Quant Question of the Day Chat

for mpt to be even any of the m,p,t should be even

statement 1:
rearrange and we find p=(t+m)/2
m+t is even so they both are either odd are even
we still have no identification of p being odd or even
say, m+t=12; p=6 even
m+t=6; p=3 odd

Not a sufficient statement

statement 2:

t-m=16
range of the three numbers is 16. hardly any solid fact to reach to the conclusion if
mpt=even; NOt sufficient


combine: (1)+(2)
2p=t+m
16=t-m

adding 2 eqn above
2p+16=2t
so, t=p+8
From statement we talked about m,t both should be odd or both even
if m is odd, t is odd; p is also odd from above derivation
if m is even. t is even; p is also even from above derivation

so mpt can be odd or even in some cases

still not suff

option E is ans ?

Think its E

This is how I approached:
1) t+m=2p
let p=3
t+m=6
we can get two answers using the same equation
t is 5, m is 1 then not even.
t is 4, m is 2, even. NS
2) t-m=16
t is larger than m, and both are positive so t can take on really any value. T can be 17 and m can be 1, or t can be 18 and m can be 2 etc
3) we can make many combinations
let t be 17 and m be 1, p is 9. not even
let t be 18 and m be 2, p is 10. even

imo that question is one that is best approached by sensible numbers and keeping good track of your work so you don’t have to do extra calculations.

We want to min, so we should max negative terms and min positive ones:
Test y is 1 and x is 1, and we get 2. That is the middle value, so we should probably test more:
test y is 0 and x is 1. we get value 3
test y is 1 and x is 2, we get value over 2.
Clearly, we cannot reduce y anymore and increasing x increases the value.
C.

Neat question. There is probably a more elegant solution, but that is how I did it

Not sure if this is the best one, but I would probably write the equation as ⇒ (x-y)^2 + (x -1)^2 + 2 , the minimum value of the first two term is 0 (as squares are non negative). Hence C

This is much nicer than my brute force method haha.

Any update on the first question you posted today gmatophobia?

This one ?

DS Question 1 - Dec 11

If wxyz does not equal 0, is w/x > y/z?

(1) wz > xy

(2) xz > 0

Source: Kaplan | Difficulty: Hard

PS Question 1 - Dec 11

a, b and c are three interior angles of a triangle ABC. If a, b and c are three integers, then what is the number of possible values of a – b + c, which are less than zero ?

A.88
B.90
C.178
D.179
E.180

Source: e-GMAT | Difficulty: Hard

Is this really a hard Q? I solved in 45 seconds
Given: wxyz are nonzero
1)wz>xy
We have two cases here:
if z and y share the same sign, then we have
w/x>y/z
If z and x are opposite signs, then we have the flipped inequality. INS.
2) This tells us that xz share the same sign, but we know nothing about wy. INS.

3) we know from 1) that if they share the same sign, the condition is satisfied. 2) tells us they share teh same sign.
C.

rearranging question stem, it translates to: is (wz-xy)/xz > 0 ?

individual statements are are not sufficient.
combining both -

xz is > 0 from statement_2 so x,z has same sign
if we cross multiply (wz-xy)/xz > 0 we don’t have to flip sign
so we get - is (wz-xy) > 0 ?

statement_1 takes care of this query,

Hence, both statements together make sense

option C ?

Not sure if I did this correctly.
a-b+c=0 when b=90, a and c are 45.
That means for all b higher than 90, the equation is less than 0.
because we have 2 more integer angles, the max value b can take is 178 (a and c are 1 respectively).
therefore, 91<=b<=178
total values of b= 178-91+1=88
A.

a?

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Precents & Interest Rates Problems on the GMAT

https://www.youtube.com/watch?v=MVVBSQRdYiQ

Statistics on this question -

The question is marked 75% hard and has an accuracy of 48% over 230 test takers

Is this really a hard Q?

Interesting! Maybe many people fall into the trap of dividing variables w/o knowing signs

DS Question 1 - Nov 12

If x and y are positive integers, is xy even?

(1) x^2 + y^2 − 1 is divisible by 4.
(2) x + y is odd.

Source: Official Guide | Difficulty: Medium

1)
x^2+y^2=4k+1
odd sum, so x and y must be odd and even. xy is always even
2) same logic as 1.
suff
D.

Can also be solved using smart numbers, but the algebra approach is
much quicker.