Four of the following five are alike in a certain way and hence form a group. Which is the one that does not belong to that group?
1. SMILE: T NKLI
2. BRING: CSHMH
3. FLOUR: GMNVQ
4. HOUSE: IPVTF
5. TRUTH: USVUI

Question

Prepp Team · Accepted Answer

Logical Reasoning: Analyzing Alphabet Coding Patterns

This question asks us to identify which word pair among the five options does not follow the same logical pattern as the others. We need to find a common characteristic shared by four pairs and identify the one pair that deviates from this characteristic. The typical method involves analyzing the shift in alphabetical positions between the letters of the original word and its coded counterpart.

Alphabetical Shifts Analysis: SMILE

First, let's determine the alphabetical shifts for the word SMILE and its corresponding code T NKLI. We calculate the difference in position for each letter in the alphabet (A=1, B=2, ..., Z=26).

Original Letter	Alphabet Position	Coded Letter	Coded Position	Shift Value
S	19	T	20	\(+1\)
M	13	N	14	\(+1\)
I	9	K	11	\(+2\)
L	12	L	12	\(0\)
E	5	I	9	\(+4\)

The shifts observed are \(+1\), \(+1\), \(+2\), \(0\), and \(+4\). The set of distinct shift values used here is {\(+1\), \(+2\), \(0\), \(+4\)}. This involves four unique shift values.

Letter Pattern Breakdown: BRING

Next, we analyze the shifts for the word BRING and its code CSHMH.

Original Letter	Alphabet Position	Coded Letter	Coded Position	Shift Value
B	2	C	3	\(+1\)
R	18	S	19	\(+1\)
I	9	H	8	\(-1\)
N	14	M	13	\(-1\)
G	7	H	8	\(+1\)

The shifts observed are \(+1\), \(+1\), \(-1\), \(-1\), and \(+1\). The set of distinct shift values used here is {\(+1\), \(-1\)}. This involves two unique shift values.

Coding Logic Comparison: FLOUR

Now, let's examine the shifts for the word FLOUR and its code GMNVQ.

Original Letter	Alphabet Position	Coded Letter	Coded Position	Shift Value
F	6	G	7	\(+1\)
L	12	M	13	\(+1\)
O	15	N	14	\(-1\)
U	21	V	22	\(+1\)
R	18	Q	17	\(-1\)

The shifts observed are \(+1\), \(+1\), \(-1\), \(+1\), and \(-1\). The set of distinct shift values used here is {\(+1\), \(-1\)}. This involves two unique shift values.

Identifying Pattern Group: HOUSE

Let's analyze the shifts for the word HOUSE and its code IPVTF.

Original Letter	Alphabet Position	Coded Letter	Coded Position	Shift Value
H	8	I	9	\(+1\)
O	15	P	16	\(+1\)
U	21	V	22	\(+1\)
S	19	T	20	\(+1\)
E	5	F	6	\(+1\)

The shifts observed are \(+1\), \(+1\), \(+1\), \(+1\), and \(+1\). The set of distinct shift values used here is {\(+1\)}. This involves only one unique shift value.

Commonality Check: TRUTH

Finally, we analyze the shifts for the word TRUTH and its code USVUI.

Original Letter	Alphabet Position	Coded Letter	Coded Position	Shift Value
T	20	U	21	\(+1\)
R	18	S	19	\(+1\)
U	21	V	22	\(+1\)
T	20	U	21	\(+1\)
H	8	I	9	\(+1\)

The shifts observed are \(+1\), \(+1\), \(+1\), \(+1\), and \(+1\). The set of distinct shift values used here is {\(+1\)}. This involves only one unique shift value.

Determining the Outlier Word

Let's summarize the number of distinct shift values identified for each word pair:

SMILE: 4 distinct values ({\(+1\), \(+2\), \(0\), \(+4\)})
BRING: 2 distinct values ({\(+1\), \(-1\)})
FLOUR: 2 distinct values ({\(+1\), \(-1\)})
HOUSE: 1 distinct value ({\(+1\)})
TRUTH: 1 distinct value ({\(+1\)})

We observe that the pairs BRING, FLOUR, HOUSE, and TRUTH all utilize a limited set of shift values (either one or two distinct values). This consistency forms the basis of the group.

The pair SMILE, however, uses four distinct shift values. This significantly differs from the pattern observed in the other four pairs, making it the one that does not belong to the group.

Conclusion: Outlier Identification

Therefore, based on the analysis of the number of unique shift values applied in the coding process, SMILE: T NKLI is the pair that does not fit the pattern established by the other four.