Question 133
If $$2^{36} - 1 = 68 a$$ 19476735, when all the digits are correct except a, the correct value of a is
Solution
Expression : $$(2)^{36}-1$$
= $$(2^3)^{12}-1=(8)^{12}-1$$
Now, to check whether the number is divisible by 9, we have : $$(-1)^{12}-1=0$$
Thus, $$(2)^{36}-1$$ is divisible by 9, hence sum of its digits is also divisible by 9.
=> $$6+8+a+1+9+4+7+6+7+3+5=56+a$$
Thus, $$56+a=63$$
=> $$a=7$$
=> Ans - (C)
Get AI Help
Video Solution
Click on the Email ☝️ to Watch the Video Solution
SRCC Quant Questions | SRCC Quantitative Ability
SRCC DILR Questions | LRDI Questions For SRCC
SRCC Verbal Ability Questions | VARC Questions For SRCC
Free SRCC Quant Questions
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Session:Free CAT Mentorship
Phone:
Date:
Time:
Enter OTP
Didn't receive the OTP?
