If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?

Question: If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?

1. 101
2. 12
3. 157
4. 170
5. 197

“If \(\sqrt{3+\sqrt{x-1}}=4\), what is the value of x? ”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Write down the original expression:

\(\sqrt{3+\sqrt{x-1}}=4\)

Square the given expression both sides, we will get:

\(3+\sqrt{x-1}=4^2=16\)

Rearrange the following:

\(\sqrt{x-1}\)= 16 – 3

\(\sqrt{x-1}\)= 13

Squaring on both sides:

x – 1 = 169

x = 170

Correct Answer: D

Suggested GMAT Quant Questions

• Is Triangle ABC an Isosceles?
• p, r, s, t, u An Arithmetic Sequence is a Sequence in Which each Term After the First Term is Equal to the Sum of the Preceding Term and a Constant
• The Selling Price of an Article is Equal to the Cost of the Article Plus the Markup
• Of the 150 houses in a certain development, 60 percent have air-conditioning, 50 percent have a sunporch, and 30 percent have a swimming pool
• A is twice as good a workman as B and together they finish a piece of work in 16 days.
• If 100,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, How Many Angstroms Equal 1 micron?
• If The Average (arithmetic mean) of The Four Numbers 3, 15, 32, and (N + 1) is 18, then N =
• The Average Age of Chief Executive Officers (CEO’s) in a Large Sample of Companies is 57
• 2x+3y
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), for every n≥1, then a11 equals
• The Closing Price of Stock X Changed on Each Trading Day Last Month The Percent Change in the Closing Price of Stock X
• A Right Angled Triangle has its Sides in Arithmetic Progression and Being Integers
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X?
• What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2
• Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage, It is 45km/hr
• Last Year 26 Members of a Certain Club Traveled to England, 26 Members Traveled to France, and 32 Members Traveled to Italy.
• A Clock Strikes 4 taking 9 seconds. In Order to Strike 12 at the Same Rate, the Time Taken is
• A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
• Two Athletes Cover the Distance from A to B at the Rate of 10 and 15 kmph respectively
• What is the Largest Power of 3 Contained in 200!