mathewhe/aqua_rat huggingface dataset:
Question: Present ages of Abi and Suji are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Suji's present age in years?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: present ages = 5x:4x
Three hence =5x+3:4x+3
5x+3:4x+3=11:9
weget x=6
suji age is =4x=4*6=24
ANSWER:E
Answer: (E) 24
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7 kmph
(B) 4 kmph
(C) 8 kmph
(D) 3 kmph
(E) 9 kmph
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: (B) 4 kmph
Question: 1 quarter Kg of potatoes cost 60 paise. Calculate the cost of 200 grams
(A) 48 paise
(B) 77 paise
(C) 96 paise
(D) 66 paise
(E) 55 paise
Rationale: Explanation:
Let 200 gm potato cost X paise
According to question,
Cost of 1/4 Kg potato = 60 Paise
=> Cost of 250 gm potato = 60 Paise
=> 1 Kg = 1000 gm
=> 1/4 Kg = 1000/4 gm = 250 gm
By direct proportion, more quantity, more cost
200 grams : 250 grams = X : 60
=> 200*60 = 250 X
=> 12000 = 250 X
=> X = 48
=> Thus, the cost of 200 grams is 48 paise.
ANSWER: A
Answer: (A) 48 paise
Question: In how many ways can you line up 7 apples in a row if one of them cannot be in the middle or at the either end?
(A) 1,790
(B) 52
(C) 2,880
(D) 98
(E) 2,560
Rationale: Since the apple cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: C.
Answer: (C) 2,880
Question: A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest is 12% per annum,how much cash should he pay ?
(A) Rs. 9025.20
(B) Rs. 9200
(C) Rs. 9600
(D) Rs. 9560
(E) None of these
Rationale: Solution
Required money = P.W. of Rs.10028 due 9 months hence
= Rs. [ 10028x 100/100+( 12 x9/12)] = Rs. 9200
Answer B
Answer: (B) Rs. 9200
Question: The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?
(A) 440
(B) 512
(C) 620
(D) 700
(E) 750
Rationale: Solved it the prime factorization way
440= 2*2*2*5*11 Sum=22
512= 2^6 Sum=2*6=12
620=2*2*5*31 Sum=40>35
Hence correct.
Ans is C
Answer: (C) 620
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
(A) 2.15 p.m
(B) 1.15 p.m
(C) 4.15 p.m
(D) 3.15 p.m
(E) 12.15 p.m
Rationale: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Ans: A
Answer: (A) 2.15 p.m
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is ?
(A) 9! * ⁷P₆
(B) 6! * ⁷P₆
(C) 9! * ⁷P₆
(D) 6! * ⁷9₆
(E) 7! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways = 6! * ⁷P₆
Answer:B
Answer: (B) 6! * ⁷P₆
Question: Solve below question 2x + 1 = -15
(A) -8
(B) -9
(C) 9
(D) 8
(E) -7
Rationale: 2x + 1 = -15
x = -8
A
Answer: (A) -8
Question: If Sam shares his books in the ratio of 1/8 : 1/9 : 1/10 : 1/11 between his four friends A, B, C and D, then find the total number of books Sam should have?
(A) 1611
(B) 1692
(C) 1591
(D) 1691
(E) 16911
Rationale: Here, A : B : C : D = 1/8 : 1/9 : 1/10 : 1/11
1) L.C.M of 8 : 9 : 10 : 11 is 3960
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/8) x 3960 = 495
B = (1/9) x 3960 = 440
C = (1/10) x 3960 = 396
D = (1/11) x 3960 = 360
3) Total number of toys = (495 x + 440 x + 396 x + 360 x) = 1691 x
Minimum number of pens (x) = 1
Therefore, total number of items = 1691 items.
Correct option :E
Answer: (E) 16911
Question: A sum of Rs. 2665 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
(A) 2387
(B) 1640
(C) 2781
(D) 2778
(E) 1781
Rationale: (x*8*3)/100 = ((2665 - x)*3*5)/100
24x/100 = 39975/100 - 15x/100
39x = 39975 => x = 1025
Second sum = 2665 – 1025 = 1640
Answer: B
Answer: (B) 1640
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is?
(A) 23
(B) 25
(C) 27
(D) 31
(E) 35
Rationale: Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = 529 = 23.
Option A
Answer: (A) 23
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
(A) Insufficient data
(B) 3 : 1
(C) 1 : 3
(D) 3 : 2
(E) 2 : 3
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x + y) = 23
=> (27x + 17 y) = 23(x + y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
ANSWER:D
Answer: (D) 3 : 2
Question: Sentence B can only be a concluding sentence; we find in the answer choice–b, a sequence of the sentences logically leading to the concluding sentence
(A) 17
(B) 88
(C) 171
(D) 19
(E) 111
Rationale: Answer:B
Answer: (B) 88
Question: 35% of the people read newspaper X, 55% read newspaper Y and 15% read both the papers.What percentage of the people read neither newspaper ?
(A) 20%
(B) 10%
(C) 15%
(D) 30%
(E) 25%
Rationale: n(A)=35,n(B)=55,n(AnB)=15.
n(AuB)=n (A)+n (B)-n(AnB)=35+55-15=75.
Hence, percentage passed =(100-75)%=25%.
Answer is E
Answer: (E) 25%
Question: 5100−(102÷20.4)=?
(A) 5200
(B) 5150
(C) 5250
(D) 6150
(E) 5095
Rationale: Explanation:
=5100−(102/204×10)
=5100−5=5095
Option E
Answer: (E) 5095
Question: Two trains 130 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9
(B) 10.7
(C) 10.3
(D) 10.44
(E) 10.8
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 130 + 160 = 290 m.
Required time = 290 * 9/250 = 261/25 = 10.44 sec.
'Answer: D
Answer: (D) 10.44
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 671.5
(B) 600
(C) 672.5
(D) 673
(E) 773.5
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 900 kilometers per hour is 1/900 hours = 3,600/900 seconds = 4 seconds;
Time to cover this distance at regular speed is 900+2=902 seconds = 902/3,600 hours = 1/600 hours;
So, we get that to cover 1 kilometer 1/600 hours is needed --> regular speed 600 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: B.
Answer: (B) 600
Question: In a sequence of 11 numbers, each term, except for the first one, is 11^11 less than the previous term. If the greatest term in the sequence is 11^12, what is the smallest term in the sequence?
Thus, A12 = A1+12-1d
Where d is the difference between each pairs of consecutive terms. Since each term is 1211 less than the previous term, d=-1211Click individual answer choices for specific explanations.
From what I undersltand the formula for an arithmetic sequence represents
some-number-in-the-sequence= first-number-in-sequence +the-place-of-that-number - 1x the-difference-of-each-#-in-the-sequence
(A) −12^11
(B) 0
(C) 11^11
(D) 11·12^11
(E) 12^12
Rationale: there are total 11 terms. andgreatestterm is 11^12. Each term is 11^11 less than previous one. What does this signify? This shows it is an AP - a decreasing one. (NoticeEach term is 11^11 less than previous one')
Therefore, 11^12 is the first term of the AP and -11^11 is the difference between successive terms, the smallest term should be the last one.
Last term = First term + (n-1)*d
therefore, Last term = 11^12 + 10*(-11^11)
=> Last term = 11^12 - 10*11^11
=> Last term = 11^11 (11-10) = 11^11
Which is the smallest term.
Hence Ans C it is.
Answer: (C) 11^11
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 10. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 13. How many cooks does the restaurant have?
(A) 4
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Originally there were 3k cooks and 10k waiters.
13k = 10k+12
k=4
There are 12 cooks.
The answer is D.
Answer: (D) 12
Question: How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,U,R,S,and T so that letter P is to the left of letter R?
(A) 60
(B) 30
(C) 90
(D) 120
(E) 75
Rationale: Two positions can be selected out of 5 positions in 5C2 ways = 10 ways.
And the remaining 3 letters can be placed in 3 posions in 3! Ways = 6 ways.
So the final Answer = number of ways letters P and R can be arranged x number
of ways the other 3 letters can be arranged
Final Answer = 10 x 6 = 60 ways
A
Answer: (A) 60
Question: If the product 4864*9 P 2 is divisible by 12, the value of p?
(A) 1
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: Explanation:
clearly 4864 is divisible by 4
So 9 P 2 must be divisible by 3.So(9+P+2) must be divisible by 3.
so P=1.
Answer: A) 1
Answer: (A) 1
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 144 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 120
(E) 126
Rationale: Set up equation:
x = total number of workers
144 = 0,4 * 2/3 * x + 0,8 * 1/3 * x
144 = 16/30 x
x = 270
270 - 144 = 126
Answer E
Answer: (E) 126
Question: The average (arithmetic mean) of eight numbers is 44.1. If the sum of half of these numbers is 156.4, what is the average of the other half?
(A) 12.8
(B) 24.2
(C) 49.1
(D) 72.1
(E) 96.8
Rationale: The average of this half is 156.4/4 = 39.1
This is 5 below the overall average, thus the average of the other half of the numbers must be 5 above the overall age, that is 44.1+5 = 49.1
The answer is C.
Answer: (C) 49.1
Question: What is the median from the below series 90, 92, 93, 88, 95, 88, 97, 87, and 98
(A) 80
(B) 85
(C) 92
(D) 97
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88, 90, 92, 93, 95, 96, 98
The median quiz score was 92. (Four quiz scores were higher than 92 and four were lower.)
C
Answer: (C) 92
Question: 12 men can complete any work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only the women were to complete the remaining work in 4 days, then how many women would be required?
(A) 60
(B) 74
(C) 68
(D) 75
(E) 70
Rationale: 1 Man, 1 Day work=1/(12*36)
1 Woman, 1 Day work=1/(18*60)
So 8 men and 20 women's 20 days work= 20[ 8/(12*36) + 20/(18*60) ] =20/27
Remaining work= 7/27
If remaining work is to be completed by 'x' women in 4 days, then 4*x/(18*60)= 7/27
=> x=(7*18*60)/(27*4)=70
ANSWER:B
Answer: (B) 74
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec.
(B) 6 sec
(C) 3 sec.
(D) 1 sec.
(E) 8 sec.
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Answer: (B) 6 sec
Question: An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
(A) 23.000 degrees / second
(B) 43.000 degrees / second
(C) 52.000 degrees / second
(D) 18.000 degrees / second
(E) 29.000 degrees / second
Rationale: 3000 revolutions / minute
= 3000*360 degrees / 60 seconds
= 18,000 degrees / second
correct answer D
Answer: (D) 18.000 degrees / second
Question: A car traveled the first quarter of a certain distance at five times the speed it traveled the remaining distance. What proportion of the total time traveled, was the time taken to travel the first quarter of the distance?
(A) 1/14
(B) 1/15
(C) 1/16
(D) 1/17
(E) 1/18
Rationale: These problems can be solved through algebra or sly number picking. Being a big fan of solving problems with numbers, let's pick a total distance divisible by 4 (say 40) so we can break it up into quarters, and a speed that can easily be five times, say 10. Each quarter is thus 10 kilometers (or miles or feet or angstroms for all it matters), and the runner's speed is 10 km/h for the first quarter and 2 km/h for the remaining quarters.
He'll take 1 hour to do the first quarter and then 15 hours for the second ,third and fourth quarter. On total he will take 16 hours to complete this race, of which 1 hour was spent on the first quarter. So 1/16. Answer C.
Answer: (C) 1/16
Question: Jerry received a 10% raise each month for two consecutive months. What was his starting salary if after the two raises his salary is $1452?
(A) $1,200
(B) $1,300
(C) $1,331
(D) $1,380
(E) $1,403
Rationale: S * 1.1 * 1.1 = 1452 so,
S = 1200
Answer: A
Answer: (A) $1,200
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32
(B) 28
(C) 40
(D) 27
(E) 21
Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
Answer: C
Answer: (C) 40
Question: 30 men can do a work in 40 days. When should 20 men leave the work so that the entire work is completed in 40 days after they leave the work?
(A) 11
(B) 10
(C) 19
(D) 187
(E) 12
Rationale: Total work to be done = 30 * 40 = 1200
Let 20 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (20 * 40) = 1200
40P = 400 => P = 10 days. Answer: B
Answer: (B) 10
Question: A baseball player just signed a new contract in which he will earn a 12% raise in base pay over last year. Last year he earned no performance bonus, but this year he will have the opportunity to earn up to $50,000 in extra pay through performance. If he earns the full performance bonus, his salary will effectively have been raised by 12.5% from the last year. Assuming he earns the full performance bonus, what will his new salary be?
(A) 5,150,000
(B) 10,550,000
(C) 11,250,000
(D) 11,450,000
(E) 12,250,000
Rationale: let x = the old salary
the new base pay + 50,000 = the new pay
(1+.12)*x + 50,000 = (1+.125)*x
1.12x + 50,000 = 1.125x
50,000 = .005x
10,000,000 = x
thus the new pay = (1+.125)*10,000,000 = 11,250,000
C
Answer: (C) 11,250,000
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 6628
(C) 6520
(D) 6629
(E) 6609
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: (A) 6620
Question: The average of 6 observations is 12. A new observation is included and the new average is decreased by 1. The seventh observation is?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (72 + X) / 7 = 11
=> X = 5.
Hence, the seventh observation is 5.
ANSWER:C
Answer: (C) 5
Question: Company A has 13 employees, 8 of whom belong to the union. If 5 people work any one shift, and the union contract specifies that at least 3 union members work each shift, then how many different combinations of employees might work any given shift?
(A) 56
(B) 231
(C) 336
(D) 350
(E) 406
Rationale: Looks easy: -- 8C3*5C1 + 8C5 -- 336 (C).
Answer: (C) 336
Question: The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:
(A) 20
(B) 30
(C) 40
(D) 50
(E) None of these
Rationale: Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131.
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400.
(a + b + c) = 400 = 20
Answer:A
Answer: (A) 20
Question: A cylindrical water tower with radius 28 m and height 10 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?
(A) 840 2/7
(B) 820 6/7
(C) 821
(D) 821 3/7
(E) 840
Rationale: initial volume = (3/4)×∏×28²×10 = 5880∏
Relative Drain/ min = .08∏ - .03∏ = .05∏ m³/min drain
Relative drain / hour = .05∏×60 = 3∏ m³/ hr
Every one hour starting from 1pm, 4∏ m³ of water is drained. It means that only at the hour the water is drained and NOT “in that 1 hour“
So after 1 hr the relative drain would be 3∏ + 4∏ = 7∏m³ of water drain
What i did initially was formed an equation 5880∏ = 7∏×n (n is the number of hrs) so ended up with 840. E
Answer: (E) 840
Question: Which of the following numbers has four distinct prime factors?
(A) 204
(B) 231
(C) 308
(D) 320
(E) 390
Rationale: 204=2^2*3*17
231=3*7*11
308=2^2*77
320=2^6*5
390=2*3*5*13
390 has 4 distinct prime factors
Answer E
Answer: (E) 390
Question: A new apartment complex purchased 60 toilets and 20 shower heads. If the price of a toilet is three times the price of a shower head, what percent of the total cost was the cost of all the shower heads?
(A) 9%
(B) 10%
(C) 11%
(D) 13%
(E) 15%
Rationale: LET PRICE OF SHOWER HEADS=X
THEN ,, ,, TIOLETS=3X
TOTALCOST=20*X+60*3X=200x
% OF TOTAL COST WAS THE COST OF ALL THE SHOWER HEADS=(20X/200X)*100=10%
ANSWER:B
Answer: (B) 10%
Question: For the symbol, m”n=n^2−m for all values of m and n. What is the value of 4”2?
(A) 5
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: 4”2= 4 - 4=0
Answer: E
Answer: (E) 0
Question: If 7 spiders make 7 webs in 7 days, then how many days are needed for 1 spider to make 1 web?
(A) 1
(B) 7
(C) 3
(D) 14
(E) 15
Rationale: Explanation :
Let, 1 spider make 1 web in x days.
More spiders, Less days (Indirect proportion)
More webs, more days (Direct proportion)
⇒ 7 × 1 × 7 = 1 × 7 × x
⇒x=7. Answer : Option B
Answer: (B) 7
Question: In a party every person shakes hands with every other person. If there were a total of 190 handshakes in the party then what is the number of persons present in the party ?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 20
Rationale: Explanation :
Let the number of persons be n
âˆ´ total handshakes = nC2 = 190
n(n-1)/2 = 190 âˆ´ n = 20
Answer : Option E
Answer: (E) 20
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 5
(D) 6
(E) 3
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2
= 8
Answer:B
Answer: (B) 8
Question: A trader marks his articles 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent?
(A) 6%
(B) 8%
(C) 5%
(D) 2%
(E) 4%
Rationale: Let CP of an article = RS. 100
MP= Rs. 120
Discount = 20%
SP = M[(100 - d%)/100] = 120(80/100) = Rs. 96
Clearly, the trader gets 4% loss.
Answer: E
Answer: (E) 4%
Question: The difference between the place values of two threes in the numerical 40378273 is
(A) 29997
(B) 299997
(C) 297
(D) 0
(E) None of them
Rationale: Required difference = (300000-3)
=299997.
Answer is B
Answer: (B) 299997
Question: Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly?
(A) Rs.1978
(B) Rs.1979
(C) Rs.1951
(D) Rs.1968
(E) Rs.1929
Rationale: P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25)
= Rs. 17576 C.I.
= 17576 - 15625 = Rs. 1951.
Answer:C
Answer: (C) Rs.1951
Question: Kiran, an eight years old boy has 27 toys. He gave 19 toys to his brother Gourav, while Gourav playing all but 6 got destroyed. While Kiran playing all but 3 got destroyed. Finally how many toys left with both of them?
(A) 9
(B) 1
(C) 8
(D) 76
(E) 2
Rationale: While Gourav playing 'All but 6 got destroyed' means 'All except 6 got destroyed'. i.e., 13 toys got destroyed. It means now Gourav has 6 toys. While Kiran is playing 'All but 3 got destroyed' means 'except 3 all are not working i.e; 3 toys are good working so total toys at both of them is 6 + 3 = 9.
Answer:A
Answer: (A) 9
Question: What is the units digit of (5!*5! + 6!*5!)/3?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: (5!*5! + 6!*5!)/3
=5!(5! + 6!)/3
=120 ( 120 + 720)/3
=(120 * 840)/3
= 120 * 280
Units digit of the above product will be equal to 0
Answer E
Answer: (E) 0
Question: A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
(A) 3 days.
(B) 2 days.
(C) 4 days.
(D) 1 days.
(E) 6 days.
Rationale: B's 10 day's work =(1/15 x 10)=2/3.
Remaining work =(1 -2/3)=1/3.
Now,	1/18	work is done by A in 1 day.
1/3	work is done by A in	(18 x 1/3)= 6 days.
Answer: Option E
Answer: (E) 6 days.
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. 3
II. -4
III. 8
IV. 5
(A) I and II only
(B) I and III only
(C) II and III only
(D) II and IV only
(E) I, II, III, and IV
Rationale: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 3 satisfy both inequalities.
Answer: A.
Answer: (A) I and II only
Question: If x < 0 and 0 < y < 1, which of the following has the greatest value W?
(A) x^2
(B) (xy)^2
(C) (x/y)^2
(D) x^2/y
(E) x^2*y
Rationale: Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
Answer: (C) (x/y)^2
Question: Find the invalid no.from the following series 13, 18, 25, 30, 37, 40
(A) 23
(B) 25
(C) 40
(D) 46
(E) 48
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong.
C
Answer: (C) 40
Question: A class average mark in an exam is 70. The average of students who scored below 60 is 50. The average of students who scored 60 or more is 75. If the total number of students in this class is 20, how many students scored below 60?
(A) 5
(B) 10
(C) 15
(D) 17
(E) 20
Rationale: Let n the number of students who scored below 60 and N the number of students who scored 60 or more. Xi the grades below 60 and Yi the grades 60 or above.
[sum(Xi) + sum(Yi)] / 20 = 70 : class average
sum(Xi) / n = 50 : average for less that 60
sum(Yi) / N = 75 : average for 60 or more
50n + 75N = 1400 : combine the above equations
n + N = 20 : total number of students
n = 4 and N = 16 : solve the above system
Answer: (E) 20
Question: In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and chuck are not seated next to each other?
(A) 72
(B) 48
(C) 56
(D) 76
(E) 96
Rationale: When the constraint on an arrangement says,Two people should not be seated together,we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....
These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.
Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
Answer :A
Answer: (A) 72