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# Quant Question of the Day Chat

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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 19 A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Source: Official Guide | Difficulty: Hard

D?

Assuming the numbers as a, b, and c. We’re asked whether a+b+c/3 = b --> a+c = 2b.

On solving both statements, we’re getting this. Hence D.

ChandlerBong wrote:
D? Assuming the numbers as a, b, and c. We’re asked whether a+b+c/3 = b --> a+c = 2b. On solving both statements, we’re getting this. Hence D.

*a < b <c

Originally posted by ChandlerBong on 19 Mar 2023, 00:40.
Last edited by alexsr on 20 Mar 2023, 04:42, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 19 A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Source: Official Guide | Difficulty: Hard

Both (1) & (2) are true

I am new here n to gmat prep, why I see "D" mentioned by few folks when there are no options.. are A,B,C,D standard?

gmatophobia wrote:
PS Question 1 - Mar 19 If a + b 4 B. a < -4 C. a < -2 D. 2 < a < 4 E. None of the above. Source: Other | Difficulty: Hard

B

Originally posted by Saakshi2407 on 19 Mar 2023, 11:01.
Last edited by Saakshi2407 on 19 Mar 2023, 11:05, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
Correcting myself, its C for PS question

Apologies, its B

C is not possible as that will result in b < 3 which isn’t possible so eliminated

Originally posted by Saakshi2407 on 19 Mar 2023, 11:09.
Last edited by Saakshi2407 on 19 Mar 2023, 11:15, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Mar 19 If a + b 4 B. a < -4 C. a < -2 D. 2 < a < 4 E. None of the above. Source: Other | Difficulty: Hard

C

gmatophobia wrote:
DS Question 1 - Mar 19 A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Source: Official Guide | Difficulty: Hard

D

DS Question 1 - Mar 20

If a and b are positive integers, is a^4−b^4 divisible by 4?

1) a + b is divisible by 4

2) The remainder is 2 when a^2 + b^2 is divided by 4

Source: Math Revolution | Difficulty: Hard

PS Question 1 - Mar 20

What is the largest prime factor of the expression 3^8 − 2^12?

A. 2
B. 3
C. 5
D. 17
E. 29

Source: VeritasPrep | Difficulty: Hard

Originally posted by gmatophobia on 19 Mar 2023, 23:28.
Last edited by gmatophobia on 19 Mar 2023, 23:34, edited 3 times in total.
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Re: Quant Question of the Day Chat [#permalink]
PS Question 1 - Mar 20 Ans - 29

DS i guess statment 1 sufficient... For the 2nd one don’t know

Originally posted by Aniket229 on 19 Mar 2023, 23:52.
Last edited by Aniket229 on 20 Mar 2023, 00:02, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Mar 20 What is the largest prime factor of the expression 3^8 − 2^12? A. 2 B. 3 C. 5 D. 17 E. 29 Source: VeritasPrep | Difficulty: Hard

E. 29 (Using the expansion property of a^2-b^2)
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 20 If a and b are positive integers, is a^4−b^4 divisible by 4? 1) a + b is divisible by 4 2) The remainder is 2 when a^2 + b^2 is divided by 4 Source: Math Revolution | Difficulty: Hard

DS (1)

2 is incorrect
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 20 If a and b are positive integers, is a^4−b^4 divisible by 4? 1) a + b is divisible by 4 2) The remainder is 2 when a^2 + b^2 is divided by 4 Source: Math Revolution | Difficulty: Hard

D?

Statement 1 is pretty simple. Sufficient.

Statement 2 we can take a^2+b^2 = 4k + 2 where k>0 is the divisor and then use this to simplify the question stem. Sufficient.

Both cases we’re getting a "Yes"
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Re: Quant Question of the Day Chat [#permalink]
ChandlerBong wrote:
D? Statement 1 is pretty simple. Sufficient. Statement 2 we can take a^2+b^2 = 4k + 2 where k>0 is the divisor and then use this to simplify the question stem. Sufficient. Both cases we’re getting a "Yes"

Can you elaborate this "and then use this to simplify the question stem" ?
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Re: Quant Question of the Day Chat [#permalink]
a^4 - b^4 = (a^2 - b^2)(a^2+b^2) --- (1)

Using statement 2 -> a^2+b^2 = 4k + 2 -> a^2 = 4k +2 - b^2

Using the value of a^2 in (1), -> (4k + 2 - b^2 - b^2) ( 4k + 2 ) [ As b^2 gets cancelled]

-> (4k + 2 - 2b^2) ( 4k+2) (Now we take 2 as common from both)

-> 2 * 2 ( 2k + 1 - b^2) ( 2k + 1)

Hence it’s divisible by 4. Sufficient.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Mar 20 What is the largest prime factor of the expression 3^8 − 2^12? A. 2 B. 3 C. 5 D. 17 E. 29 Source: VeritasPrep | Difficulty: Hard

E

gmatophobia wrote:
DS Question 1 - Mar 20 If a and b are positive integers, is a^4−b^4 divisible by 4? 1) a + b is divisible by 4 2) The remainder is 2 when a^2 + b^2 is divided by 4 Source: Math Revolution | Difficulty: Hard

D

gmatophobia wrote:
DS Question 1 - Mar 19 A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. Source: Official Guide | Difficulty: Hard

Can someone tell me how S2 is sufficient ? I thought if a,b,c are numbers then a+b+c = 3b (only this case satisfy what question stem is asking)

Originally posted by rickyric395 on 20 Mar 2023, 01:41.
Last edited by rickyric395 on 20 Mar 2023, 01:44, edited 2 times in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 20 If a and b are positive integers, is a^4−b^4 divisible by 4? 1) a + b is divisible by 4 2) The remainder is 2 when a^2 + b^2 is divided by 4 Source: Math Revolution | Difficulty: Hard

gmatophobia wrote:
PS Question 1 - Mar 20 What is the largest prime factor of the expression 3^8 − 2^12? A. 2 B. 3 C. 5 D. 17 E. 29 Source: VeritasPrep | Difficulty: Hard

DS Question 1 - Mar 21

A bank account earned 2% annual interest, compounded daily, for as long as the balance was under \$1,000, starting when the account was opened. Once the balance reached \$1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?

(1) The account earned exactly \$25 in interest at the 2.5% rate.
(2) The account was open for exactly three years.

Source: Official Guide | Difficulty: Medium

PS Question 1 - Mar 21

The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?

A. −4 ≤ y ≤ 36

B. −10 ≤ y ≤ 30

C. −10 ≤ y ≤ 36

D. 0 ≤ y ≤ 40

E. 2 ≤ y ≤ 5

Source: Princeton Review | Difficulty: Hard

Originally posted by gmatophobia on 21 Mar 2023, 00:55.
Last edited by gmatophobia on 21 Mar 2023, 00:56, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 21 A bank account earned 2% annual interest, compounded daily, for as long as the balance was under \$1,000, starting when the account was opened. Once the balance reached \$1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate? (1) The account earned exactly \$25 in interest at the 2.5% rate. (2) The account was open for exactly three years. Source: Official Guide | Difficulty: Medium

stem: Is, interest @2% p.a. > interest @2.5% p.a. ?
or I1 > I2 ?

if "m" is the principal amount to start with and for "n" days the account operated

\$1000 will be the new amount at the end of 2% interest scenario.

1000 = m(1+2/(100*365))^t , assuming this goes on for "t" days
we get value of "m" if we have "t"

then interest, I1 = m(1+2/(100*365))^t - m

another case where 2.5% is interest rate., 1000 is the principal to start with
then, total interest earned, I2= 1000(1+2.5/(100*365))^n-t - 1000

WE need value of t,n to make a comparison;

both statements individually are not sufficient;
statement1: we get to know I2 = 25, so, "n-t" can be known
statement2: we get time of 3 years, that is we can say "n" is given in years. so we can get "t"

combine both, we have all the info we need, so option C
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
PS Question 1 - Mar 21 The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y? A. −4 ≤ y ≤ 36 B. −10 ≤ y ≤ 30 C. −10 ≤ y ≤ 36 D. 0 ≤ y ≤ 40 E. 2 ≤ y ≤ 5 Source: Princeton Review | Difficulty: Hard

here, 2 <= x + y <= 5
so, 4 <= 2x+2y <= 10
hence, -4 >= -2x-2y >= -10
or the same as, -10 <= -2x-2y <= -4

and another inequality, 0 <= 2x + 3y <= 40

therefore -10 <= y <= 36 ... option C ?
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Re: Quant Question of the Day Chat [#permalink]
gmatophobia wrote:
DS Question 1 - Mar 21 A bank account earned 2% annual interest, compounded daily, for as long as the balance was under \$1,000, starting when the account was opened. Once the balance reached \$1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate? (1) The account earned exactly \$25 in interest at the 2.5% rate. (2) The account was open for exactly three years. Source: Official Guide | Difficulty: Medium

C

gmatophobia wrote:
PS Question 1 - Mar 21 The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y? A. −4 ≤ y ≤ 36 B. −10 ≤ y ≤ 30 C. −10 ≤ y ≤ 36 D. 0 ≤ y ≤ 40 E. 2 ≤ y ≤ 5 Source: Princeton Review | Difficulty: Hard

C

DS Question 1 - March 22

If m and n are positive integers greater than 1, is m + n odd?

(A) m is a divisor of 16

(B) The units digit of 12^m + 28^n is 6.

Source: GMATWhiz | Difficulty: Hard

PS Question 1 - March 22

If the sum of the first 11 terms of an arithmetic progression consisting 16 terms is zero, then which of the following COULD be true ? (An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant)

I. 11th smallest term is zero
II. 6th largest term is zero
III. All terms are non negative

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Source: GMAT Club Tests | Difficulty: Hard

Originally posted by gmatophobia on 22 Mar 2023, 00:25.
Last edited by gmatophobia on 22 Mar 2023, 00:29, edited 1 time in total.
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Re: Quant Question of the Day Chat [#permalink]
DS Qn - clearly m is even & m can be (2,4,8,16) given m,n great than 1... But it’s not sufficient so answer m+n... Statement 2 individual also not sufficient to answer... With together 1 & 2 we can say n also even... So m+n even & Answer= together sufficient to answer the question
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Re: Quant Question of the Day Chat [#permalink]
PS Q1 - D

As III doesnt seem possible, for sum to be 0 of 11 terms, they have to offset so half would be positive and half negative

Originally posted by Saakshi2407 on 22 Mar 2023, 02:23.
Last edited by Saakshi2407 on 22 Mar 2023, 02:24, edited 1 time in total.
Re: Quant Question of the Day Chat [#permalink]
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