Naveen was counting down from 32. Mano was counting upwards the number...
Solution:
Naveen is counting down from 32 and Mano is counting upwards the numbers starting from 1 and calling out only the even numbers. They will call out at the same time when they reach a common number. Let's find out what that common number is.
Counting down from 32:
32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
Counting upwards from 1 (only even numbers):
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100
Finding the common number:
To find the common number, we need to look for the even numbers in the counting down list that match the even numbers in the counting upwards list. The even numbers in the counting down list are:
32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2
Out of these, only 22 is present in the counting upwards list. Therefore, the common number they will call out at the same time is 22.
Answer: (a) 22.
Naveen was counting down from 32. Mano was counting upwards the number...
Solution:
Naveen is counting down from 32. So the numbers he will call out are 32, 31, 30, 29, ..........
Mano is counting upwards from 1 and calling out only the even numbers. So the numbers he will call out are 2, 4, 6, 8, 10, .........
To find the common number they will call out at the same time, we need to find the LCM (Least Common Multiple) of the two sequences.
Step 1: Write down the two sequences.
Naveen: 32, 31, 30, 29, ..........
Mano: 2, 4, 6, 8, 10, .........
Step 2: Find the multiples of each sequence until you find a common multiple.
Multiples of Naveen's sequence:
32, 64, 96, 128, 160, 192, 224, 256, 288, 320, 352, 384, 416, 448, 480, 512, 544, 576, 608, 640, 672, 704, 736, 768, 800, 832, 864, 896, 928, 960, 992, 1024, 1056, 1088, 1120, 1152, 1184, 1216, 1248, 1280, 1312, 1344, 1376, 1408, 1440, 1472, 1504, 1536, 1568, 1600, 1632, 1664, 1696, 1728, 1760, 1792, 1824, 1856, 1888, 1920, 1952, 1984, 2016, 2048, 2080, 2112, 2144, 2176, 2208, 2240, 2272, 2304, 2336, 2368, 2400, 2432, 2464, 2496, 2528, 2560, 2592, 2624, 2656, 2688, 2720, 2752, 2784, 2816, 2848, 2880, 2912, 2944, 2976, 3008, 3040, 3072, 3104, 3136, 3168, 3200, 3232, 3264, 3296, 3328, 3360, 3392, 3424, 3456, 3488, 3520, 3552, 3584, 3616, 3648, 3680, 3712, 3744, 3776, 3808, 3840, 3872, 3904, 3936, 3968, 4000, 4032, 4064, 4096
Multiples of Mano's sequence:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22,