9261
C)9229
D)9285
E)2788
Rationale: A = 8000(21/20)3
= 9261
Answer: B
Answer: B
Question: If 0 < A < Y, A is an odd number and Y is a prime number, which of the following can be the value of A + Y ?
Options:
A)11.
B)13.
C)17.
D)10.
E)7.
Rationale: If A is odd ,implies a(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2A=1 since 0<A<Y therefore A+Y =3. But 3 is not an option
which implies y is odd,
Now A(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: D
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 7 parts pure wine and 5 parts soda. Compare the strength of the wine.
Options:
A)35;36
B)7 : 8
C)15 : 14
D)14 : 5
E)None of these
Rationale: 5/8 : 7/12
LCM of 8,12 = 24
(5/8)*24 : (7/12)*24
15:14
Answer is C.
Answer: C
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams S could be selected from the eight candidates?
Options:
A)56
B)120
C)210
D)1120
E)6720
Rationale: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways S= 8*7*20=1120..
ans D...
Answer: D
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
Options:
A)1080
B)10080
C)10025
D)11080
E)12000
Rationale: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER:B
Answer: B
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/2 of his salary. What fraction of his income came from tips ?
Options:
A)4/9
B)5/4
C)5/8
D)5/7
E)6/9
Rationale: Income = salary (s) +tips = s + s*5/2 = s*7/2
Tips = s*7/2
fraction of his income came from tips = (s*5/2)/(s*7/2)= 5/7
ANSWER:D
Answer: D
Question: A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work?
Options:
A)20days
B)15days
C)30days
D)45days
E)50days
Rationale: 10days work of A = 10/40 = 1/4
remaining work = 1-1/4 = 3/4
B can finish 3/4 work = 60*3/4 = 45days
Answer is D
Answer: D
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder K when N is divided by 30?
Options:
A)(a) 4
B)(b) 7
C)(c) 11
D)(d) 13
E)(e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder K when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: C
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 60 of this series?
Options:
A)5330
B)5670
C)5990
D)6240
E)6550
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 60, the sum of the series is:
3(1+2+...+60) + 60(3) =
3(60)(61)/2 + 60(3) =
90*61 + 180 = 5670
The answer is B.
Answer: B
Question: Which of the following is closer to (6!+4!)*(6!-4!)?
Options:
A)587945
B)647280
C)587920
D)658230
E)954120
Rationale: Notice that 6! = (6*5)(4!)
(6!+4!)*(6!-4!)=[6!(30+1)]*[6!(30-1)]
= 21/19
≈ 647280
Answer: B
Answer: B
Question: |5 - 2| - |6 - 9| = ?
Options:
A)3
B)2
C)1
D)0
E)4
Rationale: |5 - 2| - |6 - 9| = | 3 | - | -3 | = 3 - 3 = 0
correct answer D
Answer: D
Question: In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:4, If Rs 30,000 was their profit, how much amount did B receive.
Options:
A)1235
B)62896
C)6666
D)8974
E)5626
Rationale: Explanation:
A:B = 3:4 = 3:4
=> A:C = 3:2 = 3:2
=> A:B:C = 3:4:2
C share = (2/9)*30000
= 6666
Option C
Answer: C
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ems does the wheel move in 1 hour?
Options:
A)20000
B)14000
C)23000
D)120000
E)None of these
Rationale: Explanation :
Number of wheel moves in 1 hour = 10 * 60 = 600distance moved = 600 * 200 = 12000
Answer : D
Answer: D
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 13 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
Options:
A)25
B)64
C)36
D)48
E)61
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
13 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 52
b = 39
Number of freshmen who take Art = 39 + 20 + 5 = 64
Answer B
Answer: B
Question: Find the value of x from logx 100 = 2
Options:
A)10
B)12
C)13
D)14
E)15
Rationale: solution:
logb 1000 = 3
We can write it as,
b3 = 1000
b3 = 103
So from the above equation
b = 10
ANSWER IS A
Answer: A
Question: The bankerâ€™s discount of a certain sum of money is Rs. 90 and the true discount on the same sum for the same time is Rs. 60. The sum due is
Options:
A)210
B)180
C)360
D)450
E)None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[90 * 60 / 90 - 60] = Rs. [90 * 60 / 30] = Rs. 180
Answer B
Answer: B
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 4 km in stationary water
Options:
A)40 min
B)1hr
C)1hr 15 min
D)1hr 30 min
E)4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(4/4)=1 hr
Answer(B)
Answer: B
Question: A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.
Options:
A)$1200
B)$1100
C)$1400
D)$1000
E)$1500
Rationale: Given:
After a% decrease the price of the article is reduced by $180 --> pa=180;
After one more such change the price is further reduced by $153. After the first decrease the price became $(p−180), thus (p−180)a=153--> pa−180a=153a=15--->a=15 --> p∗0.15=180--> p=1,200
Answer: A.
Answer: A
Question: A question paper has 2 parts, A & B, each containing 7 questions. If a student has to choose 5 from part A & 4 from part B, in how many ways can he choose the questions?
Options:
A)1100
B)1200
C)1235
D)1354
E)735
Rationale: There 7 questions in part A out of which 5 question can be chosen as = 7C5.
Similarly, 4 questions can be chosen from 7 questions of Part B as = 7C4.
Hence, total number of ways,
=7C5*7C4
=[7!/(2!5!)]*[7!/(3!*4!)]
= {21}*{7*6*5*4/(4*3*2*1)}
= 735.
E
Answer: E
Question: If x = 3 and y = −2, what is the value of (x − 2y)^y?
Options:
A)−100
B)0.02
C)0.25
D)4
E)8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
Answer: B
Answer: B
Question: How many different positive integers are factors of 324 ?
Options:
A) 9
B) 16
C) 25
D) 36
E) 49
Rationale: 18×18=6^2 × 3^2
So total factors = (5+1)(5+1) = 36
Answer: D
Answer: D
Question: The average monthly salary of the employees of a firm is Rs.60 out of the employees 12 officers get an average of Rs.400 per month and the rest an average of Rs. 56 per month , Find the number of emp
Options:
A)1032
B)2766
C)2882
D)2788
E)2772
Rationale: Actual average salary of 12 officers = 400
\inline \fn_jvn \therefore Total salary of 12 officers = 400 x 12 = 4800
Average of these 12 officers as a whole =60
Total salary of 12 officers as a whole = 60 x 12 = 720
The total salary of rest = 4800 - 720 = 4080
Difference in average of the rest of officers = 60 - 56 = 4
Rest of the officers = \inline \fn_jvn \frac{4080}{4}=1020
Total number of employees = 1020 + 12 = 1032
ANSWER:A
Answer: A
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
Options:
A)21
B)22
C)23
D)24
E)None of these
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 + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
ANSWER:C
Answer: C