Question 78

Consider the expression $$(xxx)_{b}=x^3$$, where b is the base, and x is any digit of base b. Find the value of b:

Solution

$$(xxx)_{b}=x^3$$
=> $$xb^2+xb+x = x^3$$
=> $$b^2+b+1=x^2$$
On substituting b=1,and b=2, we get $$x^2$$ as $$3$$, and $$7$$. Since $$3$$ and $$7$$ are not perfect squares, we can infer that no number satisfies the given condition. Therefore, option E is the right answer.

Create a FREE account and get:

All Quant Formulas and shortcuts PDF
XAT previous papers with solutions PDF
XAT Trial Classes for FREE

CAT Quant Questions | CAT Quantitative Ability

CAT Percentages Questions CAT Arithmetic Questions CAT Averages Questions CAT Number Systems Questions CAT Logarithms Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Data Interpretation Basics Questions CAT Quant Based DI Questions CAT Venn Diagrams Questions CAT Special Charts Questions CAT Table with Missing values Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Jumbles Questions CAT Miscellaneous Questions CAT Odd One Out Questions CAT Vocabulary Questions CAT Para Summary Questions

XAT 2013 Question Paper

Consider the expression $$(xxx)_{b}=x^3$$, where b is the base, and x is any digit of base b. Find the value of b:

CAT Quant Questions | CAT Quantitative Ability

CAT DILR Questions | LRDI Questions For CAT

CAT Verbal Ability Questions | VARC Questions For CAT

Free Quant Questions

Login to your Cracku account

Hello! 👋

Ready to Unlock Your Success?

Please Enter Your OTP

Please enter the following details

Create a free Cracku account