Question 7 SSC CGL 2018 June 4 Shift 1

Posted by Parveen(Hoven),
Aptitude Trainer and Software Developer

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Question 7 SSC-CGL 2018 June 4
[NOTE: only math questions solved]

Question: If a number of 9 digits is 985x3678y, the number is divisible by 72, then the value of (4x - 3y) will be:

1. 4
2. 6
3. 5
4. 3

Method 1

72 is the product of two co-primes: 9 and 8. Hence, for a number to be divisible by 72, it must necessarily be divisible by both 8 and 9. [see NCERT class VI maths]

If you know only the divisibility criterion for 9, and nothing else, then this method helps:

We have to find (4x - 3y). Or, we can say that we have to find x + 3(x - y).

Keeping the options in mind, we can conclude that (x - y) cannot be more than 1 [why? because if (x - y) were 2, say, then x + 3 (x - y) would be more than 6, and none of the options is greater than 6]

So x and y are either equal or consecutive.

By the divisibility rule of 9, the sum of digits = 46 + x + y should be divisible by 9. Hence x + y = 8

TIP: Don't do full addition, neglect 9 and all those pairs that add to 9 because they are already multiples of 9. $\displaystyle \cancel{9}85\text{x}\cancel{36}78\text{y}$ = (28 + x + y) gives x + y =8 again.

The only possibilities is x = y = 4. [Why? because out of (1,7), (2, 6), (3, 5) and (4, 4), only (4, 4) meets the criterion of (x, y) being either consecutive or equal!]

Hence the answer is 4x - 3y = 4, option (a).

Method 2

72 is the product of two co-primes: 9 and 8. Hence, for a number to be divisible by 72, it must necessarily be divisible by both 8 and 9. [see NCERT class VI maths]

If you know only the divisibility criterion for 8, and nothing else, then this method helps:

By the divisibility criterion for 8, the last three digits should be divisible by 8. So 78y should be divisible by 8. Since, 784/8 = 98, this means y should be 4.

Now 4x - 3y will be $\displaystyle 4x - 3 \times 4 = 4x - 12$. Cycle through the options.

option (a) 4x - 12 = 4 gives x = 4, could be possible.

option (b) 4x - 12 = 6 gives x = 9/2, impossible.

option (c) 4x - 12 = 5 gives x = 17/4, impossible.

option (d) 4x - 12 = 3 gives x = 15/4, impossible.

Hence the answer is 4x - 3y = 4, option (a).

Method 3

72 is the product of two co-primes: 9 and 8. Hence, for a number to be divisible by 72, it must necessarily be divisible by both 8 and 9. [see NCERT class VI maths]

By the divisibility criterion for 8, we obtain y = 4, as explained in method 2 above.

Our number becomes 985x36784

By the divisibility criterion for 9, the sum of digits, i.e., 32 + x is divisible by 9 if x = 4.

Hence 4x - 3y = 4, option (a) answer.