Quantitative Aptitude - Arithmetic Ability Questions

The given number series is 720, 732, 708, 742, 696

720

720 + 12 = 732

732 - 24 = 708

708 + 36 = 744 (Not 742)

744 - 48 = 696

Hence, the odd man in the given number series is 742.

Commission up to 10000 = 10000x9100 = 900 

Again after 10000, 

              Commission    :   Bonus 

                           9       :   3 

                         3x        :   x

 Therefore,   Bonus = 1380-900×14 = Rs. 120

At 3 O'clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins. 

Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5° 

Hence, Angle between Hour and the Minute hand = ( 60 - 12.5 ) = 47.5°

Arithmetic Series ::

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

That is given by Sn = n(a1 + an)2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + n-1d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, $$\begin{gathered} an= a1 + n - 1d \\ a36= 2 + 36 - 13 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.

This sunday morning at 8:00 AM, the watch is 5 min. Slow, and the next sunday at 8:00PM it becomes 5 min 48 sec fast.  The watch gains 5+54860 min in a time of  (7×24)+12 = 180 hours. 

To show the correct time, it has to gain 5 min.

545min→180hours

5min ->

5542×180

8313hrs=72hrs+1113hrs=3days+11hrs+20min

So the correct time will be shown on wednesday at 7:20 PM

Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6,  and C =k/10 .

A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.

Hence, C's share (4650 *  6/31) = Rs, 900.

The given number series is 180, 90, 60, 40, 36

It follows a pattern that,

180 x 1/2 = 90

90 x 2/3  = 60

60 x 3/4  = 45 (NOT 40)

45 x 4/5  = 36

Hence, the wrong number in the given series is 40.